GLRM/GLRM_R_Segmentation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering Notebook in R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notes and References \n",
    "\n",
    "sample size for clustering\n",
    "https://journals.sagepub.com/doi/full/10.1177/0047287513496475\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Connection successful!\n",
      "\n",
      "R is connected to the H2O cluster: \n",
      "    H2O cluster uptime:         1 hours 9 minutes \n",
      "    H2O cluster timezone:       America/Los_Angeles \n",
      "    H2O data parsing timezone:  UTC \n",
      "    H2O cluster version:        3.32.0.1 \n",
      "    H2O cluster version age:    1 month and 23 days  \n",
      "    H2O cluster name:           H2O_started_from_R_rcluk_xeo316 \n",
      "    H2O cluster total nodes:    1 \n",
      "    H2O cluster total memory:   3.48 GB \n",
      "    H2O cluster total cores:    8 \n",
      "    H2O cluster allowed cores:  5 \n",
      "    H2O cluster healthy:        TRUE \n",
      "    H2O Connection ip:          localhost \n",
      "    H2O Connection port:        54321 \n",
      "    H2O Connection proxy:       NA \n",
      "    H2O Internal Security:      FALSE \n",
      "    H2O API Extensions:         Amazon S3, Algos, AutoML, Core V3, TargetEncoder, Core V4 \n",
      "    R Version:                  R version 4.0.3 (2020-10-10) \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Import the necessary Libraries to run all the clustering algorithms \n",
    "library(clustMixType)\n",
    "library(e1071)\n",
    "library(caTools)\n",
    "library(caret)\n",
    "library(nnet)\n",
    "library(tidyr)\n",
    "library(forecast)\n",
    "library(FactoMineR)\n",
    "library(dplyr)\n",
    "library(MASS)\n",
    "library(moments)\n",
    "library(readxl)\n",
    "library(e1071)\n",
    "library(factoextra)\n",
    "library(ClusterR)\n",
    "library(ggplot2)\n",
    "library(wesanderson)\n",
    "library(randomForest)\n",
    "library(mclust)\n",
    "library(NbClust)\n",
    "library(kableExtra)\n",
    "library(PCAmixdata)\n",
    "library(factoextra)\n",
    "library(reshape2)\n",
    "library(bestNormalize)\n",
    "library(PerformanceAnalytics)\n",
    "library(corrplot)\n",
    "library(descr)\n",
    "library(gridExtra)\n",
    "library(cluster)\n",
    "library(h2o)\n",
    "library(purrr)\n",
    "h2o.init(nthreads = 5)\n",
    "library(openxlsx)\n",
    "library(xgboost)\n",
    "library(ggpubr)\n",
    "\n",
    "# Other Configurations for Jupyter Notebook\n",
    "options(jupyter.plot_scale=1)  # sets the plot size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Build Functions\n",
    "These functions are necessary to build the algorithm and transform the data.  Do not change or modify these functions! \n",
    "<hr>\n",
    "\n",
    "*h2o_glrm* - this function compresses the dataset (variables) down to k dimensions - recommend 2 or 3 <br>\n",
    "*famd_pca* - this function is similar to the first one, but uses a different algorithm; it's not as good as the first one <br>\n",
    "*make_cluster* - this function runs three different clustering algorithms on the dimension-reduced data <br>\n",
    "*rf_valid* - this function runs the random-forest and ANOVA validation on the final cluster solutions <br>\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build Functions to process the data\n",
    "\n",
    "# this function uses Generalized Low Rank Model to reduce multivariate mixed data to k dimensions\n",
    "h2o_glrm <- function(data, k) {\n",
    "    df_h2o <- as.h2o(data)\n",
    "    m_glrm = h2o.glrm(training_frame = df_h2o, loss = \"Quadratic\", gamma_x = .25, gamma_y = 1, transform = \"standardize\", k = k,\n",
    "                  seed = 123, max_iterations = 1000, recover_svd=TRUE, init=\"SVD\",\n",
    "                      regularization_x = \"L1\",\n",
    "                      regularization_y = \"L1\")\n",
    "    X.m = as.data.frame(h2o.getFrame(m_glrm@model$representation_name))\n",
    "    return(X.m)\n",
    "}\n",
    "\n",
    "famd_pca <- function(data, k) {\n",
    "    PCA_famd <-FAMD(data, ncp=k, graph=FALSE)\n",
    "    y <- get_famd_ind(PCA_famd)\n",
    "    df_famd <- as.data.frame(y$coord)\n",
    "    return(df_famd)\n",
    "}\n",
    "\n",
    "# Function to perform various clustering algorithms\n",
    "make_cluster <- function(data, k, meth) {\n",
    "    tot_withinss = map_dbl(1:10, function(k)\n",
    "      {\n",
    "      model=kmeans(x = data, centers = k)\n",
    "      model$tot.withinss\n",
    "      })\n",
    "\n",
    "    elbow_df <- data.frame(k = 1:10, tot_withinss = tot_withinss)\n",
    "\n",
    "    plot1 <- ggplot(elbow_df, aes(x = k, y = tot_withinss)) + geom_line() +\n",
    "      scale_x_continuous(breaks = 1:10)\n",
    "     \n",
    "    if(meth == 'kmeans'){\n",
    "        set.seed(45)\n",
    "        model_cl = kmeans(data, k, nstart = 25)\n",
    "        plot2 <- fviz_cluster(model_cl, data = data, geom = 'point')\n",
    "        clusters <- model_cl$cluster\n",
    "        sil <- silhouette(model_cl$cluster, dist(data))\n",
    "        }\n",
    "    \n",
    "    else if(meth == 'gmm'){\n",
    "        gmm = GMM(data, k, dist_mode = \"eucl_dist\", seed_mode = \"random_subset\", km_iter = 15, em_iter = 15, verbose = F)\n",
    "        pr <- predict_GMM(data, gmm$centroids, gmm$covariance_matrices, gmm$weights)\n",
    "        clusters <- pr$cluster_labels\n",
    "        plot2 <- ggplot() + geom_point(data = data, mapping = aes(x = data[,1], y = data[,2], col = as.factor(pr$cluster_labels))) + scale_fill_brewer(palette=\"Set1\")\n",
    "        sil <- silhouette(pr$cluster_labels, dist(data))\n",
    "        }\n",
    "    \n",
    "    else if(meth == 'hier'){\n",
    "        # Dissimilarity matrix\n",
    "        d <- dist(data, method = \"minkowski\", p=5)\n",
    "\n",
    "        # Hierarchical clustering using Complete Linkage\n",
    "        hc1 <- hclust(d, method = \"ward.D2\" )\n",
    "        clusters <- cutree(hc1, k = k)\n",
    "        plot2 <- ggplot() + geom_point(data = data, mapping = aes(x = data[,1], y = data[,2], col = as.factor(clusters))) + scale_fill_brewer(palette=\"Set1\")\n",
    "        sil <- silhouette(clusters, dist(data))\n",
    "        }\n",
    "    plot3 <- fviz_silhouette(sil)\n",
    "    \n",
    "    return(list(plot1, plot2, plot3, clusters))\n",
    "}\n",
    "\n",
    "# Function to perform Validation using Random Forest and ANOVA\n",
    "rf_valid <- function(clusters, data, trees, depth) {\n",
    "    c <- clusters\n",
    "    df_crm1 = as.data.frame(data)\n",
    "    df_crm1$clusters <- c\n",
    "    df_crm1$clusters <- as.factor(df_crm1$clusters)\n",
    "    df_rf <- as.h2o(df_crm1)\n",
    "    \n",
    "    # Random Forest \n",
    "    predictors <- c(\"thry_day_es_n\", \"env_purch_n\", \"env_sent_life_n\", \"num_trx_n\", \"mmr_n\")\n",
    "    response <- \"clusters\"\n",
    "    \n",
    "    dfr_split <- h2o.splitFrame(data = df_rf, ratios = 0.65, seed = 1234)\n",
    "    train <- dfr_split[[1]]\n",
    "    valid <- dfr_split[[2]]\n",
    "    \n",
    "    \n",
    "    # Build and train the model:\n",
    "    ds_drf <- h2o.randomForest(x = predictors,\n",
    "                             y = response,\n",
    "                             ntrees = trees,\n",
    "                             balance_classes=TRUE,\n",
    "                             stopping_metric = \"AUTO\",\n",
    "                             stopping_rounds = 20, \n",
    "                             stopping_tolerance = 0.001,\n",
    "                             histogram_type='RoundRobin',\n",
    "                             sample_rate = .6,\n",
    "                             col_sample_rate_per_tree = .75,\n",
    "                             nbins=25,\n",
    "                             mtries=-1,\n",
    "                             max_depth = depth,\n",
    "                             min_rows = 1,\n",
    "                             nfolds = 10,\n",
    "                             training_frame = train,\n",
    "                             validation_frame = valid)\n",
    "    \n",
    "    cm1 <- h2o.confusionMatrix(ds_drf)\n",
    "    cm2 <- h2o.confusionMatrix(ds_drf, valid)\n",
    "    varimp <- h2o.varimp(ds_drf)\n",
    "\n",
    "    return(list(ds_drf, df_crm1, cm1, cm2, varimp))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "run_h2 <- function(data, comp, clust, algo, trees, depth) {\n",
    "    h2o_pca <- h2o_glrm(data, comp)\n",
    "    famd_pca <- famd_pca(data, comp)\n",
    "    cl <- make_cluster(h2o_pca, clust, algo)\n",
    "    cluster_plot <- cl[[2]]\n",
    "    elbow_plot <- cl[[1]]\n",
    "    sil_plot <- cl[[3]]\n",
    "    clusters <- cl[[4]]\n",
    "    val <- rf_valid(cl[[4]], as.data.frame(df_crm_i), trees, depth)\n",
    "    #val <- rf_valid(oc, as.data.frame(df_crm_i))\n",
    "    return(list(val,cluster_plot, elbow_plot, sil_plot, clusters))\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load the Data Set \n",
    "<hr>\n",
    "The data has had pre-processed in Excel - namely to remove certain values (i.e. Real Estate, Free Accounts, etc.) and to recombine some levels in the Categorical variables due to low counts (i.e. less than 5).  The following modifications were made:<br><br>\n",
    "1. \"Former Customers\" were excluded <br>\n",
    "2. Vertical: Real-estate were excluded <br>\n",
    "3. Non-Paying customers were removed <br> \n",
    "4. Pricing Model = Free were removed <br>\n",
    "5. customers from the survey that could not be found in the CRM data were removed <br>\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 6 × 46</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>uid</th><th scope=col>q1</th><th scope=col>q2</th><th scope=col>q3</th><th scope=col>q4</th><th scope=col>q5</th><th scope=col>q6</th><th scope=col>q7</th><th scope=col>q8</th><th scope=col>q9</th><th scope=col>...</th><th scope=col>q30</th><th scope=col>q32</th><th scope=col>q33</th><th scope=col>q34</th><th scope=col>q35</th><th scope=col>q36</th><th scope=col>q37</th><th scope=col>q38i</th><th scope=col>q39i</th><th scope=col>q40i</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>...</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 6</td><td>1</td><td>0</td><td>0</td><td>10</td><td>6</td><td>1</td><td>4</td><td>500</td><td> 500</td><td>...</td><td>19470</td><td>135054</td><td> 515</td><td>89</td><td> 85740</td><td>830</td><td> 9388.89</td><td> 515</td><td>89</td><td>830</td></tr>\n",
       "\t<tr><td> 7</td><td>1</td><td>1</td><td>1</td><td> 2</td><td>5</td><td>2</td><td>4</td><td> 10</td><td>  30</td><td>...</td><td>  357</td><td>   374</td><td> 450</td><td>85</td><td>  2101</td><td>213</td><td>  350.62</td><td> 450</td><td>85</td><td>213</td></tr>\n",
       "\t<tr><td> 8</td><td>1</td><td>0</td><td>0</td><td> 4</td><td>4</td><td>2</td><td>4</td><td>  6</td><td>   6</td><td>...</td><td>  528</td><td>   768</td><td>1098</td><td> 0</td><td>   150</td><td>269</td><td>  481.25</td><td>1098</td><td>NA</td><td>269</td></tr>\n",
       "\t<tr><td>10</td><td>1</td><td>1</td><td>1</td><td> 5</td><td>3</td><td>1</td><td>4</td><td>200</td><td> 200</td><td>...</td><td> 7321</td><td> 24382</td><td> 650</td><td>40</td><td>  7603</td><td> 99</td><td> 7793.30</td><td> 650</td><td>40</td><td> 99</td></tr>\n",
       "\t<tr><td>11</td><td>1</td><td>0</td><td>0</td><td> 9</td><td>6</td><td>2</td><td>4</td><td>  8</td><td> 100</td><td>...</td><td> 4985</td><td>  5032</td><td>2000</td><td>92</td><td>  1025</td><td>324</td><td>21457.50</td><td>2000</td><td>92</td><td>324</td></tr>\n",
       "\t<tr><td>12</td><td>0</td><td>1</td><td>0</td><td> 6</td><td>5</td><td>2</td><td>2</td><td>200</td><td>1000</td><td>...</td><td>59125</td><td>253718</td><td> 115</td><td>30</td><td>249291</td><td>130</td><td>48369.83</td><td> 115</td><td>30</td><td>130</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 46\n",
       "\\begin{tabular}{lllllllllllllllllllll}\n",
       " uid & q1 & q2 & q3 & q4 & q5 & q6 & q7 & q8 & q9 & ... & q30 & q32 & q33 & q34 & q35 & q36 & q37 & q38i & q39i & q40i\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ... & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t  6 & 1 & 0 & 0 & 10 & 6 & 1 & 4 & 500 &  500 & ... & 19470 & 135054 &  515 & 89 &  85740 & 830 &  9388.89 &  515 & 89 & 830\\\\\n",
       "\t  7 & 1 & 1 & 1 &  2 & 5 & 2 & 4 &  10 &   30 & ... &   357 &    374 &  450 & 85 &   2101 & 213 &   350.62 &  450 & 85 & 213\\\\\n",
       "\t  8 & 1 & 0 & 0 &  4 & 4 & 2 & 4 &   6 &    6 & ... &   528 &    768 & 1098 &  0 &    150 & 269 &   481.25 & 1098 & NA & 269\\\\\n",
       "\t 10 & 1 & 1 & 1 &  5 & 3 & 1 & 4 & 200 &  200 & ... &  7321 &  24382 &  650 & 40 &   7603 &  99 &  7793.30 &  650 & 40 &  99\\\\\n",
       "\t 11 & 1 & 0 & 0 &  9 & 6 & 2 & 4 &   8 &  100 & ... &  4985 &   5032 & 2000 & 92 &   1025 & 324 & 21457.50 & 2000 & 92 & 324\\\\\n",
       "\t 12 & 0 & 1 & 0 &  6 & 5 & 2 & 2 & 200 & 1000 & ... & 59125 & 253718 &  115 & 30 & 249291 & 130 & 48369.83 &  115 & 30 & 130\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 46\n",
       "\n",
       "| uid &lt;dbl&gt; | q1 &lt;dbl&gt; | q2 &lt;dbl&gt; | q3 &lt;dbl&gt; | q4 &lt;dbl&gt; | q5 &lt;dbl&gt; | q6 &lt;dbl&gt; | q7 &lt;dbl&gt; | q8 &lt;dbl&gt; | q9 &lt;dbl&gt; | ... ... | q30 &lt;dbl&gt; | q32 &lt;dbl&gt; | q33 &lt;dbl&gt; | q34 &lt;dbl&gt; | q35 &lt;dbl&gt; | q36 &lt;dbl&gt; | q37 &lt;dbl&gt; | q38i &lt;dbl&gt; | q39i &lt;dbl&gt; | q40i &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "|  6 | 1 | 0 | 0 | 10 | 6 | 1 | 4 | 500 |  500 | ... | 19470 | 135054 |  515 | 89 |  85740 | 830 |  9388.89 |  515 | 89 | 830 |\n",
       "|  7 | 1 | 1 | 1 |  2 | 5 | 2 | 4 |  10 |   30 | ... |   357 |    374 |  450 | 85 |   2101 | 213 |   350.62 |  450 | 85 | 213 |\n",
       "|  8 | 1 | 0 | 0 |  4 | 4 | 2 | 4 |   6 |    6 | ... |   528 |    768 | 1098 |  0 |    150 | 269 |   481.25 | 1098 | NA | 269 |\n",
       "| 10 | 1 | 1 | 1 |  5 | 3 | 1 | 4 | 200 |  200 | ... |  7321 |  24382 |  650 | 40 |   7603 |  99 |  7793.30 |  650 | 40 |  99 |\n",
       "| 11 | 1 | 0 | 0 |  9 | 6 | 2 | 4 |   8 |  100 | ... |  4985 |   5032 | 2000 | 92 |   1025 | 324 | 21457.50 | 2000 | 92 | 324 |\n",
       "| 12 | 0 | 1 | 0 |  6 | 5 | 2 | 2 | 200 | 1000 | ... | 59125 | 253718 |  115 | 30 | 249291 | 130 | 48369.83 |  115 | 30 | 130 |\n",
       "\n"
      ],
      "text/plain": [
       "  uid q1 q2 q3 q4 q5 q6 q7 q8  q9   ... q30   q32    q33  q34 q35    q36\n",
       "1  6  1  0  0  10 6  1  4  500  500 ... 19470 135054  515 89   85740 830\n",
       "2  7  1  1  1   2 5  2  4   10   30 ...   357    374  450 85    2101 213\n",
       "3  8  1  0  0   4 4  2  4    6    6 ...   528    768 1098  0     150 269\n",
       "4 10  1  1  1   5 3  1  4  200  200 ...  7321  24382  650 40    7603  99\n",
       "5 11  1  0  0   9 6  2  4    8  100 ...  4985   5032 2000 92    1025 324\n",
       "6 12  0  1  0   6 5  2  2  200 1000 ... 59125 253718  115 30  249291 130\n",
       "  q37      q38i q39i q40i\n",
       "1  9388.89  515 89   830 \n",
       "2   350.62  450 85   213 \n",
       "3   481.25 1098 NA   269 \n",
       "4  7793.30  650 40    99 \n",
       "5 21457.50 2000 92   324 \n",
       "6 48369.83  115 30   130 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1123</li><li>46</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1123\n",
       "\\item 46\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1123\n",
       "2. 46\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1123   46"
      ]
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the Data\n",
    "df <- read_excel(\"C:/Users/rcluk/Python_Projects/data.xlsx\")\n",
    "head(df) # just show the first couple of lines to confirm that the data loaded properly\n",
    "dim(df) # check the dimensions - there should be 1118 rows of respondents and 38 variables (columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploratory Data Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A psych: 46 × 13</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>vars</th><th scope=col>n</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>median</th><th scope=col>trimmed</th><th scope=col>mad</th><th scope=col>min</th><th scope=col>max</th><th scope=col>range</th><th scope=col>skew</th><th scope=col>kurtosis</th><th scope=col>se</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>uid</th><td> 1</td><td>1123</td><td>   845.045</td><td>    463.324</td><td> 868.0</td><td> 852.764</td><td> 581.179</td><td> 6</td><td>     1618</td><td>     1612</td><td>-0.128</td><td>  -1.161</td><td>    13.826</td></tr>\n",
       "\t<tr><th scope=row>q1</th><td> 2</td><td>1123</td><td>     0.915</td><td>      0.280</td><td>   1.0</td><td>   1.000</td><td>   0.000</td><td> 0</td><td>        1</td><td>        1</td><td>-2.961</td><td>   6.774</td><td>     0.008</td></tr>\n",
       "\t<tr><th scope=row>q2</th><td> 3</td><td>1123</td><td>     0.240</td><td>      0.427</td><td>   0.0</td><td>   0.175</td><td>   0.000</td><td> 0</td><td>        1</td><td>        1</td><td> 1.219</td><td>  -0.515</td><td>     0.013</td></tr>\n",
       "\t<tr><th scope=row>q3</th><td> 4</td><td>1123</td><td>     0.159</td><td>      0.365</td><td>   0.0</td><td>   0.073</td><td>   0.000</td><td> 0</td><td>        1</td><td>        1</td><td> 1.868</td><td>   1.489</td><td>     0.011</td></tr>\n",
       "\t<tr><th scope=row>q4</th><td> 5</td><td>1123</td><td>     3.387</td><td>      2.447</td><td>   3.0</td><td>   3.057</td><td>   2.965</td><td> 0</td><td>       13</td><td>       13</td><td> 1.165</td><td>   1.252</td><td>     0.073</td></tr>\n",
       "\t<tr><th scope=row>q5</th><td> 6</td><td>1123</td><td>     3.516</td><td>      2.110</td><td>   3.0</td><td>   3.277</td><td>   1.483</td><td> 1</td><td>       12</td><td>       11</td><td> 1.046</td><td>   1.196</td><td>     0.063</td></tr>\n",
       "\t<tr><th scope=row>q6</th><td> 7</td><td>1123</td><td>     1.629</td><td>      0.951</td><td>   1.0</td><td>   1.443</td><td>   0.000</td><td> 1</td><td>        6</td><td>        5</td><td> 1.836</td><td>   3.828</td><td>     0.028</td></tr>\n",
       "\t<tr><th scope=row>q7</th><td> 8</td><td>1123</td><td>     2.866</td><td>      1.461</td><td>   3.0</td><td>   2.763</td><td>   1.483</td><td> 1</td><td>        7</td><td>        6</td><td> 0.422</td><td>  -0.631</td><td>     0.044</td></tr>\n",
       "\t<tr><th scope=row>q8</th><td> 9</td><td>1123</td><td>    42.265</td><td>    198.963</td><td>   5.0</td><td>   9.567</td><td>   4.448</td><td> 0</td><td>     3000</td><td>     3000</td><td>10.974</td><td> 143.537</td><td>     5.937</td></tr>\n",
       "\t<tr><th scope=row>q9</th><td>10</td><td>1123</td><td>   181.606</td><td>   1545.472</td><td>   9.0</td><td>  20.524</td><td>  10.378</td><td> 0</td><td>    32000</td><td>    32000</td><td>15.645</td><td> 272.526</td><td>    46.118</td></tr>\n",
       "\t<tr><th scope=row>q10</th><td>11</td><td>1123</td><td>    70.678</td><td>   1797.570</td><td>   1.0</td><td>   1.956</td><td>   0.000</td><td> 0</td><td>    60000</td><td>    60000</td><td>33.016</td><td>1097.155</td><td>    53.641</td></tr>\n",
       "\t<tr><th scope=row>q11</th><td>12</td><td>1123</td><td>    22.398</td><td>     29.888</td><td>  10.0</td><td>  15.776</td><td>  11.861</td><td> 0</td><td>      100</td><td>      100</td><td> 1.685</td><td>   1.516</td><td>     0.892</td></tr>\n",
       "\t<tr><th scope=row>q12</th><td>13</td><td>1123</td><td>     4.393</td><td>      0.790</td><td>   5.0</td><td>   4.533</td><td>   0.000</td><td> 1</td><td>        5</td><td>        4</td><td>-1.380</td><td>   2.013</td><td>     0.024</td></tr>\n",
       "\t<tr><th scope=row>q13</th><td>14</td><td>1123</td><td>     3.890</td><td>      0.932</td><td>   4.0</td><td>   4.011</td><td>   0.000</td><td> 1</td><td>        5</td><td>        4</td><td>-0.935</td><td>   0.710</td><td>     0.028</td></tr>\n",
       "\t<tr><th scope=row>q11_grp*</th><td>15</td><td>1123</td><td>     1.095</td><td>      0.294</td><td>   1.0</td><td>   1.000</td><td>   0.000</td><td> 1</td><td>        2</td><td>        1</td><td> 2.753</td><td>   5.585</td><td>     0.009</td></tr>\n",
       "\t<tr><th scope=row>q14*</th><td>16</td><td>1123</td><td>     1.978</td><td>      0.808</td><td>   2.0</td><td>   1.972</td><td>   1.483</td><td> 1</td><td>        3</td><td>        2</td><td> 0.040</td><td>  -1.468</td><td>     0.024</td></tr>\n",
       "\t<tr><th scope=row>q15*</th><td>17</td><td>1123</td><td>     4.976</td><td>      2.613</td><td>   5.0</td><td>   4.970</td><td>   2.965</td><td> 1</td><td>        9</td><td>        8</td><td>-0.034</td><td>  -1.156</td><td>     0.078</td></tr>\n",
       "\t<tr><th scope=row>q16*</th><td>18</td><td>1123</td><td>     3.039</td><td>      1.351</td><td>   4.0</td><td>   3.049</td><td>   1.483</td><td> 1</td><td>        5</td><td>        4</td><td>-0.190</td><td>  -1.348</td><td>     0.040</td></tr>\n",
       "\t<tr><th scope=row>q17*</th><td>19</td><td>1123</td><td>     1.874</td><td>      1.271</td><td>   1.0</td><td>   1.637</td><td>   0.000</td><td> 1</td><td>        5</td><td>        4</td><td> 1.175</td><td>   0.098</td><td>     0.038</td></tr>\n",
       "\t<tr><th scope=row>q18*</th><td>20</td><td>1123</td><td>     2.806</td><td>      1.087</td><td>   2.0</td><td>   2.882</td><td>   1.483</td><td> 1</td><td>        4</td><td>        3</td><td>-0.076</td><td>  -1.517</td><td>     0.032</td></tr>\n",
       "\t<tr><th scope=row>q19*</th><td>21</td><td>1123</td><td>     2.066</td><td>      0.809</td><td>   2.0</td><td>   2.082</td><td>   1.483</td><td> 1</td><td>        3</td><td>        2</td><td>-0.120</td><td>  -1.466</td><td>     0.024</td></tr>\n",
       "\t<tr><th scope=row>q20*</th><td>22</td><td>1123</td><td>     2.478</td><td>      0.745</td><td>   3.0</td><td>   2.597</td><td>   0.000</td><td> 1</td><td>        3</td><td>        2</td><td>-1.032</td><td>  -0.447</td><td>     0.022</td></tr>\n",
       "\t<tr><th scope=row>q21*</th><td>23</td><td>1123</td><td>     2.322</td><td>      0.894</td><td>   3.0</td><td>   2.403</td><td>   0.000</td><td> 1</td><td>        3</td><td>        2</td><td>-0.677</td><td>  -1.409</td><td>     0.027</td></tr>\n",
       "\t<tr><th scope=row>q22*</th><td>24</td><td>1123</td><td>     2.132</td><td>      0.931</td><td>   2.0</td><td>   2.056</td><td>   1.483</td><td> 1</td><td>        4</td><td>        3</td><td> 0.385</td><td>  -0.769</td><td>     0.028</td></tr>\n",
       "\t<tr><th scope=row>q23*</th><td>25</td><td>1123</td><td>     2.946</td><td>      1.777</td><td>   3.0</td><td>   2.932</td><td>   2.965</td><td> 1</td><td>        5</td><td>        4</td><td> 0.059</td><td>  -1.779</td><td>     0.053</td></tr>\n",
       "\t<tr><th scope=row>q24*</th><td>26</td><td>1123</td><td>     1.576</td><td>      0.950</td><td>   1.0</td><td>   1.346</td><td>   0.000</td><td> 1</td><td>        4</td><td>        3</td><td> 1.643</td><td>   1.523</td><td>     0.028</td></tr>\n",
       "\t<tr><th scope=row>q25*</th><td>27</td><td>1123</td><td>     1.801</td><td>      0.400</td><td>   2.0</td><td>   1.875</td><td>   0.000</td><td> 1</td><td>        2</td><td>        1</td><td>-1.502</td><td>   0.257</td><td>     0.012</td></tr>\n",
       "\t<tr><th scope=row>q26*</th><td>28</td><td>1123</td><td>     1.217</td><td>      0.413</td><td>   1.0</td><td>   1.147</td><td>   0.000</td><td> 1</td><td>        2</td><td>        1</td><td> 1.369</td><td>  -0.125</td><td>     0.012</td></tr>\n",
       "\t<tr><th scope=row>q28_grp*</th><td>29</td><td>1123</td><td>     3.485</td><td>      1.547</td><td>   4.0</td><td>   3.606</td><td>   1.483</td><td> 1</td><td>        5</td><td>        4</td><td>-0.446</td><td>  -1.347</td><td>     0.046</td></tr>\n",
       "\t<tr><th scope=row>vertical*</th><td>30</td><td>1123</td><td>    10.603</td><td>      5.344</td><td>  10.0</td><td>  10.594</td><td>   7.413</td><td> 1</td><td>       21</td><td>       20</td><td> 0.025</td><td>  -1.387</td><td>     0.159</td></tr>\n",
       "\t<tr><th scope=row>rank_prefer_content*</th><td>31</td><td>1123</td><td>     3.028</td><td>      1.454</td><td>   3.0</td><td>   3.036</td><td>   1.483</td><td> 1</td><td>        5</td><td>        4</td><td>-0.016</td><td>  -1.251</td><td>     0.043</td></tr>\n",
       "\t<tr><th scope=row>rank_help_topics*</th><td>32</td><td>1123</td><td>     2.394</td><td>      0.657</td><td>   2.0</td><td>   2.488</td><td>   1.483</td><td> 1</td><td>        3</td><td>        2</td><td>-0.625</td><td>  -0.640</td><td>     0.020</td></tr>\n",
       "\t<tr><th scope=row>rank_comm_method*</th><td>33</td><td>1123</td><td>     2.505</td><td>      0.902</td><td>   3.0</td><td>   2.506</td><td>   1.483</td><td> 1</td><td>        4</td><td>        3</td><td>-0.109</td><td>  -0.777</td><td>     0.027</td></tr>\n",
       "\t<tr><th scope=row>orig_clust*</th><td>34</td><td>1123</td><td>     2.060</td><td>      1.047</td><td>   2.0</td><td>   1.950</td><td>   1.483</td><td> 1</td><td>        4</td><td>        3</td><td> 0.769</td><td>  -0.586</td><td>     0.031</td></tr>\n",
       "\t<tr><th scope=row>q28</th><td>35</td><td>1123</td><td>   623.117</td><td>   4997.627</td><td>  47.0</td><td> 102.785</td><td>  59.304</td><td> 0</td><td>   129314</td><td>   129314</td><td>20.104</td><td> 461.033</td><td>   149.133</td></tr>\n",
       "\t<tr><th scope=row>q29</th><td>36</td><td>1123</td><td>121981.156</td><td>3433679.480</td><td> 800.0</td><td>2033.150</td><td> 889.560</td><td> 0</td><td>115000000</td><td>115000000</td><td>33.347</td><td>1112.653</td><td>102463.662</td></tr>\n",
       "\t<tr><th scope=row>q30</th><td>37</td><td>1123</td><td>  9173.904</td><td> 104261.285</td><td> 483.0</td><td>1141.360</td><td> 636.035</td><td> 0</td><td>  3137853</td><td>  3137853</td><td>25.766</td><td> 736.534</td><td>  3111.238</td></tr>\n",
       "\t<tr><th scope=row>q32</th><td>38</td><td>1123</td><td> 22260.205</td><td> 194670.541</td><td>1175.0</td><td>3021.568</td><td>1610.104</td><td> 0</td><td>  4388004</td><td>  4388004</td><td>18.863</td><td> 383.119</td><td>  5809.120</td></tr>\n",
       "\t<tr><th scope=row>q33</th><td>39</td><td>1027</td><td>  1894.662</td><td>   8569.916</td><td> 110.0</td><td> 314.849</td><td> 152.708</td><td> 1</td><td>   142459</td><td>   142458</td><td> 9.242</td><td> 109.324</td><td>   267.418</td></tr>\n",
       "\t<tr><th scope=row>q34</th><td>40</td><td> 833</td><td>    65.709</td><td>     24.326</td><td>  77.0</td><td>  68.925</td><td>  14.826</td><td> 0</td><td>      100</td><td>      100</td><td>-0.953</td><td>  -0.104</td><td>     0.843</td></tr>\n",
       "\t<tr><th scope=row>q35</th><td>41</td><td>1123</td><td> 17994.023</td><td> 184799.428</td><td>1250.0</td><td>2611.335</td><td>1559.695</td><td> 0</td><td>  4766870</td><td>  4766870</td><td>22.503</td><td> 532.846</td><td>  5514.558</td></tr>\n",
       "\t<tr><th scope=row>q36</th><td>42</td><td>1109</td><td>   650.200</td><td>    665.860</td><td> 354.0</td><td> 531.883</td><td> 357.307</td><td>13</td><td>     2664</td><td>     2651</td><td> 1.314</td><td>   0.623</td><td>    19.995</td></tr>\n",
       "\t<tr><th scope=row>q37</th><td>43</td><td>1123</td><td>  4481.684</td><td>  48841.278</td><td> 348.3</td><td> 841.520</td><td> 430.517</td><td> 0</td><td>  1572917</td><td>  1572917</td><td>29.900</td><td> 946.932</td><td>  1457.462</td></tr>\n",
       "\t<tr><th scope=row>q38i</th><td>44</td><td>1123</td><td>  1880.551</td><td>   8195.266</td><td> 138.0</td><td> 442.226</td><td> 197.186</td><td> 1</td><td>   142459</td><td>   142458</td><td> 9.670</td><td> 119.901</td><td>   244.553</td></tr>\n",
       "\t<tr><th scope=row>q39i</th><td>45</td><td>1107</td><td>    66.867</td><td>     19.713</td><td>  70.0</td><td>  69.290</td><td>  19.274</td><td> 1</td><td>      100</td><td>       99</td><td>-0.987</td><td>   0.483</td><td>     0.593</td></tr>\n",
       "\t<tr><th scope=row>q40i</th><td>46</td><td>1123</td><td>   650.057</td><td>    661.700</td><td> 359.0</td><td> 531.674</td><td> 370.650</td><td>13</td><td>     2664</td><td>     2651</td><td> 1.323</td><td>   0.669</td><td>    19.746</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A psych: 46 × 13\n",
       "\\begin{tabular}{r|lllllllllllll}\n",
       "  & vars & n & mean & sd & median & trimmed & mad & min & max & range & skew & kurtosis & se\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tuid &  1 & 1123 &    845.045 &     463.324 &  868.0 &  852.764 &  581.179 &  6 &      1618 &      1612 & -0.128 &   -1.161 &     13.826\\\\\n",
       "\tq1 &  2 & 1123 &      0.915 &       0.280 &    1.0 &    1.000 &    0.000 &  0 &         1 &         1 & -2.961 &    6.774 &      0.008\\\\\n",
       "\tq2 &  3 & 1123 &      0.240 &       0.427 &    0.0 &    0.175 &    0.000 &  0 &         1 &         1 &  1.219 &   -0.515 &      0.013\\\\\n",
       "\tq3 &  4 & 1123 &      0.159 &       0.365 &    0.0 &    0.073 &    0.000 &  0 &         1 &         1 &  1.868 &    1.489 &      0.011\\\\\n",
       "\tq4 &  5 & 1123 &      3.387 &       2.447 &    3.0 &    3.057 &    2.965 &  0 &        13 &        13 &  1.165 &    1.252 &      0.073\\\\\n",
       "\tq5 &  6 & 1123 &      3.516 &       2.110 &    3.0 &    3.277 &    1.483 &  1 &        12 &        11 &  1.046 &    1.196 &      0.063\\\\\n",
       "\tq6 &  7 & 1123 &      1.629 &       0.951 &    1.0 &    1.443 &    0.000 &  1 &         6 &         5 &  1.836 &    3.828 &      0.028\\\\\n",
       "\tq7 &  8 & 1123 &      2.866 &       1.461 &    3.0 &    2.763 &    1.483 &  1 &         7 &         6 &  0.422 &   -0.631 &      0.044\\\\\n",
       "\tq8 &  9 & 1123 &     42.265 &     198.963 &    5.0 &    9.567 &    4.448 &  0 &      3000 &      3000 & 10.974 &  143.537 &      5.937\\\\\n",
       "\tq9 & 10 & 1123 &    181.606 &    1545.472 &    9.0 &   20.524 &   10.378 &  0 &     32000 &     32000 & 15.645 &  272.526 &     46.118\\\\\n",
       "\tq10 & 11 & 1123 &     70.678 &    1797.570 &    1.0 &    1.956 &    0.000 &  0 &     60000 &     60000 & 33.016 & 1097.155 &     53.641\\\\\n",
       "\tq11 & 12 & 1123 &     22.398 &      29.888 &   10.0 &   15.776 &   11.861 &  0 &       100 &       100 &  1.685 &    1.516 &      0.892\\\\\n",
       "\tq12 & 13 & 1123 &      4.393 &       0.790 &    5.0 &    4.533 &    0.000 &  1 &         5 &         4 & -1.380 &    2.013 &      0.024\\\\\n",
       "\tq13 & 14 & 1123 &      3.890 &       0.932 &    4.0 &    4.011 &    0.000 &  1 &         5 &         4 & -0.935 &    0.710 &      0.028\\\\\n",
       "\tq11\\_grp* & 15 & 1123 &      1.095 &       0.294 &    1.0 &    1.000 &    0.000 &  1 &         2 &         1 &  2.753 &    5.585 &      0.009\\\\\n",
       "\tq14* & 16 & 1123 &      1.978 &       0.808 &    2.0 &    1.972 &    1.483 &  1 &         3 &         2 &  0.040 &   -1.468 &      0.024\\\\\n",
       "\tq15* & 17 & 1123 &      4.976 &       2.613 &    5.0 &    4.970 &    2.965 &  1 &         9 &         8 & -0.034 &   -1.156 &      0.078\\\\\n",
       "\tq16* & 18 & 1123 &      3.039 &       1.351 &    4.0 &    3.049 &    1.483 &  1 &         5 &         4 & -0.190 &   -1.348 &      0.040\\\\\n",
       "\tq17* & 19 & 1123 &      1.874 &       1.271 &    1.0 &    1.637 &    0.000 &  1 &         5 &         4 &  1.175 &    0.098 &      0.038\\\\\n",
       "\tq18* & 20 & 1123 &      2.806 &       1.087 &    2.0 &    2.882 &    1.483 &  1 &         4 &         3 & -0.076 &   -1.517 &      0.032\\\\\n",
       "\tq19* & 21 & 1123 &      2.066 &       0.809 &    2.0 &    2.082 &    1.483 &  1 &         3 &         2 & -0.120 &   -1.466 &      0.024\\\\\n",
       "\tq20* & 22 & 1123 &      2.478 &       0.745 &    3.0 &    2.597 &    0.000 &  1 &         3 &         2 & -1.032 &   -0.447 &      0.022\\\\\n",
       "\tq21* & 23 & 1123 &      2.322 &       0.894 &    3.0 &    2.403 &    0.000 &  1 &         3 &         2 & -0.677 &   -1.409 &      0.027\\\\\n",
       "\tq22* & 24 & 1123 &      2.132 &       0.931 &    2.0 &    2.056 &    1.483 &  1 &         4 &         3 &  0.385 &   -0.769 &      0.028\\\\\n",
       "\tq23* & 25 & 1123 &      2.946 &       1.777 &    3.0 &    2.932 &    2.965 &  1 &         5 &         4 &  0.059 &   -1.779 &      0.053\\\\\n",
       "\tq24* & 26 & 1123 &      1.576 &       0.950 &    1.0 &    1.346 &    0.000 &  1 &         4 &         3 &  1.643 &    1.523 &      0.028\\\\\n",
       "\tq25* & 27 & 1123 &      1.801 &       0.400 &    2.0 &    1.875 &    0.000 &  1 &         2 &         1 & -1.502 &    0.257 &      0.012\\\\\n",
       "\tq26* & 28 & 1123 &      1.217 &       0.413 &    1.0 &    1.147 &    0.000 &  1 &         2 &         1 &  1.369 &   -0.125 &      0.012\\\\\n",
       "\tq28\\_grp* & 29 & 1123 &      3.485 &       1.547 &    4.0 &    3.606 &    1.483 &  1 &         5 &         4 & -0.446 &   -1.347 &      0.046\\\\\n",
       "\tvertical* & 30 & 1123 &     10.603 &       5.344 &   10.0 &   10.594 &    7.413 &  1 &        21 &        20 &  0.025 &   -1.387 &      0.159\\\\\n",
       "\trank\\_prefer\\_content* & 31 & 1123 &      3.028 &       1.454 &    3.0 &    3.036 &    1.483 &  1 &         5 &         4 & -0.016 &   -1.251 &      0.043\\\\\n",
       "\trank\\_help\\_topics* & 32 & 1123 &      2.394 &       0.657 &    2.0 &    2.488 &    1.483 &  1 &         3 &         2 & -0.625 &   -0.640 &      0.020\\\\\n",
       "\trank\\_comm\\_method* & 33 & 1123 &      2.505 &       0.902 &    3.0 &    2.506 &    1.483 &  1 &         4 &         3 & -0.109 &   -0.777 &      0.027\\\\\n",
       "\torig\\_clust* & 34 & 1123 &      2.060 &       1.047 &    2.0 &    1.950 &    1.483 &  1 &         4 &         3 &  0.769 &   -0.586 &      0.031\\\\\n",
       "\tq28 & 35 & 1123 &    623.117 &    4997.627 &   47.0 &  102.785 &   59.304 &  0 &    129314 &    129314 & 20.104 &  461.033 &    149.133\\\\\n",
       "\tq29 & 36 & 1123 & 121981.156 & 3433679.480 &  800.0 & 2033.150 &  889.560 &  0 & 115000000 & 115000000 & 33.347 & 1112.653 & 102463.662\\\\\n",
       "\tq30 & 37 & 1123 &   9173.904 &  104261.285 &  483.0 & 1141.360 &  636.035 &  0 &   3137853 &   3137853 & 25.766 &  736.534 &   3111.238\\\\\n",
       "\tq32 & 38 & 1123 &  22260.205 &  194670.541 & 1175.0 & 3021.568 & 1610.104 &  0 &   4388004 &   4388004 & 18.863 &  383.119 &   5809.120\\\\\n",
       "\tq33 & 39 & 1027 &   1894.662 &    8569.916 &  110.0 &  314.849 &  152.708 &  1 &    142459 &    142458 &  9.242 &  109.324 &    267.418\\\\\n",
       "\tq34 & 40 &  833 &     65.709 &      24.326 &   77.0 &   68.925 &   14.826 &  0 &       100 &       100 & -0.953 &   -0.104 &      0.843\\\\\n",
       "\tq35 & 41 & 1123 &  17994.023 &  184799.428 & 1250.0 & 2611.335 & 1559.695 &  0 &   4766870 &   4766870 & 22.503 &  532.846 &   5514.558\\\\\n",
       "\tq36 & 42 & 1109 &    650.200 &     665.860 &  354.0 &  531.883 &  357.307 & 13 &      2664 &      2651 &  1.314 &    0.623 &     19.995\\\\\n",
       "\tq37 & 43 & 1123 &   4481.684 &   48841.278 &  348.3 &  841.520 &  430.517 &  0 &   1572917 &   1572917 & 29.900 &  946.932 &   1457.462\\\\\n",
       "\tq38i & 44 & 1123 &   1880.551 &    8195.266 &  138.0 &  442.226 &  197.186 &  1 &    142459 &    142458 &  9.670 &  119.901 &    244.553\\\\\n",
       "\tq39i & 45 & 1107 &     66.867 &      19.713 &   70.0 &   69.290 &   19.274 &  1 &       100 &        99 & -0.987 &    0.483 &      0.593\\\\\n",
       "\tq40i & 46 & 1123 &    650.057 &     661.700 &  359.0 &  531.674 &  370.650 & 13 &      2664 &      2651 &  1.323 &    0.669 &     19.746\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A psych: 46 × 13\n",
       "\n",
       "| <!--/--> | vars &lt;dbl&gt; | n &lt;dbl&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | median &lt;dbl&gt; | trimmed &lt;dbl&gt; | mad &lt;dbl&gt; | min &lt;dbl&gt; | max &lt;dbl&gt; | range &lt;dbl&gt; | skew &lt;dbl&gt; | kurtosis &lt;dbl&gt; | se &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| uid |  1 | 1123 |    845.045 |     463.324 |  868.0 |  852.764 |  581.179 |  6 |      1618 |      1612 | -0.128 |   -1.161 |     13.826 |\n",
       "| q1 |  2 | 1123 |      0.915 |       0.280 |    1.0 |    1.000 |    0.000 |  0 |         1 |         1 | -2.961 |    6.774 |      0.008 |\n",
       "| q2 |  3 | 1123 |      0.240 |       0.427 |    0.0 |    0.175 |    0.000 |  0 |         1 |         1 |  1.219 |   -0.515 |      0.013 |\n",
       "| q3 |  4 | 1123 |      0.159 |       0.365 |    0.0 |    0.073 |    0.000 |  0 |         1 |         1 |  1.868 |    1.489 |      0.011 |\n",
       "| q4 |  5 | 1123 |      3.387 |       2.447 |    3.0 |    3.057 |    2.965 |  0 |        13 |        13 |  1.165 |    1.252 |      0.073 |\n",
       "| q5 |  6 | 1123 |      3.516 |       2.110 |    3.0 |    3.277 |    1.483 |  1 |        12 |        11 |  1.046 |    1.196 |      0.063 |\n",
       "| q6 |  7 | 1123 |      1.629 |       0.951 |    1.0 |    1.443 |    0.000 |  1 |         6 |         5 |  1.836 |    3.828 |      0.028 |\n",
       "| q7 |  8 | 1123 |      2.866 |       1.461 |    3.0 |    2.763 |    1.483 |  1 |         7 |         6 |  0.422 |   -0.631 |      0.044 |\n",
       "| q8 |  9 | 1123 |     42.265 |     198.963 |    5.0 |    9.567 |    4.448 |  0 |      3000 |      3000 | 10.974 |  143.537 |      5.937 |\n",
       "| q9 | 10 | 1123 |    181.606 |    1545.472 |    9.0 |   20.524 |   10.378 |  0 |     32000 |     32000 | 15.645 |  272.526 |     46.118 |\n",
       "| q10 | 11 | 1123 |     70.678 |    1797.570 |    1.0 |    1.956 |    0.000 |  0 |     60000 |     60000 | 33.016 | 1097.155 |     53.641 |\n",
       "| q11 | 12 | 1123 |     22.398 |      29.888 |   10.0 |   15.776 |   11.861 |  0 |       100 |       100 |  1.685 |    1.516 |      0.892 |\n",
       "| q12 | 13 | 1123 |      4.393 |       0.790 |    5.0 |    4.533 |    0.000 |  1 |         5 |         4 | -1.380 |    2.013 |      0.024 |\n",
       "| q13 | 14 | 1123 |      3.890 |       0.932 |    4.0 |    4.011 |    0.000 |  1 |         5 |         4 | -0.935 |    0.710 |      0.028 |\n",
       "| q11_grp* | 15 | 1123 |      1.095 |       0.294 |    1.0 |    1.000 |    0.000 |  1 |         2 |         1 |  2.753 |    5.585 |      0.009 |\n",
       "| q14* | 16 | 1123 |      1.978 |       0.808 |    2.0 |    1.972 |    1.483 |  1 |         3 |         2 |  0.040 |   -1.468 |      0.024 |\n",
       "| q15* | 17 | 1123 |      4.976 |       2.613 |    5.0 |    4.970 |    2.965 |  1 |         9 |         8 | -0.034 |   -1.156 |      0.078 |\n",
       "| q16* | 18 | 1123 |      3.039 |       1.351 |    4.0 |    3.049 |    1.483 |  1 |         5 |         4 | -0.190 |   -1.348 |      0.040 |\n",
       "| q17* | 19 | 1123 |      1.874 |       1.271 |    1.0 |    1.637 |    0.000 |  1 |         5 |         4 |  1.175 |    0.098 |      0.038 |\n",
       "| q18* | 20 | 1123 |      2.806 |       1.087 |    2.0 |    2.882 |    1.483 |  1 |         4 |         3 | -0.076 |   -1.517 |      0.032 |\n",
       "| q19* | 21 | 1123 |      2.066 |       0.809 |    2.0 |    2.082 |    1.483 |  1 |         3 |         2 | -0.120 |   -1.466 |      0.024 |\n",
       "| q20* | 22 | 1123 |      2.478 |       0.745 |    3.0 |    2.597 |    0.000 |  1 |         3 |         2 | -1.032 |   -0.447 |      0.022 |\n",
       "| q21* | 23 | 1123 |      2.322 |       0.894 |    3.0 |    2.403 |    0.000 |  1 |         3 |         2 | -0.677 |   -1.409 |      0.027 |\n",
       "| q22* | 24 | 1123 |      2.132 |       0.931 |    2.0 |    2.056 |    1.483 |  1 |         4 |         3 |  0.385 |   -0.769 |      0.028 |\n",
       "| q23* | 25 | 1123 |      2.946 |       1.777 |    3.0 |    2.932 |    2.965 |  1 |         5 |         4 |  0.059 |   -1.779 |      0.053 |\n",
       "| q24* | 26 | 1123 |      1.576 |       0.950 |    1.0 |    1.346 |    0.000 |  1 |         4 |         3 |  1.643 |    1.523 |      0.028 |\n",
       "| q25* | 27 | 1123 |      1.801 |       0.400 |    2.0 |    1.875 |    0.000 |  1 |         2 |         1 | -1.502 |    0.257 |      0.012 |\n",
       "| q26* | 28 | 1123 |      1.217 |       0.413 |    1.0 |    1.147 |    0.000 |  1 |         2 |         1 |  1.369 |   -0.125 |      0.012 |\n",
       "| q28_grp* | 29 | 1123 |      3.485 |       1.547 |    4.0 |    3.606 |    1.483 |  1 |         5 |         4 | -0.446 |   -1.347 |      0.046 |\n",
       "| vertical* | 30 | 1123 |     10.603 |       5.344 |   10.0 |   10.594 |    7.413 |  1 |        21 |        20 |  0.025 |   -1.387 |      0.159 |\n",
       "| rank_prefer_content* | 31 | 1123 |      3.028 |       1.454 |    3.0 |    3.036 |    1.483 |  1 |         5 |         4 | -0.016 |   -1.251 |      0.043 |\n",
       "| rank_help_topics* | 32 | 1123 |      2.394 |       0.657 |    2.0 |    2.488 |    1.483 |  1 |         3 |         2 | -0.625 |   -0.640 |      0.020 |\n",
       "| rank_comm_method* | 33 | 1123 |      2.505 |       0.902 |    3.0 |    2.506 |    1.483 |  1 |         4 |         3 | -0.109 |   -0.777 |      0.027 |\n",
       "| orig_clust* | 34 | 1123 |      2.060 |       1.047 |    2.0 |    1.950 |    1.483 |  1 |         4 |         3 |  0.769 |   -0.586 |      0.031 |\n",
       "| q28 | 35 | 1123 |    623.117 |    4997.627 |   47.0 |  102.785 |   59.304 |  0 |    129314 |    129314 | 20.104 |  461.033 |    149.133 |\n",
       "| q29 | 36 | 1123 | 121981.156 | 3433679.480 |  800.0 | 2033.150 |  889.560 |  0 | 115000000 | 115000000 | 33.347 | 1112.653 | 102463.662 |\n",
       "| q30 | 37 | 1123 |   9173.904 |  104261.285 |  483.0 | 1141.360 |  636.035 |  0 |   3137853 |   3137853 | 25.766 |  736.534 |   3111.238 |\n",
       "| q32 | 38 | 1123 |  22260.205 |  194670.541 | 1175.0 | 3021.568 | 1610.104 |  0 |   4388004 |   4388004 | 18.863 |  383.119 |   5809.120 |\n",
       "| q33 | 39 | 1027 |   1894.662 |    8569.916 |  110.0 |  314.849 |  152.708 |  1 |    142459 |    142458 |  9.242 |  109.324 |    267.418 |\n",
       "| q34 | 40 |  833 |     65.709 |      24.326 |   77.0 |   68.925 |   14.826 |  0 |       100 |       100 | -0.953 |   -0.104 |      0.843 |\n",
       "| q35 | 41 | 1123 |  17994.023 |  184799.428 | 1250.0 | 2611.335 | 1559.695 |  0 |   4766870 |   4766870 | 22.503 |  532.846 |   5514.558 |\n",
       "| q36 | 42 | 1109 |    650.200 |     665.860 |  354.0 |  531.883 |  357.307 | 13 |      2664 |      2651 |  1.314 |    0.623 |     19.995 |\n",
       "| q37 | 43 | 1123 |   4481.684 |   48841.278 |  348.3 |  841.520 |  430.517 |  0 |   1572917 |   1572917 | 29.900 |  946.932 |   1457.462 |\n",
       "| q38i | 44 | 1123 |   1880.551 |    8195.266 |  138.0 |  442.226 |  197.186 |  1 |    142459 |    142458 |  9.670 |  119.901 |    244.553 |\n",
       "| q39i | 45 | 1107 |     66.867 |      19.713 |   70.0 |   69.290 |   19.274 |  1 |       100 |        99 | -0.987 |    0.483 |      0.593 |\n",
       "| q40i | 46 | 1123 |    650.057 |     661.700 |  359.0 |  531.674 |  370.650 | 13 |      2664 |      2651 |  1.323 |    0.669 |     19.746 |\n",
       "\n"
      ],
      "text/plain": [
       "                     vars n    mean       sd          median trimmed  mad     \n",
       "uid                   1   1123    845.045     463.324  868.0  852.764  581.179\n",
       "q1                    2   1123      0.915       0.280    1.0    1.000    0.000\n",
       "q2                    3   1123      0.240       0.427    0.0    0.175    0.000\n",
       "q3                    4   1123      0.159       0.365    0.0    0.073    0.000\n",
       "q4                    5   1123      3.387       2.447    3.0    3.057    2.965\n",
       "q5                    6   1123      3.516       2.110    3.0    3.277    1.483\n",
       "q6                    7   1123      1.629       0.951    1.0    1.443    0.000\n",
       "q7                    8   1123      2.866       1.461    3.0    2.763    1.483\n",
       "q8                    9   1123     42.265     198.963    5.0    9.567    4.448\n",
       "q9                   10   1123    181.606    1545.472    9.0   20.524   10.378\n",
       "q10                  11   1123     70.678    1797.570    1.0    1.956    0.000\n",
       "q11                  12   1123     22.398      29.888   10.0   15.776   11.861\n",
       "q12                  13   1123      4.393       0.790    5.0    4.533    0.000\n",
       "q13                  14   1123      3.890       0.932    4.0    4.011    0.000\n",
       "q11_grp*             15   1123      1.095       0.294    1.0    1.000    0.000\n",
       "q14*                 16   1123      1.978       0.808    2.0    1.972    1.483\n",
       "q15*                 17   1123      4.976       2.613    5.0    4.970    2.965\n",
       "q16*                 18   1123      3.039       1.351    4.0    3.049    1.483\n",
       "q17*                 19   1123      1.874       1.271    1.0    1.637    0.000\n",
       "q18*                 20   1123      2.806       1.087    2.0    2.882    1.483\n",
       "q19*                 21   1123      2.066       0.809    2.0    2.082    1.483\n",
       "q20*                 22   1123      2.478       0.745    3.0    2.597    0.000\n",
       "q21*                 23   1123      2.322       0.894    3.0    2.403    0.000\n",
       "q22*                 24   1123      2.132       0.931    2.0    2.056    1.483\n",
       "q23*                 25   1123      2.946       1.777    3.0    2.932    2.965\n",
       "q24*                 26   1123      1.576       0.950    1.0    1.346    0.000\n",
       "q25*                 27   1123      1.801       0.400    2.0    1.875    0.000\n",
       "q26*                 28   1123      1.217       0.413    1.0    1.147    0.000\n",
       "q28_grp*             29   1123      3.485       1.547    4.0    3.606    1.483\n",
       "vertical*            30   1123     10.603       5.344   10.0   10.594    7.413\n",
       "rank_prefer_content* 31   1123      3.028       1.454    3.0    3.036    1.483\n",
       "rank_help_topics*    32   1123      2.394       0.657    2.0    2.488    1.483\n",
       "rank_comm_method*    33   1123      2.505       0.902    3.0    2.506    1.483\n",
       "orig_clust*          34   1123      2.060       1.047    2.0    1.950    1.483\n",
       "q28                  35   1123    623.117    4997.627   47.0  102.785   59.304\n",
       "q29                  36   1123 121981.156 3433679.480  800.0 2033.150  889.560\n",
       "q30                  37   1123   9173.904  104261.285  483.0 1141.360  636.035\n",
       "q32                  38   1123  22260.205  194670.541 1175.0 3021.568 1610.104\n",
       "q33                  39   1027   1894.662    8569.916  110.0  314.849  152.708\n",
       "q34                  40    833     65.709      24.326   77.0   68.925   14.826\n",
       "q35                  41   1123  17994.023  184799.428 1250.0 2611.335 1559.695\n",
       "q36                  42   1109    650.200     665.860  354.0  531.883  357.307\n",
       "q37                  43   1123   4481.684   48841.278  348.3  841.520  430.517\n",
       "q38i                 44   1123   1880.551    8195.266  138.0  442.226  197.186\n",
       "q39i                 45   1107     66.867      19.713   70.0   69.290   19.274\n",
       "q40i                 46   1123    650.057     661.700  359.0  531.674  370.650\n",
       "                     min max       range     skew   kurtosis se        \n",
       "uid                   6       1618      1612 -0.128   -1.161     13.826\n",
       "q1                    0          1         1 -2.961    6.774      0.008\n",
       "q2                    0          1         1  1.219   -0.515      0.013\n",
       "q3                    0          1         1  1.868    1.489      0.011\n",
       "q4                    0         13        13  1.165    1.252      0.073\n",
       "q5                    1         12        11  1.046    1.196      0.063\n",
       "q6                    1          6         5  1.836    3.828      0.028\n",
       "q7                    1          7         6  0.422   -0.631      0.044\n",
       "q8                    0       3000      3000 10.974  143.537      5.937\n",
       "q9                    0      32000     32000 15.645  272.526     46.118\n",
       "q10                   0      60000     60000 33.016 1097.155     53.641\n",
       "q11                   0        100       100  1.685    1.516      0.892\n",
       "q12                   1          5         4 -1.380    2.013      0.024\n",
       "q13                   1          5         4 -0.935    0.710      0.028\n",
       "q11_grp*              1          2         1  2.753    5.585      0.009\n",
       "q14*                  1          3         2  0.040   -1.468      0.024\n",
       "q15*                  1          9         8 -0.034   -1.156      0.078\n",
       "q16*                  1          5         4 -0.190   -1.348      0.040\n",
       "q17*                  1          5         4  1.175    0.098      0.038\n",
       "q18*                  1          4         3 -0.076   -1.517      0.032\n",
       "q19*                  1          3         2 -0.120   -1.466      0.024\n",
       "q20*                  1          3         2 -1.032   -0.447      0.022\n",
       "q21*                  1          3         2 -0.677   -1.409      0.027\n",
       "q22*                  1          4         3  0.385   -0.769      0.028\n",
       "q23*                  1          5         4  0.059   -1.779      0.053\n",
       "q24*                  1          4         3  1.643    1.523      0.028\n",
       "q25*                  1          2         1 -1.502    0.257      0.012\n",
       "q26*                  1          2         1  1.369   -0.125      0.012\n",
       "q28_grp*              1          5         4 -0.446   -1.347      0.046\n",
       "vertical*             1         21        20  0.025   -1.387      0.159\n",
       "rank_prefer_content*  1          5         4 -0.016   -1.251      0.043\n",
       "rank_help_topics*     1          3         2 -0.625   -0.640      0.020\n",
       "rank_comm_method*     1          4         3 -0.109   -0.777      0.027\n",
       "orig_clust*           1          4         3  0.769   -0.586      0.031\n",
       "q28                   0     129314    129314 20.104  461.033    149.133\n",
       "q29                   0  115000000 115000000 33.347 1112.653 102463.662\n",
       "q30                   0    3137853   3137853 25.766  736.534   3111.238\n",
       "q32                   0    4388004   4388004 18.863  383.119   5809.120\n",
       "q33                   1     142459    142458  9.242  109.324    267.418\n",
       "q34                   0        100       100 -0.953   -0.104      0.843\n",
       "q35                   0    4766870   4766870 22.503  532.846   5514.558\n",
       "q36                  13       2664      2651  1.314    0.623     19.995\n",
       "q37                   0    1572917   1572917 29.900  946.932   1457.462\n",
       "q38i                  1     142459    142458  9.670  119.901    244.553\n",
       "q39i                  1        100        99 -0.987    0.483      0.593\n",
       "q40i                 13       2664      2651  1.323    0.669     19.746"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_e <- psych::describe(df)\n",
    "round(df_e, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary \n",
    "\n",
    "Among the numeric variables, significant skew is observed in the folowing variables:  q4, q6, q8, q9, q10, q11, q12.  These variables should be transformed prior to being included in the analysis. \n",
    "\n",
    "The CRM variables (q27 - q33) also show severe skew (except q29); these will all need to be transformed before further analysis.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluate Variables for Skew\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the code below shows the distribution of the original, untransformed quant variables from the survey.  The results show\n",
    "# the presence of significant skew in all the variables.  This is problematic for distance-based clustering algoithms such as kmeans\n",
    "# hierarchical methods.  The variables need to be transformed to better approximate a Normal distribution of each variable. \n",
    "cols <- c(\"q4\", \"q5\", \"q6\", \"q7\", \"q8\", \"q9\", \"q10\", \"q11\", \"q12\", \"q13\")\n",
    "\n",
    "df %>% \n",
    "  pivot_longer(q4:q13, names_to = \"question\", values_to = \"response\") %>% \n",
    "  ggplot(aes(x = response)) +\n",
    "  geom_histogram() +\n",
    "  facet_wrap(vars(question), ncol = 3) +\n",
    "  labs(x = \"distribution)\", y = \"frequency\")\n",
    "\n",
    "# apply the transformation and save to new dataframe\n",
    "test_df <- lapply(df[cols], bestNormalize)\n",
    "q4t<- test_df$q4[[1]]\n",
    "q5t<- test_df$q5[[1]]\n",
    "q6t<- test_df$q6[[1]]\n",
    "q7t<- test_df$q7[[1]]\n",
    "q8t<- test_df$q8[[1]]\n",
    "q9t<- test_df$q9[[1]]\n",
    "q10t<- test_df$q10[[1]]\n",
    "q11t<- test_df$q11[[1]]\n",
    "q12t<- test_df$q12[[1]]\n",
    "q13t<- test_df$q13[[1]]\n",
    "df_t = as.data.frame(cbind(q4t, q5t, q6t, q7t, q8t, q9t, q10t, q11t, q12t, q13t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the plots below show the result after applying the optimal normalization method to each variable.  The R Package 'bestNormalize' \n",
    "# is a convenient package that applies a number of various transformations to each variable and then selects the transformation\n",
    "# which yields the best approach - best in this case means closest to a Gaussian distribution. \n",
    "\n",
    "df_t %>% \n",
    "  pivot_longer(q4t:q13t, names_to = \"question\", values_to = \"response\") %>% \n",
    "  ggplot(aes(x = response)) +\n",
    "  geom_histogram() +\n",
    "  facet_wrap(vars(question), ncol = 3) +\n",
    "  labs(x = \"distribution\", y = \"frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# Transform All Variables\n",
    "The code in this blocks transforms all the numeric variables to remove skew, and the re-combines all the numeric and categorical variables into the final dataframe for analysis\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SCALE VARIABLES #####################################################################################\n",
    "# Scale Variables (n = 10)\n",
    "\n",
    "q4n <- df$q4 %>% bestNormalize() %>% .[[1]]  # count of departments using [product] (q18)\n",
    "q5n <- df$q5 %>% bestNormalize() %>% .[[1]]  # number of [product] features used (q28)\n",
    "q6n <- df$q6 %>% bestNormalize() %>% .[[1]]  # count of roles of [product] users (q19)\n",
    "q7n <- df$q7 %>% bestNormalize() %>% .[[1]]  # count of admin portal features used (q27)\n",
    "q8n <- df$q8 %>% bestNormalize() %>% .[[1]]  # number of unique senders managed (q51)\n",
    "q9n <- df$q9 %>% bestNormalize() %>% .[[1]]  # number of unique senders in company (q13)\n",
    "q10n <- df$q10 %>% bestNormalize() %>% .[[1]] # number of [product] accounts (q14)\n",
    "q11n <- df$q11 %>% bestNormalize() %>% .[[1]] # % time on [product] activities each month (q24_4)\n",
    "q12n <- df$q12 %>% bestNormalize() %>% .[[1]] # satisfaction with [product] (q37)\n",
    "q13n <- df$q13 %>% bestNormalize() %>% .[[1]] # confidence level with [product] (q21)\n",
    "\n",
    "df_scale <- cbind(df$q4, df$q5, df$q6, df$q7, df$q8, df$q9, df$q10, df$q12, df$q13)\n",
    "\n",
    "\n",
    "#Label numeric variables for convenience: \n",
    "depts_using <- q4n\n",
    "feat_used <- q5n\n",
    "num_roles <- q6n\n",
    "admin_prtl_use <- q7n\n",
    "unq_snd_mng <- q8n\n",
    "unq_snd_cmp <- q9n \n",
    "num_ds_accnts <- q10n\n",
    "time_ds_act <- q11n\n",
    "rate_sat <- q12n\n",
    "rate_conf <- q13n\n",
    "\n",
    "\n",
    "#Combine into new DataFrame\n",
    "df_norm_s <- cbind(depts_using, feat_used, num_roles, admin_prtl_use, unq_snd_mng,unq_snd_cmp, rate_sat)\n",
    "\n",
    "\n",
    "#CATEGORICAL VARIABLES #########################################################################################\n",
    "# Survey Categorical Variables (n = 15)\n",
    "\n",
    "q1  <- df$q1\n",
    "q2  <- df$q2\n",
    "q3  <- df$q3\n",
    "num_locs <- df$q14 # Number of Locations\n",
    "dept <- df$q15 # Your Department\n",
    "job_level <- df$q16 # Level of Responsibility (Staff, Mid_management, VP, etc.)\n",
    "time_resp <- df$q17 # % time spent on responsibilities (group)\n",
    "time_ds_tasks <- df$q18 # % time DS Tasks (group)\n",
    "top_two <- df$q19 # Top 2 outcomes for your role\n",
    "ds_expr <- df$q20 # Level of DS Experience (Beginner, Int., Advanced)\n",
    "sphere_resp <- df$q21 # Sphere of responsibility\n",
    "time_using <- df$q22 # Time using DS in Role\n",
    "freq_use <- df$q23 # Frequency of DS Use\n",
    "ds_role <- df$q24 # Your DS Role\n",
    "admin <- df$q25 # Consider yourself an Admin\n",
    "ds_uni <- df$q26 # Use [product] University\n",
    "q28_grp <- df$q28_grp\n",
    "q11_grp <- df$q11_grp\n",
    "vert <- df$vertical\n",
    "r_content <- df$rank_prefer_content\n",
    "r_help <- df$rank_help_topics\n",
    "r_comm <- df$rank_comm_method\n",
    "\n",
    "# categorical variables\n",
    "df_cat = as.data.frame(cbind(num_locs, dept, time_resp, time_ds_tasks, ds_expr, ds_role, ds_uni, vert))\n",
    "df_c_s <- mutate_at(df_cat, vars(num_locs, dept, time_resp, time_ds_tasks, ds_expr, ds_role, ds_uni, vert), as.factor)\n",
    "\n",
    "\n",
    "# CRM Variables ##################################################################################################\n",
    "\n",
    "#CRM: original untransformed data\n",
    "q28 <- df$q28\n",
    "q29 <- df$q29\n",
    "q30 <- df$q30 \n",
    "q32 <- df$q32 \n",
    "q33 <- df$q38i \n",
    "q34 <- df$q39i \n",
    "q35 <- df$q35\n",
    "q36 <- df$q40i\n",
    "q37 <- df$q37  \n",
    "\n",
    "\n",
    "# transformed CRM variables to remove skew and normalize\n",
    "thry_day_es_n <- df$q28 %>% bestNormalize() %>% .[[1]]\n",
    "env_purch_n <- df$q29 %>% bestNormalize() %>% .[[1]]\n",
    "env_sent_term_n <- df$q30 %>% bestNormalize() %>% .[[1]]\n",
    "env_sent_life_n <- df$q32 %>% bestNormalize() %>% .[[1]]\n",
    "num_empl_n <- df$q33 %>% bestNormalize() %>% .[[1]]\n",
    "adp_indx_n <- df$q34 %>% bestNormalize() %>% .[[1]]\n",
    "num_trx_n <- df$q35 %>% bestNormalize() %>% .[[1]]\n",
    "days_cust_n <- df$q36 %>% bestNormalize() %>% .[[1]]\n",
    "mmr_n <- df$q37 %>% bestNormalize() %>% .[[1]]\n",
    "num_emp_imp <- df$q38i %>% bestNormalize() %>% .[[1]]  \n",
    "adp_indx_imp <- df$q39i %>% bestNormalize() %>% .[[1]] \n",
    "days_cust_imp <- df$q40i %>% bestNormalize() %>% .[[1]]\n",
    "\n",
    "df_crm_i <- cbind(thry_day_es_n, env_purch_n, env_sent_life_n, num_trx_n, mmr_n)\n",
    "\n",
    "\n",
    "#New DataFrame for Analysis ######################################################################################\n",
    "\n",
    "df_all = cbind(df_norm_s, df_c_s)\n",
    "\n",
    "##################################################################################################################\n",
    "\n",
    "# isolate the original clusters (from the previous vendor)\n",
    "oc = factor(df$orig_clust)\n",
    "\n",
    "# PCA to transform all the CRM variables into a single variable\n",
    "crm_pca <- PCA(df_crm_i, scale.unit = FALSE, ncp = 1, graph = FALSE)\n",
    "DV1 <- crm_pca$ind$coord"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Check Correlations and Shape of Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in use.package(\"data.table\"):\n",
      "\"data.table cannot be used without R package bit64 version 0.9.7 or higher.  Please upgrade to take advangage of data.table speedups.\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
      "  |======================================================================| 100%\n"
     ]
    }
   ],
   "source": [
    "df_h2o <- as.h2o(df_all)\n",
    "m_glrm = h2o.glrm(training_frame = df_h2o, loss = \"quadratic\", gamma_x = 0, gamma_y = 1, transform = \"standardize\", k = 2,\n",
    "              seed = 123, max_iterations = 1000, recover_svd=TRUE, init=\"SVD\",\n",
    "                  regularization_x = \"L1\",\n",
    "                  regularization_y = \"L1\")\n",
    "X.m = as.data.frame(h2o.getFrame(m_glrm@model$representation_name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TvrSEGkyAgRaYFkgs/UMfC04wSRIiNoROpvLLSGCj3tOEGkuAjpkPMnE3ymjuHn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\nkQAEQCQAARAJQID/Phl7ejZKnRcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Histogram of First GLRM PCA\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = X.m$Arch1\n",
    "m<-mean(g)\n",
    "std<-sqrt(var(g))\n",
    "hist(g, density=20, breaks=20, prob=TRUE, \n",
    "     xlab=\"x-variable\", ylim=c(0, 7), xlim=c(-1,0), \n",
    "     main=\"Histogram of First GLRM PCA\")\n",
    "curve(dnorm(x, mean=m, sd=std), \n",
    "      col=\"darkblue\", lwd=2, add=TRUE, yaxt=\"n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
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hin+RIhQgImqI7yXb5FevAX+4BxLMdI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\nrkJggg==",
      "text/plain": [
       "Plot with title \"Histogram of Second GLRM PCA\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "g2 = X.m$Arch2\n",
    "m2<-mean(g2)\n",
    "std<-sqrt(var(g2))\n",
    "hist(g2, density=20, breaks=20, prob=TRUE, \n",
    "     xlab=\"x-variable\", ylim=c(0, 7), xlim=c(-1,1), \n",
    "     main=\"Histogram of Second GLRM PCA\")\n",
    "curve(dnorm(x, mean=m2, sd=std), \n",
    "      col=\"darkblue\", lwd=2, add=TRUE, yaxt=\"n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculuate the Hopkins Statistic (> .8 is good)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.756804305489633"
      ],
      "text/latex": [
       "0.756804305489633"
      ],
      "text/markdown": [
       "0.756804305489633"
      ],
      "text/plain": [
       "[1] 0.7568043"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(factoextra)\n",
    "# Compute Hopkins statistic for iris dataset\n",
    "h.stat <- get_clust_tendency(df_norm_s, n=1122)\n",
    "h.stat$hopkins_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.908115753041221"
      ],
      "text/latex": [
       "0.908115753041221"
      ],
      "text/markdown": [
       "0.908115753041221"
      ],
      "text/plain": [
       "[1] 0.9081158"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h.stat <- get_clust_tendency(X.m, n=1122)\n",
    "h.stat$hopkins_stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.769154404968216"
      ],
      "text/latex": [
       "0.769154404968216"
      ],
      "text/markdown": [
       "0.769154404968216"
      ],
      "text/plain": [
       "[1] 0.7691544"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h.stat <- get_clust_tendency(df_crm, n=1122)\n",
    "h.stat$hopkins_stat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variable Selection using Random Forest Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       " randomForest(formula = df_var_sel$Dim.1 ~ ., data = df_var_sel,      ntree = 300, mtry = 4, nodesize = 4, maxnodes = 30, importance = TRUE,      na.action = na.omit) \n",
       "               Type of random forest: regression\n",
       "                     Number of trees: 300\n",
       "No. of variables tried at each split: 4\n",
       "\n",
       "          Mean of squared residuals: 2.047011\n",
       "                    % Var explained: 44.26"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9Jlu/rykup6i+3Cc1vntsPZ/c993l1h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\nrzcqqRcAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"rf_reg\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Combine the DV (PCA of CRM variables) with the dataframe containing all variables\n",
    "df_var_sel = cbind(DV1, df_all)\n",
    "#Run the Random Forest Model and Print the Variable Importance Chart\n",
    "rf_reg = randomForest(df_var_sel$Dim.1 ~ ., data=df_var_sel, ntree=300, mtry=4, nodesize = 4,\n",
    "maxnodes=30, importance=TRUE, na.action=na.omit)\n",
    "rf_reg\n",
    "varImpPlot(rf_reg,type=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation between Numeric Survey Variables and CRM Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7GrQHFnqFkSz0yblawnY2P11tmUNMvpra3p3Xd3/fWAB7eVt4x5XU0S3lnFw1w8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\nAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrmatrix <- cor(df_norm_s, df_crm_i)\n",
    "corrplot(corrmatrix, method = 'number')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation between GLRM PCAs and CRM Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YPAEAkAibJwAAEmHEDgAg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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrmatrix <- cor(X.m, df_crm_i)\n",
    "corrplot(corrmatrix, method = 'number')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vugh7s2P0OQgL7FVzbsvWtHkKDZpACE\n5eYnKt/f/gBBAlqTApCVV39X7ydIO/Ky0zaZuR/JyzHlZadtIkiaedlpmwYBuIfDKbkl7Ujz\nckx52WmbPgNwG5vbXtCONIYUVPsMQODuIu1II0hQ7TMASy/jJkjw2mcAri4bfd/cdqQRJKg2\nCEAcPcfeN7sdYX4Gyc9em9QNgOtb3M4W/BxSfvbaJIKkmZ+9NsnKCVk/h5SfvTbJSJAYUdDt\n6/R3EKxqRxhBgm7fgpTqOkYiSNCtG4BHb64h/Poz/2tnAwQJuvUCEHZzNO90EkHagqfdtsjI\nJUKejihPu20Rs3aaedpti4yckPV0RHnabYsIEiBgeNFqUDzE7hlcVrYjihxBueFtFEn5b9I+\nDnJZO7IIEpT7OmunateOIEG54a3mzRZJ0yVCvgbJ134bNNy1C4ozsY+g94mx89uR5euA8rXf\nBg0CENVzdvHYu2e0I8rXAeVrvw0aBuA3LmL0WN2OJF8HlK/9NsjGlQ0MKChnIkjkCNr1r2zo\nXd2wuB1xBAnaESRAwOCEbHBLJdoR5W2QvO24PZ8BuBQfzfc7/2mrBGkL3nbcnpHp7+JM0kXV\n9Le348nbjtszFoD0Frrmoy7XtCPG2/HkbcftGQ9AdmGyAZhhJABJsUFykZ5r7cgR1PsMwOMa\nOBde5x4iEST4bXg/kosTgXYkESSoN9giFUdH+RZp7gQ4QdqCvz03ZyQAz2LvLg/T2nbE+Duc\n/O25OeMBeKqatfN3OPnbc3PGApAV03Yhs3bH87fn5ny5suE694NkCRK8Nnqt3ezJb4IEzxm4\n+pscQb/PAMzdpfvWjiCCBP0M3GrucZA87ro1BEkzj7tuDUHSzOOuW0OQNPO469YQJEAAQQIE\nDAPwiIvL7OKZZ5O2CxI5ggHjD9EvTszOSxJBgtc+A3B3UVYE6e7mffYlQdqCz303ZvhBY1n1\nYX1qbqPweTD53Hdjxj76kiBp4XPfjfkMQFhvkRIXrmpHjs+Dyee+G/PlGOkRuPuqduQwmGDA\nIABx/VkU0cp2xBAkGDB+HsnFv6vbkUKQYID6KxvIESwgSJp53Xlbxqa/S0Gwqh0xXo8lrztv\ny7cgpVrOI3k9lrzuvC3dADxcl5LzSF6PJa87b0svAGE3R/Meg0KQ4LWvx0gr2xFDkGABs3aA\nAO2zduQIJmiftfM7SH733hTts3Z+DyW/e2+K9lk7v4eS3703Rfusnd9Dye/em6J91o6hBBO0\nP46LIMEE7Y/jIkgwQfnjuMgRbFD+OC7Pg+R59y1R/jguz0eS5923RPnjuDwfSZ533xLlj+Py\nfCR53n1LlD+Oi5EEG5Q/josgwQblVzYQJNhAkAABuoPke458778hw/NIrVXtyPB9IPnef0MI\nkma+99+QLwF4RrFIOyv5PpB8778h3wKQqbholYEEI74GgF07YLpvAbg7DY/jIkgw4vtkw21V\nOzIIEoz4FqRw3jWr2wTJ+xx5XwA7VJ+Q9X4ceV8AOwiSZt4XwI5hAH4jNVd/ez+OvC+AHeNP\nEVJyPxLjCFYM75ANHvk/Ou6QJUiwYvjMhqT8V8UzGwgSrPj67G8NVzYQJFjxfYt0/JUN5IgK\nmKH5GIlhRAXM0DxrxzCiAmaMnEdS8xQhhhEVMEPzlQ0MI5hBkAABBAkQMAjAPVTz8BOCBDM+\nA3BT9BQhgkQFzBh+0NjMO/q+tCOAUUQJ7Ph6idDKdgQwiiiBHZ8BuLpMpB0BjCJKYMfw85Gi\np0g76zGKYEc3AK5vcTtCCBLsIEiAAMUnZAkS7CBImlECM/Tu2jGIqIEhBEkzamCG3l07BhE1\nMIQgAQL6u3aaPvqSIMEQggQIYNcOEECQNKMGZozcIft6paELZ166Kh4kxtCLIhjyGYBHcWwU\nFIdI85JEkLZAEcz4DEDkfssH6P/OfEIkQdoCRTBj7A7ZxF2Pf4g+YwiWjAUpdg+CBMwx3LVL\nHsUHUbBrB8wwMtng3K3YID1WtbMaQYIlw+nvoDhCeoUzn6JPkLZAEcxQe0KWMfSiCIZoDRJD\nqEAVzCBImlEFMwgSIIAgAQIIEiCAIAECCJJmVMGMYQAecXm9Xbq2nXUYQgWqYMYgAFH1uAYX\nzEuScJAYQSXKYMZnAO4uyoog3d1lVTsrMYJKlMGM4UdfZtUdFMfeRsEIgi1j9yMRJGCmzwCE\n9RapuN18TTsrESTY8uUY6TH3080JErw2/AzZ+jmr826QJUiboAxmjJ9HcvHM+/oI0iYogxlK\nr2xgBJUogxk6g8QAqlAHM4bT363ouqKddRhAMOaPILnisVxL21mHIMGYQQAuQfEcrkfgnq/Y\nTd8mESR47TMAV5eU/yYuemUzTsoSJHht7BKh9n9mXCZEkLZAHcwYXrTabJECgnQ46mDGcNeu\nOUa6znr+N0HaAnUwY/zGvuoSITfjejvRIDF+ahTCjG+XCBWbpeJh+svbWYHxA2tUXtlAkGAN\nQQIEfA3AM5ZpZwmCBGsGAbi2Fwita2cNglSjEGYMp78bB35iH+OnRiHMGJ6Q/X1FLk0j91zV\nziqMnxqFMGPsEqFbvjVKDvwwZoZPg0qYMRakR3Ei9sBjJIYPzPkMQJzv2qUufD0JEjDdZwAe\nRYDKy4SOe2QxQYI5gwDcilcubsY9fePtrECQYI7GKxsIUoNKmDE4Rpq5JfrWzhoMnwaVMOPr\nHbIr21mD4dOgEmaMPURfop01GD4NKmHGZwCyOJp3ScOXdlZg9MCeP55rt6qdFQgS7CFIgACF\n098ECfYQJM0ohRnjDz95veJ0bTuLMXpalMKM8cdx5a8H85JEkLZAKcz48hmy+b+HXbTK6GlR\nCjOGd8hWn2p+3P1IDB4YNHaJEEECZhq7RKjIUDLjI13G2lmOIMGgL8dIj2DGc7/H2lmOIMGg\nQQDi90P0V7WzGEF6oxZmfHuI/u/qdpZi8LxRCzP0XdnA4HmjFmYMbqMQamc5Bs8btTBjMP0d\nzXtU8bd2FmPswKLh9Ldz1wW39hEkeG0QgPSWZym8zd3FI0jw2lgA0mvg5u7iESR47UsA7ofd\nIUuQOiiGGaNbpHLvbt6ZJIK0BYphxvgxUnCdeV8fQdoExTBjbNbuwqydEhTDjOF5pLkXB423\nsxhjBxZ9u7IhuQar2lmKHMGk0QBUx0nr21mAIMGkYQCy3+I4ae6VQgQJXvsMwG/5FCE3d9KO\nIG2CapjRC8Dj4oqp72TBZ7sQpC1QDTO6AQiKFBVT3wRJCaphRjcA7QfHDoJ0DfKIda9jvYcf\nLxCkLVANMyZtkarjps5jha7lC0EnSQQJXhs7Rnp+BOnpguSVBK694CFxl+zjYaxCQSJHsGnK\nrN3VFXPhv+7WvBBXP9XNG0GC176dR4o755HiMleJiz9/liABlSlXNrjhBqiQdZ99R5C2QDnM\n+BaA7rV2X4J0d4/69dkflPkVI6eHcpgxJQDjQUqD7q4eQdoC5TBjcZCyoPdQY4K0BcphxpQA\nBGNBivqfVkGQ4LUpAahm7dLurF0aRv3rWgkSvDYlALdyVuHRXEBU/v/nh1XIBIkcwagpARhc\n2ZAOP/SFIMFrkwIQvj8xqTxQutSfoSR+QpYg9VEPMyYFICuv/q7eX32+LEHaBfUwQ9fnIzFw\n+qiHGQRJM+phBkECBBAkQICqIJEjWEWQAAEESTMKYgZB0oyCmEGQNKMgZhAkzSiIGQQJEECQ\nAAGagkSOYBZBAgQQJM2oiBkESTMqYgZB0oyKmEGQNKMiZhAkQABBAgQQJECAoiCRI9hFkDSj\nJGYQJM0oiRkESTNKYgZB0oySmEGQAAEECRBAkAABeoJEjmAYQdKMmphBkDSjJmYQJM2oiRkE\nSTNqYgZBAgQQJEAAQQIEqAkSOYJlBEkzimIGQdKMophBkDSjKGYQJM0oihkECRBAkAABBAkQ\nQJAAAVqCRI7GUBUzCJJmVMUMgqQZVTGDIGlGVcwgSIAAggQIIEiAAIIECFASJHI0irKYQZA0\noyxmECTNKIsZBEkzymIGQQIEECRAAEECBBAkQABB0oyymKEjSAyYcdTFDIKkGXUxgyBpRl3M\nIEiAAIIECCBIgACCBAggSJpRFzNUBInx8gWFMYMgaUZhzCBImlEYMwgSIIAgAQIIEiCAIAEC\nCJJmFMYMDUFiuHxDZcwgSJpRGTMIkmZUxgyCBAggSIAAggQIIEiAAIKkGZUxgyBpRmXMUBAk\nRstXlMYMgqQZpTGDIAECCBIggCABAggSIIAgaUZpzCBImlEaM44PEoPlO2pjBkHSjNqYQZAA\nAQQJEECQAAEECRBAkDSjNmYQJM2ojRmHB4mx8geKYwZB0ozimEGQAAEECRBAkAABBAkQQJA0\nozhmECTNKI4ZBEkzimPG0UFiqPyF6phBkAABBAkQQJAAAQQJEECQNKM6ZhAkzaiOGQRJM6pj\nxsFBYqT8ifKYQZAAAQQJEECQAAEECRBAkDSjPGYQJM0ojxkESTPKYwZB0ozymHFskBgoOAmC\nBAggSIAAggQIIEiaUR8zCJJm1McMgqQZ9TGDIGlGfcw4NEiME5wFQQIEECRAAEECBBAkzSiQ\nGQRJMwpkBkHSjAKZQZA0o0BmHBkkhglOgyABAggSIIAgAQIIkmZUyAyCpBkVMoMgaUaFzCBI\nmlEhMwgSIODAIJEjnAdBAgQQJEAAQdKMEplBkDSjRGYQJM0okRkESTNKZAZBAgQcFyRyhBMh\nSIAAggQIIEiaUSMzCJJm1MgMgqQZNTKDIGlGjcwgSICAw4JEjnAmBAkQQJAAAQRJM4pkBkHS\njCKZQZA0o0hmECTNKJIZBAkQQJAAAUcFiRzhVAgSIIAgaUaVzCBImlElMwiSZlTJDIKkGVUy\ngyABAggSIOCgIJEjnAtBAgQQJM0okxkESTPKZAZB0owymUGQNKNMZhAkQABBAgQQJEDAMUEi\nRzgZgqQZdTKDIGlGncwgSJpRJzMIkmbUyQyCBAggSIAAggQIOCRI5AhnQ5A0o1BmECTNKJQZ\nBEkzCmUGQdKMQplBkAAB0wJwDVxwzf56gSDBa5MCELlC+McLBAl+mxKApwuSVxK459cX5gWJ\nHOF0pgTg6h75f3/d7esLs4L080OSJqJQZkwJQOzS/L+Ji7++MCdIPz8kaSrqZMaUADjX/Wfs\nhRlB+vkhSZNRJjMEglROPBCkLVAmM9giAQJ2DxLHSDijKQEIPnMzeIFZO3hu+qxd+jlrly6b\ntQNOaEoAbuVpo4e7fn2BIG2DTbcZR1zZgKkIkhmTAhCWE9xR+X738cKcdjATQTJjUgCy8mLv\n6v3u44U57WAmgmTGQZ9GAZwLQQIEECRAAEECBBAkzZhsMIMgaUaQzCBImhEkMwiSZgTJDIIE\nCCBIgACCBAggSIAAgqQZkw1mECTNCJIZBEkzgmQGQdKMIJlBkAABBAkQQJAAAQQJEECQNGOy\nwQyCpBlBMoMgaUaQzCBImhEkM8SCBPhHPkizQqexqZOv1Mm7d/xKESTxllSu1Mm7d/xKESTx\nllSu1Mm7d/xKESTxllSu1Mm7d/xKMdsGCCBIgACCBAggSIAAggQIIEiAgAOCdJda5j10wTUT\naCi7OHdJBBqqPEU6OLgIZbmk6F8q0NDIpTFLVR9DLPHbe73ypqLH+mbagblk1fYPUiIzOPLu\nlr/SQOB3EZQtSSUpCyQ6mMgF6SFWqCZHweqW0qrmgUS8o7Kp29pm2oFZtRfO++ndg5QEQkFK\n3CUr/opcVrd0Ldq4ulhgpQqxSAcTsfV5BUHyymJ3/f87p3m45+o2LuXqXAV+e/kQiLJip2Ll\nH8J2YD5dXq/8q3md3DtIea+FghRXzQi0FrhMpqHSr8xm5L7+T2zttxyzmcBmpJIFAhF3Yr+9\nfANSDPl05R+K98C8umI38Xdm/fcOUt5dqRFbNyh2I4jMQEuF/lLc3V2glcLqv9UfYieyN13+\nI1H0JpPRulbagRm7Yn9z7h7B3kFKBId+IVtZv9ZVaOBGLhXpYOwel/yQV6Cl0L1uQbkfLCIR\n2Ue81bt2AptdmY1b8tnQzPYOmLUTDdLdCUzXlPtjMocQN/cr08G4OqwX+DPhXCwzQVAR2SDl\nv7hitiGQ+OMVlluQ5/qq+xykVGJ/PXePA5FjknKHQKSDLk/kK5PYTrri4Dk/GJc55kok5gde\nxV8ckam2sqU4eyUCO9QeBykLhHbsXsWhhMCfx7CYZJbs4NxZ2BHVxH4q0FLhKrMLcC/2ADKR\nmhjBfLkAAAQkSURBVFdnLwTmSj0OUiQzOEoS01qXcpRJbnIF2hKcIHu1swRrheUOosTfiTKP\nwU2gf3ULgXdBSsNI4nxeQ2TMyp36b1pc3YTceYKX3Okt2XS/ihVbncnerF2qfNbuJVe8h9SE\nXXUeSWLfRzBIzUqtH7e3cjOZylRLala++rMvcnKrqtR9faXq31pVr8fM2Se7QRIaGa/6/HoW\ni524EengtTyIkDgiyf9ClGf+fwXWKv9zLXNSKu9eVndyfVP5r+8Zru+fqSsbXmJBusjtRQVS\nM80VkQ5m1UrJnLOR614oM/ndXNAmsVJ1pdZvupvfW7hk1ewGSfJw5Bq4UGp7JNXBTG6lHpHM\nqd2X5EFNeYm1SEtp/jc1FphLbPqWLVk17kcCBBAkQABBAgQQJEAAQQIEECRAAEECBBAkQABB\nAgQQpJ245qq5v68NmHnlQPFEvsE5+K9tTDz7L/tQDU9Qs52093qLBikeu8v0WxvhxLYJ0gLU\nbCftiBcNknMjd2R9a2Nq2wRpAWq2E+eqh3RIB2lGGwRpQ9RsJ87VN5cWw7QaqvX/3YobpYsH\nMF+r167tpcfFw83v1TuzsHOfQP56eV34x9XvxSOw08ESimu/y0djt28eNNu8o13VsjWxJ1R6\ngSDtJB+dl/Jesc8glXcLPaL65qP62VnlzTBxe19M+Wo7qdDeytMPUtQ84bu/hHv1rnsbpEGz\n7Tveq1rkSO65Mj4gSDvJR2f1qI/PIEVZMZLL/wb1s7OSoLjd81E+0zpyj/pdjd/3W7p7Yb/F\ney5VGLtLCIp7Wn+LRVevDZt9v6NdVXI0F0HaSbVxuA+DVG2l3rtk1QMD4uZJjFn1pLzOfc9x\n/Zbo1QtSXLwnq8LYX8KjswpjzbqP+9nL3UtyNA9B2kk5iosbtQfHSK/h1/X/trcA9w7/uw/g\n6Xzj/b/9dvODrzhJukv5bPb9jubnIyfwgRN+IUg7KQft0112D1Lx4O/qg4i+Ben9jubnXSD0\nOEl/EKSdNPtVyYwgffxw/4vJQcp3A6/h+xhp9EfqdzQvPxMn89AhfxCknVSDNnVhO8yf40Eq\n9qnqY6RH/4dr8fswqvuNaHiM9BwL17dm+++9iT103xMEaSf1OL2V+1ShuxcTZ6NBqqbkHvXs\nXPXgw96I/zJrV35w3bWZtXsvoXzgWz1rl77Gmn2/o7OqIaeRZiFIO2mGfNCe24nHg3RpH9JW\nnS96H900Oo+E636jdx7pvYTf6ojoWT6vLRhr9v2OzqrmO3dSn6jkBYK0k2bIP5oJgM9ph3b3\n61pe6VC4h/WnkfeDVHy2UP3Eu943itm39t3tEqrrFoqUPMNqf23QbPuO7qre5D7E1gcECRBA\nkAABBAkQQJAAAQQJEECQAAEECRBAkAABBAkQQJAAAQQJEECQAAEECRDwD8aPaX0lT7ZfAAAA\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fviz_nbclust(X.m, kmeans, method='silhouette')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cZ9dAQn+B5SQkhwgdchDd8/FrDD55DG3okZsMLnxQZCgjMICRDgc0jcR4IzvA7p\nSUdwhM+LDbJDARsQEiCAkAABhAQI8HuxgZDgCEICBBASIICQAAEsNgACCAkQQEiAAEICBLDY\nAAggJEAAIQECCAkQwGIDIICQAAGEBAggJEAAiw2AAEICBBASIICQAAEsNgACCAkQQEiAAEIC\nBLDYAAggJEAAIQECCAkQwGIDIICQAAGEBAjwNKSkb/uAwCaeLzYAbiAkQAAhAQIICRDg6WID\n4BZCAgQQEiCAkAABLDYAAggJEEBIgABCAgSw2AAIICRAACEBAggJEMBiAyCAkAABhAQIICRA\nAIsNgABCAgQQEiCAkAABLDYAAggJEEBIgABCAgSw2AAIICRAACEBAggJECAWEhAf+ZAWRefi\nUIFvVOAXz/5GEZL4SE5uVOAXz/5GEZL4SE5uVOAXz/5GEZL4SE5uVOAXz/5GcUQCIICQAAGE\nBAggJEAAIQECCAkQYCGkq9R5Xg8qzQqBgYqzUueHwEC1u8gFHByEst5DX75cYKCRQ2PWKrJU\naO89n+VQx9v2YV4Tc82m7R/SQ2ZylBe32qWpwL5Iq5GkSipSiQv4kAvpJvaLajtKN4+U17/z\nVCLvYzXUZeswr4lZj3dY9tO7h/RIhUJ6qHOh/4qcN4+U6TEydRLYKO0kcgEfYtvzTNPHszip\nTGq8m7pvHuNcbU4msPfKKXAs9I2KjX8IXxPzrsrfV/m/ZRdy75DKSy0U0qkeRmC0VBUyA1X+\nZK5Grtv/xDb+qjlbCFyN1IpUIHEltvfKKxA95fONfyjeEzNT+mbi38Lf/94hlRdXasY2A4o9\nEURmouVCfymu6iowirb5b/WHkxK5NV19kPilt00et43ympgnpW9vLr1FsHdID8GprxUbf38v\nmdDEPapc5AKe1O1c3uUVGOmgnpe0uh0s4iFyG/HS3LQTuNqVuXJ7fA60cDwLq3aiIV2VwHJN\ndXtM5i7ERf3JXMBTfbde4M+EUieZBYKayBVSueP0akMq8cfrUF2D3Lf/1mMOKZe4vV66nlKR\n+yTVDQKRC6jKIp+FxPWk0neeyzvjMve5HhLrA0/9F0dkqa0a6VQ8HwI3qCMOqUiFbtg99V0J\ngT+PB73ILHkBl67CjqgX9nOBkbRM5ibAVd8CKER+5/WjFwJrpRGHdJSZHBWJZa1zNcskr3IF\nxhJcIHu+Vgm2OlQ3ECX+TlQ9pheBy9eMkEYXUn44Sjye1xKZs3IP/bcjbh5C7nGCp9zDW7J1\nP/WGbW6yt2qXO75q95T75d2kFuzqx5EkbvsIhtRu1PZ5e6muJnOZ35bUqnz9Z1/kwa36N3Xd\n/kmfw2YAAAOvSURBVJtq9lr9+7otXH3yNyShmfFsHl8vTmIP3IhcwKy6EyFxj6T8C1E98v8n\nsFXln2uZB6XKi1c0F3L7UOXuux+2Xz6vjmx4ioV0lrsVlUqtNNdELmBRb5TMYzZyF+8gs/jd\nHtAmsVHNb2r7VXe73w5rNs3fkCTvjmSpOkhdH0ldwEJuo25HmYd2n5J3aqpDrEVGysu/qSeB\ntcT2shVrNo3nIwECCAkQQEiAAEICBBASIICQAAGEBAggJEAAIQECCGknqj1qbvrYgIVHDuhX\n5Bs8Bv91jJmP/su+qEYk+J3t5PVcb9GQTmPPMv02xmHm2IS0Ar+znbxmvGhISo08I+vbGHPH\nJqQV+J3tRKn6RTqkQ1owBiEZxO9sJ0o1Ty7V07Seqs1nF/1Eaf0CzFn9tex16LF+cfNrfcri\n0HmeQPn16rjwj6Pf9Utg54Nz0Md+Vy+N/TrxYNj2FK9NrUYTe4XKKBDSTsrZea6eK/YZUvVs\noduxefJR89pZ1ZNhTq/nxVRffS0qvJ7K0w/p2L7Cd/8crvWprq+QBsO+TvHeVN2R3OvKxICQ\ndlLOzvqlPj5DOhZ6Jlf/ps1rZz1S/XTPW/Wa1kd1a07V+nufpHsr7E+f5lzH2D2HVD+n9U+f\ndf214bDvU7w2lY6WIqSd1FcO12FI9bXU+yZZ/YIBp/aVGIv6lfI6z3s+NSc5PnshnfRpijrG\n/jncOpswNqz6eD57dfOSjpYhpJ1Us1g/UXtwH+k5/H/z6espwL27/90X4Ol84/1pf9zyztfp\n8eiey+ew71O0P39UAm84ERdC2kk1ae/qvHtI+oW/6zci+hbS+xTtz6tU6OUk40FIO2lvVz0W\nhPTxw/3/zA6pvBmYHd73kUZ/pDlF++X7Q8m86FA8CGkn9aTN1eE1ze/jIenbVM19pFv/hxun\n992o7jeOw/tI97G4vg3bP+1F7EX3I0FIO2nm6aW6TXVQV71wNhpSvSR3a1bn6hc+7M34L6t2\n1RvXZe2q3fscqhd8a1bt8ufYsO9TdDb1wMNIixDSTtopn74e2zmNh3R+vUhb/XjR+95Nq/OS\ncN1v9B5Hep/DX32P6F69Xls6Nuz7FJ1NLW/cSb2jUhQIaSftlL+1CwCfyw6vm19ZdaSDdj00\n70beD0m/t1Dzine9b+jVt9epX+dQH7egK7kf6ttrg2Ffp+hu6kXuTWxjQEiAAEICBBASIICQ\nAAGEBAggJEAAIQECCAkQQEiAAEICBBASIICQAAGEBAj4B7L1b17UF3RyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gap_stat <- clusGap(X.m, FUN = hcut, nstart = 25, K.max = 10, B = 50)\n",
    "fviz_gap_stat(gap_stat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code to Run All Dimension Reduction and Clustering Functions and Return Plots\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in use.package(\"data.table\"):\n",
      "\"data.table cannot be used without R package bit64 version 0.9.7 or higher.  Please upgrade to take advangage of data.table speedups.\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
      "  |======================================================================| 100%\n",
      "  cluster size ave.sil.width\n",
      "1       1  344          0.52\n",
      "2       2  143          0.50\n",
      "3       3  636          0.64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in use.package(\"data.table\"):\n",
      "\"data.table cannot be used without R package bit64 version 0.9.7 or higher.  Please upgrade to take advangage of data.table speedups.\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  |======================================================================| 100%\n",
      "  |======================================================================| 100%\n"
     ]
    },
    {
     "data": {
      "image/png": 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0QSQRODSLIArQ1FpJAgEtAYkVTQxCCS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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Training Confusion Matrix\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A H2OTable: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>Error</th><th scope=col>Rate</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>292</td><td>  0</td><td>128</td><td>0.3047619</td><td>128 / 420  </td></tr>\n",
       "\t<tr><th scope=row>2</th><td>  6</td><td>339</td><td> 75</td><td>0.1928571</td><td>81 / 420   </td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 51</td><td> 11</td><td>363</td><td>0.1458824</td><td>62 / 425   </td></tr>\n",
       "\t<tr><th scope=row>Totals</th><td>349</td><td>350</td><td>566</td><td>0.2142292</td><td>271 / 1,265</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A H2OTable: 4 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & 1 & 2 & 3 & Error & Rate\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & 292 &   0 & 128 & 0.3047619 & 128 / 420  \\\\\n",
       "\t2 &   6 & 339 &  75 & 0.1928571 & 81 / 420   \\\\\n",
       "\t3 &  51 &  11 & 363 & 0.1458824 & 62 / 425   \\\\\n",
       "\tTotals & 349 & 350 & 566 & 0.2142292 & 271 / 1,265\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A H2OTable: 4 × 5\n",
       "\n",
       "| <!--/--> | 1 &lt;dbl&gt; | 2 &lt;dbl&gt; | 3 &lt;dbl&gt; | Error &lt;dbl&gt; | Rate &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 | 292 |   0 | 128 | 0.3047619 | 128 / 420   |\n",
       "| 2 |   6 | 339 |  75 | 0.1928571 | 81 / 420    |\n",
       "| 3 |  51 |  11 | 363 | 0.1458824 | 62 / 425    |\n",
       "| Totals | 349 | 350 | 566 | 0.2142292 | 271 / 1,265 |\n",
       "\n"
      ],
      "text/plain": [
       "       1   2   3   Error     Rate       \n",
       "1      292   0 128 0.3047619 128 / 420  \n",
       "2        6 339  75 0.1928571 81 / 420   \n",
       "3       51  11 363 0.1458824 62 / 425   \n",
       "Totals 349 350 566 0.2142292 271 / 1,265"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Validation Confusion Matrix\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A H2OTable: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>Error</th><th scope=col>Rate</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>33</td><td> 2</td><td> 84</td><td>0.7226891</td><td>86 / 119 </td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 1</td><td> 7</td><td> 37</td><td>0.8444444</td><td>38 / 45  </td></tr>\n",
       "\t<tr><th scope=row>3</th><td>24</td><td> 4</td><td>183</td><td>0.1327014</td><td>28 / 211 </td></tr>\n",
       "\t<tr><th scope=row>Totals</th><td>58</td><td>13</td><td>304</td><td>0.4053333</td><td>152 / 375</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A H2OTable: 4 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & 1 & 2 & 3 & Error & Rate\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & 33 &  2 &  84 & 0.7226891 & 86 / 119 \\\\\n",
       "\t2 &  1 &  7 &  37 & 0.8444444 & 38 / 45  \\\\\n",
       "\t3 & 24 &  4 & 183 & 0.1327014 & 28 / 211 \\\\\n",
       "\tTotals & 58 & 13 & 304 & 0.4053333 & 152 / 375\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A H2OTable: 4 × 5\n",
       "\n",
       "| <!--/--> | 1 &lt;dbl&gt; | 2 &lt;dbl&gt; | 3 &lt;dbl&gt; | Error &lt;dbl&gt; | Rate &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 | 33 |  2 |  84 | 0.7226891 | 86 / 119  |\n",
       "| 2 |  1 |  7 |  37 | 0.8444444 | 38 / 45   |\n",
       "| 3 | 24 |  4 | 183 | 0.1327014 | 28 / 211  |\n",
       "| Totals | 58 | 13 | 304 | 0.4053333 | 152 / 375 |\n",
       "\n"
      ],
      "text/plain": [
       "       1  2  3   Error     Rate     \n",
       "1      33  2  84 0.7226891 86 / 119 \n",
       "2       1  7  37 0.8444444 38 / 45  \n",
       "3      24  4 183 0.1327014 28 / 211 \n",
       "Totals 58 13 304 0.4053333 152 / 375"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Variable Importance\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A H2OTable: 5 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>variable</th><th scope=col>relative_importance</th><th scope=col>scaled_importance</th><th scope=col>percentage</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>mmr_n          </td><td>11593.961</td><td>1.0000000</td><td>0.3411820</td></tr>\n",
       "\t<tr><td>env_purch_n    </td><td> 7338.535</td><td>0.6329619</td><td>0.2159552</td></tr>\n",
       "\t<tr><td>num_trx_n      </td><td> 6458.486</td><td>0.5570560</td><td>0.1900575</td></tr>\n",
       "\t<tr><td>thry_day_es_n  </td><td> 4780.500</td><td>0.4123267</td><td>0.1406785</td></tr>\n",
       "\t<tr><td>env_sent_life_n</td><td> 3810.265</td><td>0.3286422</td><td>0.1121268</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A H2OTable: 5 × 4\n",
       "\\begin{tabular}{llll}\n",
       " variable & relative\\_importance & scaled\\_importance & percentage\\\\\n",
       " <chr> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t mmr\\_n           & 11593.961 & 1.0000000 & 0.3411820\\\\\n",
       "\t env\\_purch\\_n     &  7338.535 & 0.6329619 & 0.2159552\\\\\n",
       "\t num\\_trx\\_n       &  6458.486 & 0.5570560 & 0.1900575\\\\\n",
       "\t thry\\_day\\_es\\_n   &  4780.500 & 0.4123267 & 0.1406785\\\\\n",
       "\t env\\_sent\\_life\\_n &  3810.265 & 0.3286422 & 0.1121268\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A H2OTable: 5 × 4\n",
       "\n",
       "| variable &lt;chr&gt; | relative_importance &lt;dbl&gt; | scaled_importance &lt;dbl&gt; | percentage &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| mmr_n           | 11593.961 | 1.0000000 | 0.3411820 |\n",
       "| env_purch_n     |  7338.535 | 0.6329619 | 0.2159552 |\n",
       "| num_trx_n       |  6458.486 | 0.5570560 | 0.1900575 |\n",
       "| thry_day_es_n   |  4780.500 | 0.4123267 | 0.1406785 |\n",
       "| env_sent_life_n |  3810.265 | 0.3286422 | 0.1121268 |\n",
       "\n"
      ],
      "text/plain": [
       "  variable        relative_importance scaled_importance percentage\n",
       "1 mmr_n           11593.961           1.0000000         0.3411820 \n",
       "2 env_purch_n      7338.535           0.6329619         0.2159552 \n",
       "3 num_trx_n        6458.486           0.5570560         0.1900575 \n",
       "4 thry_day_es_n    4780.500           0.4123267         0.1406785 \n",
       "5 env_sent_life_n  3810.265           0.3286422         0.1121268 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>num_locs</th><th scope=col>dept</th><th scope=col>time_resp</th><th scope=col>time_ds_tasks</th><th scope=col>ds_expr</th><th scope=col>ds_role</th><th scope=col>ds_uni</th><th scope=col>vert</th><th scope=col>clusters</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>6+ </td><td>IT             </td><td>General</td><td>Creating_Templates</td><td>Intermediate</td><td>Administrator (admin)</td><td>No</td><td>Financial Services</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2-5</td><td>Human resources</td><td>General</td><td>Generalist        </td><td>Intermediate</td><td>Administrator (admin)</td><td>No</td><td>Manufacturing     </td><td>3</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2-5</td><td>Legal          </td><td>Legal  </td><td>Sending_Envelopes </td><td>Advanced    </td><td>Administrator (admin)</td><td>No</td><td>Telecommunications</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>6+ </td><td>IT             </td><td>IT     </td><td>Generalist        </td><td>Intermediate</td><td>Administrator (admin)</td><td>No</td><td>Technology        </td><td>2</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2-5</td><td>Other          </td><td>General</td><td>Sending_Envelopes </td><td>Intermediate</td><td>Administrator (admin)</td><td>No</td><td>Government        </td><td>3</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>6+ </td><td>IT             </td><td>IT     </td><td>Creating_Templates</td><td>Intermediate</td><td>Administrator (admin)</td><td>No</td><td>Financial Services</td><td>2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       "  & num\\_locs & dept & time\\_resp & time\\_ds\\_tasks & ds\\_expr & ds\\_role & ds\\_uni & vert & clusters\\\\\n",
       "  & <fct> & <fct> & <fct> & <fct> & <fct> & <fct> & <fct> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 6+  & IT              & General & Creating\\_Templates & Intermediate & Administrator (admin) & No & Financial Services & 2\\\\\n",
       "\t2 & 2-5 & Human resources & General & Generalist         & Intermediate & Administrator (admin) & No & Manufacturing      & 3\\\\\n",
       "\t3 & 2-5 & Legal           & Legal   & Sending\\_Envelopes  & Advanced     & Administrator (admin) & No & Telecommunications & 3\\\\\n",
       "\t4 & 6+  & IT              & IT      & Generalist         & Intermediate & Administrator (admin) & No & Technology         & 2\\\\\n",
       "\t5 & 2-5 & Other           & General & Sending\\_Envelopes  & Intermediate & Administrator (admin) & No & Government         & 3\\\\\n",
       "\t6 & 6+  & IT              & IT      & Creating\\_Templates & Intermediate & Administrator (admin) & No & Financial Services & 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 9\n",
       "\n",
       "| <!--/--> | num_locs &lt;fct&gt; | dept &lt;fct&gt; | time_resp &lt;fct&gt; | time_ds_tasks &lt;fct&gt; | ds_expr &lt;fct&gt; | ds_role &lt;fct&gt; | ds_uni &lt;fct&gt; | vert &lt;fct&gt; | clusters &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 6+  | IT              | General | Creating_Templates | Intermediate | Administrator (admin) | No | Financial Services | 2 |\n",
       "| 2 | 2-5 | Human resources | General | Generalist         | Intermediate | Administrator (admin) | No | Manufacturing      | 3 |\n",
       "| 3 | 2-5 | Legal           | Legal   | Sending_Envelopes  | Advanced     | Administrator (admin) | No | Telecommunications | 3 |\n",
       "| 4 | 6+  | IT              | IT      | Generalist         | Intermediate | Administrator (admin) | No | Technology         | 2 |\n",
       "| 5 | 2-5 | Other           | General | Sending_Envelopes  | Intermediate | Administrator (admin) | No | Government         | 3 |\n",
       "| 6 | 6+  | IT              | IT      | Creating_Templates | Intermediate | Administrator (admin) | No | Financial Services | 2 |\n",
       "\n"
      ],
      "text/plain": [
       "  num_locs dept            time_resp time_ds_tasks      ds_expr     \n",
       "1 6+       IT              General   Creating_Templates Intermediate\n",
       "2 2-5      Human resources General   Generalist         Intermediate\n",
       "3 2-5      Legal           Legal     Sending_Envelopes  Advanced    \n",
       "4 6+       IT              IT        Generalist         Intermediate\n",
       "5 2-5      Other           General   Sending_Envelopes  Intermediate\n",
       "6 6+       IT              IT        Creating_Templates Intermediate\n",
       "  ds_role               ds_uni vert               clusters\n",
       "1 Administrator (admin) No     Financial Services 2       \n",
       "2 Administrator (admin) No     Manufacturing      3       \n",
       "3 Administrator (admin) No     Telecommunications 3       \n",
       "4 Administrator (admin) No     Technology         2       \n",
       "5 Administrator (admin) No     Government         3       \n",
       "6 Administrator (admin) No     Financial Services 2       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 3 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>clusters</th><th scope=col>num_locs</th><th scope=col>dept</th><th scope=col>time_resp</th><th scope=col>time_ds_tasks</th><th scope=col>ds_expr</th><th scope=col>ds_role</th><th scope=col>ds_uni</th><th scope=col>vert</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>1  </td><td>Administration</td><td>General</td><td>Sending_Envelopes</td><td>Intermediate</td><td>Basic user           </td><td>No </td><td>Other             </td></tr>\n",
       "\t<tr><td>2</td><td>6+ </td><td>IT            </td><td>IT     </td><td>Generalist       </td><td>Intermediate</td><td>Administrator (admin)</td><td>Yes</td><td>Financial Services</td></tr>\n",
       "\t<tr><td>3</td><td>2-5</td><td>IT            </td><td>General</td><td>Generalist       </td><td>Intermediate</td><td>Administrator (admin)</td><td>No </td><td>Technology        </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 3 × 9\n",
       "\\begin{tabular}{lllllllll}\n",
       " clusters & num\\_locs & dept & time\\_resp & time\\_ds\\_tasks & ds\\_expr & ds\\_role & ds\\_uni & vert\\\\\n",
       " <fct> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t 1 & 1   & Administration & General & Sending\\_Envelopes & Intermediate & Basic user            & No  & Other             \\\\\n",
       "\t 2 & 6+  & IT             & IT      & Generalist        & Intermediate & Administrator (admin) & Yes & Financial Services\\\\\n",
       "\t 3 & 2-5 & IT             & General & Generalist        & Intermediate & Administrator (admin) & No  & Technology        \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 3 × 9\n",
       "\n",
       "| clusters &lt;fct&gt; | num_locs &lt;chr&gt; | dept &lt;chr&gt; | time_resp &lt;chr&gt; | time_ds_tasks &lt;chr&gt; | ds_expr &lt;chr&gt; | ds_role &lt;chr&gt; | ds_uni &lt;chr&gt; | vert &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 1   | Administration | General | Sending_Envelopes | Intermediate | Basic user            | No  | Other              |\n",
       "| 2 | 6+  | IT             | IT      | Generalist        | Intermediate | Administrator (admin) | Yes | Financial Services |\n",
       "| 3 | 2-5 | IT             | General | Generalist        | Intermediate | Administrator (admin) | No  | Technology         |\n",
       "\n"
      ],
      "text/plain": [
       "  clusters num_locs dept           time_resp time_ds_tasks     ds_expr     \n",
       "1 1        1        Administration General   Sending_Envelopes Intermediate\n",
       "2 2        6+       IT             IT        Generalist        Intermediate\n",
       "3 3        2-5      IT             General   Generalist        Intermediate\n",
       "  ds_role               ds_uni vert              \n",
       "1 Basic user            No     Other             \n",
       "2 Administrator (admin) Yes    Financial Services\n",
       "3 Administrator (admin) No     Technology        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 3 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>clusters</th><th scope=col>V1</th><th scope=col>V2</th><th scope=col>V3</th><th scope=col>V4</th><th scope=col>V5</th><th scope=col>V6</th><th scope=col>V7</th><th scope=col>V8</th><th scope=col>V9</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>2.453488</td><td>2.136628</td><td>1.305233</td><td>1.715116</td><td> 12.25872</td><td> 23.86337</td><td> 20.14244</td><td>4.383721</td><td>3.674419</td></tr>\n",
       "\t<tr><td>2</td><td>5.328671</td><td>6.055944</td><td>2.349650</td><td>4.664336</td><td>203.83916</td><td>890.31469</td><td>448.02797</td><td>4.440559</td><td>4.146853</td></tr>\n",
       "\t<tr><td>3</td><td>3.455975</td><td>3.690252</td><td>1.641509</td><td>3.084906</td><td> 22.16667</td><td>107.57704</td><td> 13.16667</td><td>4.386792</td><td>3.949686</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 3 × 10\n",
       "\\begin{tabular}{llllllllll}\n",
       " clusters & V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & V9\\\\\n",
       " <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1 & 2.453488 & 2.136628 & 1.305233 & 1.715116 &  12.25872 &  23.86337 &  20.14244 & 4.383721 & 3.674419\\\\\n",
       "\t 2 & 5.328671 & 6.055944 & 2.349650 & 4.664336 & 203.83916 & 890.31469 & 448.02797 & 4.440559 & 4.146853\\\\\n",
       "\t 3 & 3.455975 & 3.690252 & 1.641509 & 3.084906 &  22.16667 & 107.57704 &  13.16667 & 4.386792 & 3.949686\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 3 × 10\n",
       "\n",
       "| clusters &lt;fct&gt; | V1 &lt;dbl&gt; | V2 &lt;dbl&gt; | V3 &lt;dbl&gt; | V4 &lt;dbl&gt; | V5 &lt;dbl&gt; | V6 &lt;dbl&gt; | V7 &lt;dbl&gt; | V8 &lt;dbl&gt; | V9 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 2.453488 | 2.136628 | 1.305233 | 1.715116 |  12.25872 |  23.86337 |  20.14244 | 4.383721 | 3.674419 |\n",
       "| 2 | 5.328671 | 6.055944 | 2.349650 | 4.664336 | 203.83916 | 890.31469 | 448.02797 | 4.440559 | 4.146853 |\n",
       "| 3 | 3.455975 | 3.690252 | 1.641509 | 3.084906 |  22.16667 | 107.57704 |  13.16667 | 4.386792 | 3.949686 |\n",
       "\n"
      ],
      "text/plain": [
       "  clusters V1       V2       V3       V4       V5        V6        V7       \n",
       "1 1        2.453488 2.136628 1.305233 1.715116  12.25872  23.86337  20.14244\n",
       "2 2        5.328671 6.055944 2.349650 4.664336 203.83916 890.31469 448.02797\n",
       "3 3        3.455975 3.690252 1.641509 3.084906  22.16667 107.57704  13.16667\n",
       "  V8       V9      \n",
       "1 4.383721 3.674419\n",
       "2 4.440559 4.146853\n",
       "3 4.386792 3.949686"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cyDafs/HJrvjpAIKVvBO5rGPJiX/oQNu13XH3DYB1yGdSx/Cl0QQspc6IYmcn2w\n4bX77M/H9btv3gMuw7qVP4UuCCFlLnRDE5mH9NueDnw3zS7kMqxb+VvgghBS5gL3M5Wrx0Lf\nu/FHsUEHvwmJkFIK3M9Uan+KECHVRjCwMRCSg5AyJxjYGAjJoQnJLcl6+ioiGNgYCMkhCskp\nyXr6KiIY2BgIyUFImRMMbAyE5CCk3AkmNgJCchBS9gQjq0dIDkLKnmBk9eoPKTAlQsqeYGT1\nniGkoJIIKXuCkdUjJAchZU8wsnqE5CCk7AlGVo+QHISUP8HMyj1FSCElEVL+BDMrR0gOQsqf\nYGblCMmhCum6JOvRq4tgZuUIyUFIBRAMrRohOQipBIKpFSMkByGVQDC1YoTkIKQSCKZWjJAc\nhFQCwdSKEZKDkEogmFoxQnIQUgkEUytGSA5CKoFgasWeI6SAkmQhXZVkPXi1EUytGCE5CKkE\ngqkVIyQHIRVBMLZahOQgpCIIxlaLkBy6kOYlWc9ddQRjq0VIDkIqgmBstZ4kJP+SCKkMgrmV\nIiQHIZVBMLdShOQgpDII5laKkByEVAjB4CoRkoOQCiEYXCVCchBSIQSDq0RIDkIqhGBwlQjJ\nQUilEEyuECE5CKkUgskVIiQHIRVDMLo6hOQgpGIIRleHkByEVA7B7MoQkoOQyiGYXZlnCcm7\nJEIqh2B2ZQjJQUgFEQyvCiE5CKkgguFVISQHIZVEML0ihOQgpJIIplfkaULyLYmQyiKYXwlC\nchBSaQQTLEBIDkIqjWCCBZ4nJM+SCKk0ggkWICQHIZVGMMEChOQgpNIIJliAkByEVBrBBAsQ\nkoOQSiOYYAFCchBScQQjvB0hOQipQIIh3oqQHIRUIMEQb0VIDkIqkGCIt3qikPxKIqQCCYZ4\nK0JyCEOalWQ9aZUTDPFWhOQgpBIJpngjQnIQUokEU7wRITkIqUSCKd6IkByEVCTBGG9DSA5C\nKpJgjLd5ppC8SiKkMgnmeJPlkNoj9+12/k5CIqQM+M98FIshtedfZm+3Vx9i3Yc3nwUhpEL5\nzXs0hOQgpEL5zXs0QSFN77juiJAIKQc+uxvPupDOD5GannUf3nwWRBnSpSTrIXsGQXMvFxxS\ne/s+6z68+SwIIRXLc+TjWBXS9RuEREh58NnfWEJDuveWdR/efBaEkMrls7+xBIbU3nkfIRFS\nJjyHPoawkGaHwWf39qz78OazIIRUMM+hj8H/mQ3T0bp29r6RdR/efBaEkAoWOPxKPNfOQUgF\nEwzzWoTkIKSCCYZ5LUJyEFLBBMO8FiE5CKlggmFei5AchFQywTSvREgOQiqZYJpXIiQHIZVM\nMM0rPVVIPiVJQzqXZOOKHKQAAAdiSURBVD1gz0IwzSsRkoOQSiaY5pUIyUFIJRNM80qE5CCk\nognGeR1CchBS0QTjvA4hOQipbIJ5XoWQHIRUOMFAr0FIDm1IU0nW0/VEBAO9BiE5CKlwgoFe\ng5Ac4pBOJVlP1xMRDPQazxWSR0mEVDrBRK9ASA5CKp1golcgJAchlU4w0SsQkoOQSieY6BUI\nyUFIpRNM9AqE5CCk8glmOtiThbRcEiGVTzDTwZ4tpMWSCKkCgqEORUgOQqqAYKhDEZKDkCog\nGOpQhOQgpAoIhjoUITkIqQKCoQ71dCEtlURINRBMdSBCchBSDQRTHYiQHIRUA8FUB3q+kBZK\nIqQaCKY6ECE5CKkGgqkOREgOdUhjSdaD9XQEYx2GkByEVAXBWId5wpD+LomQqiAY6zCE5CCk\nKgjGOgwhOQipCoKxDkNIDkKqgmCswxCSg5CqIBjrMITkIKQqCMY6DCE5CKkKgrEOQ0gOQqqC\nYKzDEJKDkKogGOswhOQgpCoIxjoMITkIqQqCsQ5DSA5CqoJgrMM8Y0h/lkRIVRCMdRhCchBS\nFQRjHYaQHPKQhpKs5+rpCMY6DCE5CKkKgrEO85QhXdxeGUKqg2Cugzx5SL3rK0NIdRDMdRBC\nIqQqCeY6CCENLleGkOogmOsghDQ6XxlCqoNgroMQ0sl0ZfQh9SVZj9XzEcx1EEI6ma4MIVVC\nMNghCGlyujKEVAvBZAcgpMnpyhBSLQSTHYCQzsYrQ0i1EEx2AEI6G68MIdVCMNkBCOlsvDKE\nVAvBZAcgpIvhyhBSLQSTHYCQLoYrQ0i1EEx2AEK6GK4MIdVCMNkBCOliuDKEVAvBZAcgpIvh\nyhBSLQSTHYCQLoYrQ0i1EEx2AEK6GK5MhJD+EZIFwWQHIKSL4coQUi0Ekx2AkC6GK0NItRBM\ndgBCuhiuDCFVQzDa/gjpYrgyhFQNwWj7I6SL4coQUjUEo+2PkC6GK0NI1RCMtj9CmumvDCFV\nQzDa/ghppr8yhFQNwWj7I6SZ/soQUj0Es+2NkGb6K0NI9RDMtjdCmumvDCHVQzDb3ghpriOk\nqgiG2xchzXWEVBXBcPsipLmOkKoiGG5fhDTXEVJVBMPti5DmOkKqimC4fRHSXEdIVREMty9C\nmusIqSqC4fZFSHMdIVVFMNy+CGmuI6SqCIbbFyHNdYRUFcFw+yKkuY6QqiIYbl+ENNcRUlUE\nw+2LkOY6QqqKYLh9EdJcR0h1EUy3J0Ka6wipLoLp9kRIcx0h1UUw3Z4Iaa4jpLoIptsTIc11\nhFQXwXR7IqS5jpDqIphuT4Q018UJ6R8hGRFMtydCmusIqS6C6fZESHMdIdVFMN2eCGmuI6S6\nCKbbEyHNdYRUF8F0eyKkuY6Q6iKYbk+ENNcRUl0E0+2JkOY6QqqMYLz9ENIVQqqMYLz9ENIV\nQqqMYLz9ENI1QqqLYLz9ENI1QqqLYLz9ENI1QqqLYLz9ENI1QqqMYL69ENI1QqqMYL69ENI1\nQqqNYMB9ENI1QqqNYMB9ENK1OCH9s56mJyYYcB+EdI2QaiMYcB+E5CCkyggG3AchOQipMoIB\n90FIDkKqjGDAfRCSg5AqIxhwH4TkIKTKCAbcByE5CKkyggH3QUgOQqqMYMB9EJKDkCojGHAf\nhOQgpNoIJtwDITkIqTaCCfdASA5Cqo1gwj0QkoOQaiOYcA+E5CCk2ggm3AMhOQipOoIRX0ZI\nDkKqjmDElxGSg5CqIxjxZYTkIKTqCEZ8GSE5CKk6ghFfRkgOQqqOYMSXEZKDkKojGPFlhOQg\npOoIRnwZITkIqTqCEV9GSA5Cqo5gxJcRkoOQqiMY8WWE5CCk6ghGfBkhOQipOoIRX0ZIDkKq\njmDElxGSg5CqIxjxZYTkIKTqCEZ8GSE5CKk6ghFfthxSe+S+PX8fIRFS3iJkc2sxpPb8y+Xt\n+fs6QiKkvEXI5hYhOQipOhGyuUVIDkKqT4RubmwMqelZz74UIdUnVjxzilskLPn3z/o7QGSE\nlAIhVY+QUiCk6hFSCoRUPUJKgZCq5//Mhnb+9tUzG7CEkKqneK4dlhBS9QgpBUKqHiGlQEjV\nI6QUCKl6hJQCIVWPkFIgpOoRUgqEVD1CSoGQqkdIKRBS9QgpBUKqHiGlQEjVI6QUCKl6hJQC\nIVWPkFIgpOoRUgqEVD1CSoGQqkdIKRBS9QgpBUKqHiGlQEjVI6QUCKl6hJQCIVWPkFIgpOoR\nUgqEVD1CSoGQqkdIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAh\nAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEC\nhAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQE\nCBASIEBIgAAhAQKEBAgQEiBASIAAIQEChAQIEBIgQEiAACEBAoQECBASIEBIgAAhAQKEBAgQ\nEiBASIAAIQEChAQIEBIgQEiAwP8HkGujwq87sOAAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "comps = 2   # Specify the number of PCA components (> 2) \n",
    "clusters = 3 # specify the number of clusters\n",
    "ag = 'kmeans'  #choose the algorith: 'kmeans' = kmeans, 'hier' = Hierarchical, 'gmm' = Gaussian Mixture Model  \n",
    "trees = 300\n",
    "depth = 11\n",
    "\n",
    "\n",
    "# This runs all the reduction and clustering functions and returns the result. \n",
    "res <- run_h2(df_all,comps,clusters, ag, trees, depth)  \n",
    "\n",
    "\n",
    "# return specific elements from the functions\n",
    "res[[2]]\n",
    "res[[3]]\n",
    "res[[4]]\n",
    "\n",
    "print(\"Training Confusion Matrix\")\n",
    "res[[1]][[3]]\n",
    "print(\"Validation Confusion Matrix\")\n",
    "res[[1]][[4]]\n",
    "print(\"Variable Importance\")\n",
    "res[[1]][[5]]\n",
    "\n",
    "\n",
    "# This saves the new dataframe with the clusters \n",
    "res.crm = as.data.frame(res[[1]][[2]])\n",
    "\n",
    "df_c_summary <- df_c_s\n",
    "df_c_summary$clusters <- res.crm$clusters\n",
    "head(df_c_summary)\n",
    "\n",
    "df_n_summary <- as.data.frame(df_scale)\n",
    "df_n_summary$clusters <- res.crm$clusters\n",
    "\n",
    "df_c_summary %>% \n",
    "  group_by(clusters) %>% \n",
    "  summarise_if(is.factor, .funs = function(x) { x %>% table %>% which.max %>% names})\n",
    "\n",
    "df_n_summary %>% \n",
    "  group_by(clusters) %>% \n",
    "  summarise_if(is.numeric, funs(mean(., na.rm=TRUE)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 3 × 11</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>clusters</th><th scope=col>q4n</th><th scope=col>q5n</th><th scope=col>q6n</th><th scope=col>q7n</th><th scope=col>q8n</th><th scope=col>q9n</th><th scope=col>q10n</th><th scope=col>q11n</th><th scope=col>q12n</th><th scope=col>q13n</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>2.470588</td><td>-0.708078</td><td>1.302941</td><td>-0.8211004</td><td>-0.56093744</td><td>-0.56459481</td><td>-0.24593095</td><td>-0.07156078</td><td>-0.04648756</td><td>-0.25096108</td></tr>\n",
       "\t<tr><td>2</td><td>5.340278</td><td> 1.127418</td><td>2.326389</td><td> 1.1361808</td><td> 1.06058630</td><td> 1.08398150</td><td> 0.24761563</td><td> 0.14216775</td><td> 0.03687807</td><td> 0.24222605</td></tr>\n",
       "\t<tr><td>3</td><td>3.435055</td><td> 0.122689</td><td>1.644757</td><td> 0.1808515</td><td> 0.07219958</td><td> 0.06691712</td><td> 0.07505458</td><td> 0.00591409</td><td> 0.01642462</td><td> 0.07894556</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 3 × 11\n",
       "\\begin{tabular}{lllllllllll}\n",
       " clusters & q4n & q5n & q6n & q7n & q8n & q9n & q10n & q11n & q12n & q13n\\\\\n",
       " <fct> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1 & 2.470588 & -0.708078 & 1.302941 & -0.8211004 & -0.56093744 & -0.56459481 & -0.24593095 & -0.07156078 & -0.04648756 & -0.25096108\\\\\n",
       "\t 2 & 5.340278 &  1.127418 & 2.326389 &  1.1361808 &  1.06058630 &  1.08398150 &  0.24761563 &  0.14216775 &  0.03687807 &  0.24222605\\\\\n",
       "\t 3 & 3.435055 &  0.122689 & 1.644757 &  0.1808515 &  0.07219958 &  0.06691712 &  0.07505458 &  0.00591409 &  0.01642462 &  0.07894556\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 3 × 11\n",
       "\n",
       "| clusters &lt;fct&gt; | q4n &lt;dbl&gt; | q5n &lt;dbl&gt; | q6n &lt;dbl&gt; | q7n &lt;dbl&gt; | q8n &lt;dbl&gt; | q9n &lt;dbl&gt; | q10n &lt;dbl&gt; | q11n &lt;dbl&gt; | q12n &lt;dbl&gt; | q13n &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 2.470588 | -0.708078 | 1.302941 | -0.8211004 | -0.56093744 | -0.56459481 | -0.24593095 | -0.07156078 | -0.04648756 | -0.25096108 |\n",
       "| 2 | 5.340278 |  1.127418 | 2.326389 |  1.1361808 |  1.06058630 |  1.08398150 |  0.24761563 |  0.14216775 |  0.03687807 |  0.24222605 |\n",
       "| 3 | 3.435055 |  0.122689 | 1.644757 |  0.1808515 |  0.07219958 |  0.06691712 |  0.07505458 |  0.00591409 |  0.01642462 |  0.07894556 |\n",
       "\n"
      ],
      "text/plain": [
       "  clusters q4n      q5n       q6n      q7n        q8n         q9n        \n",
       "1 1        2.470588 -0.708078 1.302941 -0.8211004 -0.56093744 -0.56459481\n",
       "2 2        5.340278  1.127418 2.326389  1.1361808  1.06058630  1.08398150\n",
       "3 3        3.435055  0.122689 1.644757  0.1808515  0.07219958  0.06691712\n",
       "  q10n        q11n        q12n        q13n       \n",
       "1 -0.24593095 -0.07156078 -0.04648756 -0.25096108\n",
       "2  0.24761563  0.14216775  0.03687807  0.24222605\n",
       "3  0.07505458  0.00591409  0.01642462  0.07894556"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_n_summary <- as.data.frame(df_norm)\n",
    "df_n_summary$clusters <- res.crm$clusters\n",
    "\n",
    "\n",
    "df_n_summary %>% \n",
    "  group_by(clusters) %>% \n",
    "  summarise_if(is.numeric, funs(mean(., na.rm=TRUE)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison to Original Segmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 <- res.crm\n",
    "data1$orig_clust <- oc\n",
    "data1$clusters <- factor((data1$clusters), labels=c(\"s1\", \"s2\", \"s3\"))\n",
    "data1$clust_num = res.crm$clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test\n",
       "\n",
       "data:  table(data1$orig_clust, data1$clusters)\n",
       "X-squared = 536.12, df = 6, p-value < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "             \n",
       "               s1  s2  s3\n",
       "  basic_user  216   5 172\n",
       "  entry_level  64  47 350\n",
       "  non_engaged  63   0  15\n",
       "  power_admin   1  91  99"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#data1$crm_clust <-crm_km$cluster\n",
    "#data1\n",
    "chisq.test(table(data1$orig_clust, data1$clusters))\n",
    "table(data1$orig_clust, data1$clusters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multinomial Logistic Regression\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(nnet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1123</li><li>6</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1123\n",
       "\\item 6\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1123\n",
       "2. 6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1123    6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_mn <- res.crm\n",
    "df_mn$clusters <- factor((df_mn$clusters), labels=c(\"s1\", \"s2\", \"s3\"))\n",
    "#df_mn$clusters <- as.factor(df_mn$clusters)\n",
    "dim(df_mn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "index <- createDataPartition(df_mn$clusters, p = .70, list=FALSE)\n",
    "train <- df_mn[index,]\n",
    "test <- df_mn[-index,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_mn$clusters <- relevel(df_mn$clusters, ref = \"s1\")\n",
    "train$clusters <- relevel(train$clusters, ref = \"s1\")\n",
    "test$clusters <- relevel(test$clusters, ref = \"s1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# weights:  21 (12 variable)\n",
      "initial  value 1233.741600 \n",
      "iter  10 value 994.438262\n",
      "iter  20 value 903.004790\n",
      "final  value 902.998919 \n",
      "converged\n"
     ]
    }
   ],
   "source": [
    "multinom_model <- multinom(clusters ~ ., data = df_mn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "multinom(formula = clusters ~ ., data = df_mn)\n",
       "\n",
       "Coefficients:\n",
       "   (Intercept) thry_day_es_n env_purch_n env_sent_life_n    num_trx_n     mmr_n\n",
       "s2  -1.4006668     0.3326556   1.2808761      -0.5496012 0.4325563898 0.7897573\n",
       "s3   0.8381161     0.2677741   0.4507431      -0.2331353 0.0005329961 0.4535447\n",
       "\n",
       "Std. Errors:\n",
       "   (Intercept) thry_day_es_n env_purch_n env_sent_life_n num_trx_n     mmr_n\n",
       "s2  0.15666069     0.2890227   0.2222680       0.2278335 0.2317216 0.2093813\n",
       "s3  0.07778533     0.1580367   0.1180708       0.1296093 0.1375675 0.1142237\n",
       "\n",
       "Residual Deviance: 1805.998 \n",
       "AIC: 1829.998 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(multinom_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 6 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>(Intercept)</th><th scope=col>thry_day_es_n</th><th scope=col>env_purch_n</th><th scope=col>env_sent_life_n</th><th scope=col>num_trx_n</th><th scope=col>mmr_n</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>s2</th><td>0</td><td>0.24974579</td><td>8.275199e-09</td><td>0.01585252</td><td>0.0619425</td><td>1.620336e-04</td></tr>\n",
       "\t<tr><th scope=row>s3</th><td>0</td><td>0.09019331</td><td>1.347744e-04</td><td>0.07205766</td><td>0.9969087</td><td>7.167002e-05</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & (Intercept) & thry\\_day\\_es\\_n & env\\_purch\\_n & env\\_sent\\_life\\_n & num\\_trx\\_n & mmr\\_n\\\\\n",
       "\\hline\n",
       "\ts2 & 0 & 0.24974579 & 8.275199e-09 & 0.01585252 & 0.0619425 & 1.620336e-04\\\\\n",
       "\ts3 & 0 & 0.09019331 & 1.347744e-04 & 0.07205766 & 0.9969087 & 7.167002e-05\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 6 of type dbl\n",
       "\n",
       "| <!--/--> | (Intercept) | thry_day_es_n | env_purch_n | env_sent_life_n | num_trx_n | mmr_n |\n",
       "|---|---|---|---|---|---|---|\n",
       "| s2 | 0 | 0.24974579 | 8.275199e-09 | 0.01585252 | 0.0619425 | 1.620336e-04 |\n",
       "| s3 | 0 | 0.09019331 | 1.347744e-04 | 0.07205766 | 0.9969087 | 7.167002e-05 |\n",
       "\n"
      ],
      "text/plain": [
       "   (Intercept) thry_day_es_n env_purch_n  env_sent_life_n num_trx_n\n",
       "s2 0           0.24974579    8.275199e-09 0.01585252      0.0619425\n",
       "s3 0           0.09019331    1.347744e-04 0.07205766      0.9969087\n",
       "   mmr_n       \n",
       "s2 1.620336e-04\n",
       "s3 7.167002e-05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z <- summary(multinom_model)$coefficients/summary(multinom_model)$standard.errors\n",
    "# 2-tailed Wald z tests to test significance of coefficients\n",
    "p <- (1 - pnorm(abs(z), 0, 1)) * 2\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 6 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>(Intercept)</th><th scope=col>thry_day_es_n</th><th scope=col>env_purch_n</th><th scope=col>env_sent_life_n</th><th scope=col>num_trx_n</th><th scope=col>mmr_n</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>s2</th><td>0.2464326</td><td>1.394667</td><td>3.599792</td><td>0.5771799</td><td>1.541192</td><td>2.202862</td></tr>\n",
       "\t<tr><th scope=row>s3</th><td>2.3120073</td><td>1.307052</td><td>1.569478</td><td>0.7920464</td><td>1.000533</td><td>1.573881</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & (Intercept) & thry\\_day\\_es\\_n & env\\_purch\\_n & env\\_sent\\_life\\_n & num\\_trx\\_n & mmr\\_n\\\\\n",
       "\\hline\n",
       "\ts2 & 0.2464326 & 1.394667 & 3.599792 & 0.5771799 & 1.541192 & 2.202862\\\\\n",
       "\ts3 & 2.3120073 & 1.307052 & 1.569478 & 0.7920464 & 1.000533 & 1.573881\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 6 of type dbl\n",
       "\n",
       "| <!--/--> | (Intercept) | thry_day_es_n | env_purch_n | env_sent_life_n | num_trx_n | mmr_n |\n",
       "|---|---|---|---|---|---|---|\n",
       "| s2 | 0.2464326 | 1.394667 | 3.599792 | 0.5771799 | 1.541192 | 2.202862 |\n",
       "| s3 | 2.3120073 | 1.307052 | 1.569478 | 0.7920464 | 1.000533 | 1.573881 |\n",
       "\n"
      ],
      "text/plain": [
       "   (Intercept) thry_day_es_n env_purch_n env_sent_life_n num_trx_n mmr_n   \n",
       "s2 0.2464326   1.394667      3.599792    0.5771799       1.541192  2.202862\n",
       "s3 2.3120073   1.307052      1.569478    0.7920464       1.000533  1.573881"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "exp(coef(multinom_model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Confusion Matrix and Statistics\n",
       "\n",
       "          Reference\n",
       "Prediction  s1  s2  s3\n",
       "        s1  86   3 152\n",
       "        s2   2  25  74\n",
       "        s3  58  10 378\n",
       "\n",
       "Overall Statistics\n",
       "                                          \n",
       "               Accuracy : 0.6206          \n",
       "                 95% CI : (0.5856, 0.6546)\n",
       "    No Information Rate : 0.7665          \n",
       "    P-Value [Acc > NIR] : 1               \n",
       "                                          \n",
       "                  Kappa : 0.2461          \n",
       "                                          \n",
       " Mcnemar's Test P-Value : <2e-16          \n",
       "\n",
       "Statistics by Class:\n",
       "\n",
       "                     Class: s1 Class: s2 Class: s3\n",
       "Sensitivity             0.5890   0.65789    0.6258\n",
       "Specificity             0.7586   0.89867    0.6304\n",
       "Pos Pred Value          0.3568   0.24752    0.8475\n",
       "Neg Pred Value          0.8903   0.98108    0.3392\n",
       "Prevalence              0.1853   0.04822    0.7665\n",
       "Detection Rate          0.1091   0.03173    0.4797\n",
       "Detection Prevalence    0.3058   0.12817    0.5660\n",
       "Balanced Accuracy       0.6738   0.77828    0.6281"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predicting the values for train dataset\n",
    "train$clusterPredicted <- predict(multinom_model, newdata=train, type=\"class\")\n",
    "# Building classification table\n",
    "tab <- table(train$clusterPredicted, train$clusters)\n",
    "# Confusion Matrix\n",
    "confusionMatrix(train$clusters, train$clusterPredicted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Confusion Matrix and Statistics\n",
       "\n",
       "          Reference\n",
       "Prediction  s1  s2  s3\n",
       "        s1  44   0  59\n",
       "        s2   1   5  36\n",
       "        s3  39   6 145\n",
       "\n",
       "Overall Statistics\n",
       "                                          \n",
       "               Accuracy : 0.5791          \n",
       "                 95% CI : (0.5242, 0.6326)\n",
       "    No Information Rate : 0.7164          \n",
       "    P-Value [Acc > NIR] : 1               \n",
       "                                          \n",
       "                  Kappa : 0.1787          \n",
       "                                          \n",
       " Mcnemar's Test P-Value : 7.457e-06       \n",
       "\n",
       "Statistics by Class:\n",
       "\n",
       "                     Class: s1 Class: s2 Class: s3\n",
       "Sensitivity             0.5238   0.45455    0.6042\n",
       "Specificity             0.7649   0.88580    0.5263\n",
       "Pos Pred Value          0.4272   0.11905    0.7632\n",
       "Neg Pred Value          0.8276   0.97952    0.3448\n",
       "Prevalence              0.2507   0.03284    0.7164\n",
       "Detection Rate          0.1313   0.01493    0.4328\n",
       "Detection Prevalence    0.3075   0.12537    0.5672\n",
       "Balanced Accuracy       0.6444   0.67017    0.5652"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predicting the class for test dataset\n",
    "test$clusterPredicted <- predict(multinom_model, newdata = test, type=\"class\")\n",
    "# Building classification table\n",
    "tab <- table(test$clusters, test$clusterPredicted)\n",
    "confusionMatrix(test$clusters,test$clusterPredicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Prototypes\n",
    "<hr>\n",
    "\n",
    "With K-Prototypes we can use a mixture of numeric and categorical variables in the model.  For this analysis we have first applied PCA to only the numberic variables in the dataset and then appended the categorical variables to the PCAs to create a unified dataset.  Once created, we applied the K-Prototypes algorithm to the entire set of variables. \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n",
      "# NAs in variables:\n",
      "   depts_using      feat_used      num_roles admin_prtl_use    unq_snd_mng \n",
      "             0              0              0              0              0 \n",
      "   unq_snd_cmp       rate_sat       num_locs           dept      time_resp \n",
      "             0              0              0              0              0 \n",
      " time_ds_tasks        ds_expr        ds_role         ds_uni           vert \n",
      "             0              0              0              0              0 \n",
      "0 observation(s) with NAs.\n",
      "\n",
      "Estimated lambda: 1.541568 \n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>15017.6455703192</li><li>12837.6176403481</li><li>12135.9312403371</li><li>11668.4817262982</li><li>11277.3840965486</li><li>10828.36569377</li><li>10585.1515958152</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 15017.6455703192\n",
       "\\item 12837.6176403481\n",
       "\\item 12135.9312403371\n",
       "\\item 11668.4817262982\n",
       "\\item 11277.3840965486\n",
       "\\item 10828.36569377\n",
       "\\item 10585.1515958152\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 15017.6455703192\n",
       "2. 12837.6176403481\n",
       "3. 12135.9312403371\n",
       "4. 11668.4817262982\n",
       "5. 11277.3840965486\n",
       "6. 10828.36569377\n",
       "7. 10585.1515958152\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 15017.65 12837.62 12135.93 11668.48 11277.38 10828.37 10585.15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Combine the PCAs from the numerical dataset and the categorical variables into a single DataFrame\n",
    "  df_kp <-df_all    \n",
    "  \n",
    "#algorithm to find the optimal number of K-Prototypes clusters\n",
    "# Compute and plot wss for k = 2 to k = 15.\n",
    "  k.max <- 7\n",
    "  data <- na.omit(df_kp) # to remove the rows with NA's\n",
    "  wss <- sapply(1:k.max, \n",
    "                function(k){kproto(data, k)$tot.withinss})\n",
    "  wss\n",
    "  plot(1:k.max, wss,\n",
    "       type=\"b\", pch = 19, frame = FALSE, \n",
    "       xlab=\"Number of clusters K\",\n",
    "       ylab=\"Total within-clusters sum of squares\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1123</li><li>15</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1123\n",
       "\\item 15\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1123\n",
       "2. 15\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1123   15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(df_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1123"
      ],
      "text/latex": [
       "1123"
      ],
      "text/markdown": [
       "1123"
      ],
      "text/plain": [
       "[1] 1123"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.163426164854835"
      ],
      "text/latex": [
       "0.163426164854835"
      ],
      "text/markdown": [
       "0.163426164854835"
      ],
      "text/plain": [
       "[1] 0.1634262"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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+MKISQNhFTC4kOKdI4k7IiQgrH8kIJctbssiaqjlYUU/gWyawgpjFF5QKpnrdND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\nxAAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the K Prototype Algorithm \n",
    "  kpres <- kproto(df_kp, 3, iter.max=20, nstart=15, keep.data=TRUE, verbose=FALSE)\n",
    "  kproto_label <- kpres$cluster\n",
    "  length(kproto_label)\n",
    "  \n",
    "  ggplot() + geom_point(data = as.data.frame(X.m), mapping = aes(x = X.m[,1], y = X.m[,2], col = as.factor(kproto_label))) + scale_fill_brewer(palette=\"Set1\")\n",
    "\n",
    "  \n",
    "  # calculate index-value\n",
    "  val <- validation_kproto(method = \"silhouette\", object=kpres, data = df_kp, k = 2:5, nstart = 15)\n",
    "  val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Numeric predictors: 7 \n",
       "Categorical predictors: 8 \n",
       "Lambda: 1.541568 \n",
       "\n",
       "Number of Clusters: 3 \n",
       "Cluster sizes: 343 433 347 \n",
       "Within cluster error: 3309.35 4774.976 3970.473 \n",
       "\n",
       "Cluster prototypes:\n",
       "  depts_using  feat_used num_roles admin_prtl_use unq_snd_mng unq_snd_cmp\n",
       "1  -0.1378614  0.2610503  1.758017      0.3705006  -0.6203295  -0.7563909\n",
       "2   0.4307001  0.5281067  1.838337      0.5887428   0.7133519   0.7829930\n",
       "3  -0.4011721 -0.9170331  1.239193     -1.1008857  -0.2535075  -0.2095181\n",
       "      rate_sat num_locs           dept time_resp     time_ds_tasks      ds_expr\n",
       "1  0.149009861        1 Administration   General Sending_Envelopes Intermediate\n",
       "2 -0.005900468       6+             IT   General        Generalist Intermediate\n",
       "3 -0.139929336        1          Sales   General Sending_Envelopes Intermediate\n",
       "                ds_role ds_uni               vert\n",
       "1 Administrator (admin)     No              Other\n",
       "2 Administrator (admin)     No Financial Services\n",
       "3            Basic user     No  Business Services"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kpres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "kp_crm <- df_crm_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "kp_crm <- as.data.frame(kp_crm)\n",
    "kp_crm$clusters = kpres$cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       " randomForest(formula = as.factor(clusters) ~ ., data = na.omit(kp_crm),      ntree = 2000, mtry = 2, importance = TRUE) \n",
       "               Type of random forest: classification\n",
       "                     Number of trees: 2000\n",
       "No. of variables tried at each split: 2\n",
       "\n",
       "        OOB estimate of  error rate: 48.8%\n",
       "Confusion matrix:\n",
       "    1   2   3 class.error\n",
       "1 141  76 126   0.5889213\n",
       "2  56 323  54   0.2540416\n",
       "3 130 106 111   0.6801153"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                  Df Sum Sq Mean Sq F value  Pr(>F)   \n",
       "thry_day_es_n      1    0.1   0.135   0.221 0.63810   \n",
       "env_purch_n        1    4.1   4.080   6.673 0.00991 **\n",
       "env_sent_life_n    1    0.0   0.031   0.051 0.82139   \n",
       "num_trx_n          1    1.9   1.882   3.078 0.07963 . \n",
       "mmr_n              1    0.9   0.937   1.533 0.21592   \n",
       "Residuals       1117  682.9   0.611                   \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Random Forest \n",
    "  rf_classifier = randomForest(as.factor(clusters) ~ ., data=na.omit(kp_crm), ntree=2000, mtry=2, importance=TRUE)\n",
    "  rf_classifier\n",
    "\n",
    "\n",
    "# ANOVA \n",
    "  anova <- aov(clusters ~ ., data = na.omit(kp_crm))\n",
    "  summary(anova)\n",
    "  \n",
    "# Cluster Profiles \n",
    "  #clprofiles(kpres, df_kp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ztj7vBnh2BahCRjSEiLywf23a+9bHKHPzkEE+MsyxjyC2G7z1mmzTEdz/8dcni4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\nQEiAAUICDBASYICQAAP/B30iEFJTbh/uAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"depts_using\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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EhavNhgRL0GQtIipCAIScs3pO3p9sZx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\nAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"feat_used\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"num_roles\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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E39GVfPn8HdSziFy0hyyMwjCGn0TonnzyDc/K+Qj5DKMc9+jd8p8Xx74c+fKoSU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\nJMAAIQEGCAkwQEiAAUICDBASYOD/cJj80DKky/wAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"admin_prtl_use\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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526cPw5cbc3Xev67uy0W4aw3H1vcndrIRwXYVVuB+eBkJwtL1f68tRf4KufV89/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",
      "text/plain": [
       "Plot with title \"unq_snd_mng\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2sIh5DGDXE4xSAPa5Cz3hQhjRsy8RTW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\nVSEAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"unq_snd_cmp\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"rate_sat\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"num_locs\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zLZ79WvDxo9XpUMD/jtBBjO8n4W/Nb1QcT5cTm+Fq9BnqeWdnMuVts9ZVd1N7n7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",
      "text/plain": [
       "Plot with title \"dept\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"time_resp\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RCp2YSqaaqQdct1yDUiVg8iIVIT+g1D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\nnKina4S6AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"time_ds_tasks\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"ds_expr\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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e0+r5w9an56ez48rt++/+xVu5Oh9w9eTm+fHn67IKlX7ba/7r8SfzLM6YlvX4td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\nAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"ds_role\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"ds_uni\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mRPy2372PzIm20t5va6noK0OtL3Pj3d3gLunnd7hM+35/HOKv94mtPzNpvYnP7f\nXMfn5m7F3rcPXeid494G0vKh28H9Mtv6x6GjrLa1fx1p64I1V92BkFZf+GEHze+1TT4+ft6u\nvRUO2cVHt3jwKU/1ubkmfKaHNN6c7/BVbh8j7Zz+fX7fbrr4dkZI792/AEh7h2Mh/bSDZs+L\nhzWjU9eu1X8idvHRLR58ylM9b64Jz2GQLpl/AaR/3dPL2+eVq/zavGS2u9Gjp8X/HbpSHr3Q\nB78YUH9uk+4jO6Qfd9C8t+lT88jxGKSQXXx0iwef8lSrlyjmt0xPO4+R+sFd/7Re8xjp/QdI\n781JJmc+zTDbDFjXn/L7vN5/mL67ypPvO97nrfL360hfO6ef3xy9LJ9waC7BSUh7x70VpPkO\n+vHybm/obHb4KD9Bai/+1ZB+3EHfx+hWD4H//bSJzQmu3sXHtnjwKU/0sXlOYNx9bD9r1w/u\nFg90x1/zK9l0oe5l8QzVBtLC4PbXZqsnWeYnOvfJhu/Dzfjvc/2evtgRH+s70Ov7+XvPYp1a\n5fmPicnynQ3T5Vtv2qetFndzN09l9ZfgJKS9436vTFSrbXju9i7v596RZrPDT+z9BOnAs3Zn\nbv4epGYHrb/+1D8R1zxr9/bTJq73aMQuPrbFg095ounmB+rb96sKu7e4m1dylq8JbF7neVpe\nE7e/Nlsf/dx3sm3uWS5OvHxN5l/PZ32u39OnqyO+r0d/f/v7WafTq/y+fq9dfyfv+/SLs21e\nTtu9X/8zpL3jfq9MVOtLNNq5vFtT2ou9uyQ/HWd7Z403X7po83cgNTuo/Unz/bX+dcIfN7Gf\nGbSLj2zx4FOeaDTaPrh4F0F7P63/z+KZl6WL+QPH78e870/L9d762rKX+SIceovxbluQFue1\nehF4c67N9Dmx8fvyJr4f3X/7ZbR52fv7f4/2OplfJ8fPqy3cnH6x0992LsFpSLvHbVYmqPUl\netu5vFtTti72zpL8dJzvnbW5+BtIZ2/+DqRmBzULtHxnw+pZ68lmqXc3cTUzahcf3OLBpxw0\n7cx3JUgXdMX1P24bfmnM4n7o18TfyNQNeiBIq+fC/dFm3aAHgjR7md+ffXJ7pFv0SJCkPx1I\nUkAgSQGBJAUEkhQQSFJAIEkBgSQFBJIUEEhSQCBJAYEkBQSSFBBIUkAgSQGBJAUEkhQQSFJA\nIEkBgSQFBJIUEEhSQCBJAYEkBQSSFBBIUkAgSQGBJAUEkhQQSFJAIEkBgSQFBJIUEEhSQCBJ\nAYEkBQSSFBBIUkAgSQGBJAUEkhQQSFJAIEkBgSQFBJIUEEhSQCBJAYEkBQSSFBBIUkAgSQGB\nJAUEkhQQSOoV+lIAAABMSURBVFJAIEkBgSQFBJIUEEhSQCBJAYEkBQSSFBBIUkAgSQGBJAUE\nkhQQSFJAIEkBgSQFBJIUEEhSQCBJAYEkBQSSFBBIUkAgSQH9HwEVJcVSx7rdAAAAAElFTkSu\nQmCC",
      "text/plain": [
       "Plot with title \"vert\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 840,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cluster Profiles \n",
    "clprofiles(kpres, df_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}