diff --git a/man/HarzTraffic_files/figure-html/unnamed-chunk-1-4.png b/man/HarzTraffic_files/figure-html/unnamed-chunk-1-4.png index 6338843..09a7ed9 100644 Binary files a/man/HarzTraffic_files/figure-html/unnamed-chunk-1-4.png and b/man/HarzTraffic_files/figure-html/unnamed-chunk-1-4.png differ diff --git a/man/gamlss2.html b/man/gamlss2.html index 12231e4..eae39f2 100644 --- a/man/gamlss2.html +++ b/man/gamlss2.html @@ -545,7 +545,7 @@

Examples

*-------- n = 610 df = 13.12 res.df = 596.88 Deviance = 4770.1554 Null Dev. Red. = 33.39% -AIC = 4796.3966 elapsed = 0.79sec +AIC = 4796.3966 elapsed = 0.77sec 
## plot estimated effects
 plot(b, which = "effects")
diff --git a/man/prodist.gamlss2.html b/man/prodist.gamlss2.html index b6cd03b..d367645 100644 --- a/man/prodist.gamlss2.html +++ b/man/prodist.gamlss2.html @@ -455,10 +455,10 @@

Examples

## simulate random numbers
 random(d, 5)
-
       r_1      r_2      r_3      r_4      r_5
-1 20.08173 13.74014 14.59380 15.57188 34.09545
-2 65.40597 56.26210 31.90554 69.64569 93.96141
-3 88.13704 85.50187 64.15433 44.46626 56.20831
+
        r_1      r_2      r_3       r_4       r_5
+1  24.32901 13.29763 35.27695  33.74172  18.57794
+2  46.98782 78.05494 26.78614  66.43448  82.26054
+3 105.65839 55.72442 83.87947 135.84411 133.94615
## density and distribution
 pdf(d, 50 * -2:2)
diff --git a/search.json b/search.json index b9ad08c..c80efd6 100644 --- a/search.json +++ b/search.json @@ -113,7 +113,7 @@ "href": "man/prodist.gamlss2.html", "title": "gamlss2", "section": "", - "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 \n\"GAMLSS NO distribution (mu = 23.04, sigma = 10.06)\" \n 2 \n\"GAMLSS NO distribution (mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO distribution (mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 20.08173 13.74014 14.59380 15.57188 34.09545\n2 65.40597 56.26210 31.90554 69.64569 93.96141\n3 88.13704 85.50187 64.15433 44.46626 56.20831\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO distribution (mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)", + "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 \n\"GAMLSS NO distribution (mu = 23.04, sigma = 10.06)\" \n 2 \n\"GAMLSS NO distribution (mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO distribution (mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 24.32901 13.29763 35.27695 33.74172 18.57794\n2 46.98782 78.05494 26.78614 66.43448 82.26054\n3 105.65839 55.72442 83.87947 135.84411 133.94615\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO distribution (mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)", "crumbs": [ "Reference", "prodist.gamlss2" @@ -124,7 +124,7 @@ "href": "man/prodist.gamlss2.html#extracting-fitted-or-predicted-probability-distributions-from-gamlss2-models", "title": "gamlss2", "section": "", - "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 \n\"GAMLSS NO distribution (mu = 23.04, sigma = 10.06)\" \n 2 \n\"GAMLSS NO distribution (mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO distribution (mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 20.08173 13.74014 14.59380 15.57188 34.09545\n2 65.40597 56.26210 31.90554 69.64569 93.96141\n3 88.13704 85.50187 64.15433 44.46626 56.20831\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO distribution (mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)", + "text": "Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.\n\n\n\n## S3 method for class 'gamlss2'\nprodist(object, ...)\n\n\n\n\n\n\n\nobject\n\n\nA model object of class gamlss2.\n\n\n\n\n…\n\n\nArguments passed on to predict.gamlss2, e.g., newdata.\n\n\n\n\n\n\nTo facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).\nNote that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.\n\n\n\nAn object of class GAMLSS inheriting from distribution.\n\n\n\nZeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.\n\n\n\nGAMLSS, predict.gamlss2\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## packages, code, and data\nlibrary(\"distributions3\")\ndata(\"cars\", package = \"datasets\")\n\n## fit heteroscedastic normal GAMLSS model\n## stopping distance (ft) explained by speed (mph)\nm <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)\n\nGAMLSS-RS iteration 1: Global Deviance = 407.3541 eps = 0.125497 \nGAMLSS-RS iteration 2: Global Deviance = 405.7146 eps = 0.004024 \nGAMLSS-RS iteration 3: Global Deviance = 405.6978 eps = 0.000041 \nGAMLSS-RS iteration 4: Global Deviance = 405.6976 eps = 0.000000 \n\n## obtain predicted distributions for three levels of speed\nd <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))\nprint(d)\n\n 1 \n\"GAMLSS NO distribution (mu = 23.04, sigma = 10.06)\" \n 2 \n\"GAMLSS NO distribution (mu = 59.04, sigma = 18.51)\" \n 3 \n\"GAMLSS NO distribution (mu = 96.35, sigma = 33.95)\" \n\n## obtain quantiles (works the same for any distribution object 'd' !)\nquantile(d, 0.5)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)\n\n q_0.05 q_0.5 q_0.95\n1 6.486962 23.03912 39.59128\n2 28.589641 59.03607 89.48250\n3 40.504887 96.34896 152.19303\n\nquantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)\n\n 1 2 3 \n 6.486962 59.036073 152.193030 \n\n## visualization\nplot(dist ~ speed, data = cars)\nnd <- data.frame(speed = 0:240/4)\nnd$dist <- prodist(m, newdata = nd)\nnd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))\nmatplot(nd$speed, nd$fit, type = \"l\", lty = 1, col = \"slategray\", add = TRUE)\n\n\n\n\n\n\n\n## moments\nmean(d)\n\n 1 2 3 \n23.03912 59.03607 96.34896 \n\nvariance(d)\n\n 1 2 3 \n 101.2639 342.6244 1152.6558 \n\n## simulate random numbers\nrandom(d, 5)\n\n r_1 r_2 r_3 r_4 r_5\n1 24.32901 13.29763 35.27695 33.74172 18.57794\n2 46.98782 78.05494 26.78614 66.43448 82.26054\n3 105.65839 55.72442 83.87947 135.84411 133.94615\n\n## density and distribution\npdf(d, 50 * -2:2)\n\n d_-100 d_-50 d_0 d_50 d_100\n1 1.365786e-34 1.440750e-13 0.0028836944 0.001095127 7.891037e-15\n2 2.012473e-18 6.289547e-10 0.0001332376 0.019131662 1.862073e-03\n3 6.414012e-10 1.084300e-06 0.0002095201 0.004627633 1.168286e-02\n\ncdf(d, 50 * -2:2)\n\n p_-100 p_-50 p_0 p_50 p_100\n1 1.116699e-34 1.961566e-13 0.0110254856 0.99631019 1.0000000\n2 4.279141e-18 1.923739e-09 0.0007128545 0.31271491 0.9865531\n3 3.661574e-09 8.139843e-06 0.0022705648 0.08609812 0.5428194\n\n## Poisson example\ndata(\"FIFA2018\", package = \"distributions3\")\nm2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)\n\nGAMLSS-RS iteration 1: Global Deviance = 355.3922 eps = 0.045332 \nGAMLSS-RS iteration 2: Global Deviance = 355.3922 eps = 0.000000 \n\nd2 <- prodist(m2, newdata = data.frame(difference = 0))\nprint(d2)\n\n 1 \n\"GAMLSS PO distribution (mu = 1.237)\" \n\nquantile(d2, c(0.05, 0.5, 0.95))\n\n[1] 0 1 3\n\n## note that log_pdf() can replicate logLik() value\nsum(log_pdf(prodist(m2), FIFA2018$goals))\n\n[1] -177.6961\n\nlogLik(m2)\n\n'log Lik.' -177.6961 (df=2.005144)", "crumbs": [ "Reference", "prodist.gamlss2" @@ -365,7 +365,7 @@ "href": "man/gamlss2.html", "title": "gamlss2", "section": "", - "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.79sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002", + "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.77sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002", "crumbs": [ "Reference", "gamlss2" @@ -376,7 +376,7 @@ "href": "man/gamlss2.html#generalized-additive-models-for-location-scale-and-shape", "title": "gamlss2", "section": "", - "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.79sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002", + "text": "Estimation of generalized additive models for location scale and shape (GAMLSS). The model fitting function gamlss2() provides flexible infrastructures to estimate the parameters of a response distribution. The number of distributional parameters is not fixed, see gamlss2.family. Moreover, gamlss2() supports all smooth term constructors from the mgcv package in addition to the classical model terms as provided by gamlss and gamlss.add.\n\n\n\ngamlss2(x, ...)\n\n## S3 method for class 'formula'\ngamlss2(formula, data, family = NO,\n subset, na.action, weights, offset, start = NULL,\n control = gamlss2_control(...), ...)\n\n## S3 method for class 'list'\ngamlss2(x, ...)\n\n\n\n\n\n\n\nformula\n\n\nA GAM-type formula or Formula. All smooth terms of the mgcv package are supported, see also formula.gam.\n\n\n\n\nx\n\n\nFor gamlss.list() x is a list of formulas.\n\n\n\n\ndata\n\n\nA data frame or list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gamlss2 is called.\n\n\n\n\nfamily\n\n\nA gamlss.family or gamlss2.family object used to define distribution and the link functions of the parameters.\n\n\n\n\nsubset\n\n\nAn optional vector specifying a subset of observations to be used in the fitting process.\n\n\n\n\nna.action\n\n\nNA processing for setting up the model.frame.\n\n\n\n\nweights\n\n\nAn optional vector of prior weights to be used in the fitting process. Should be NULL or a numeric vector.\n\n\n\n\noffset\n\n\nThis can be used to specify an a priori known components to be included in the linear predictors during fitting. Please note that if only a single numeric vector is provided, the offset will be assigned to the first specified parameter of the distribution. In the case of multiple offsets, a data frame or list must be supplied. Each offset is assigned in the same order as the parameters of the distribution specified in the family object.\n\n\n\n\nstart\n\n\nStarting values for estimation algorithms.\n\n\n\n\ncontrol\n\n\nA list of control arguments, see gamlss2_control.\n\n\n\n\n…\n\n\nArguments passed to gamlss2_control.\n\n\n\n\n\n\nThe model fitting function gamlss2() provides flexible infrastructures for the estimation of GAMLSS.\n\n\nDistributional models are specified using family objects, either from the gamlss.dist package or using gamlss2.family objects.\n\n\nEstimation is carried out through a Newton-Raphson/Fisher scoring algorithm, see function RS. The estimation algorithms can also be exchanged using gamlss2_control. Additionally, if an optimizer is specified by the family object, this optimizer function will be employed for estimation.\n\n\nThe return value is determined by the object returned from the optimizer function, typically an object of class “gamlss2”. Default methods and extractor functions are available for this class. Nevertheless, users have the flexibility to supply their own optimizer function, along with user-specific methods tailored for the returned object.\n\n\n\n\n\nThe return value is determined by the object returned from the optimizer function. By default, the optimization is performed using the RS optimizer function (see gamlss2_control), yielding an object of class “gamlss2”. Default methods and extractor functions are available for this class.\n\n\n\nRigby RA, Stasinopoulos DM (2005). “Generalized Additive Models for Location, Scale and Shape (with Discussion).” Journal of the Royal Statistical Society, Series C (Applied Statistics), 54, 507–554. doi:10.1111/j.1467-9876.2005.00510.x\nRigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F (2019). Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/9780429298547\nStasinopoulos DM, Rigby RA (2007). “Generalized Additive Models for Location Scale and Shape (GAMLSS) in R.” Journal of Statistical Software, 23(7), 1–46. doi:10.18637/jss.v023.i07\nStasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017). Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973\n\n\n\nRS, gamlss2_control, gamlss2.family\n\n\n\n\nlibrary(\"gamlss2\")\n\n\n## load the abdominal circumference data\ndata(\"abdom\", package = \"gamlss.data\")\n\n## specify the model Formula\nf <- y ~ s(x) | s(x) | s(x) | s(x)\n\n## estimate model\nb <- gamlss2(f, data = abdom, family = BCT)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002 \n\n## model summary\nsummary(b)\n\nCall:\ngamlss2(formula = f, data = abdom, family = BCT)\n---\nFamily: BCT \nLink function: mu = identity, sigma = log, nu = identity, tau = log\n*--------\nParameter: mu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 226.334 1.257 180 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 4.551\n*--------\nParameter: sigma \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -2.92264 0.01101 -265.5 <2e-16 ***\n---\nSmooth terms:\n s(x)\nedf 2.5639\n*--------\nParameter: nu \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) -0.18021 0.04599 -3.918 9.95e-05 ***\n---\nSmooth terms:\n s(x)\nedf 1.0015\n*--------\nParameter: tau \n---\nCoefficients:\n Estimate Std. Error t value Pr(>|t|) \n(Intercept) 2.6548 0.0144 184.4 <2e-16 ***\n---\nSignif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n---\nSmooth terms:\n s(x)\nedf 1.0042\n*--------\nn = 610 df = 13.12 res.df = 596.88\nDeviance = 4770.1554 Null Dev. Red. = 33.39%\nAIC = 4796.3966 elapsed = 0.77sec\n\n## plot estimated effects\nplot(b, which = \"effects\")\n\n\n\n\n\n\n\n## plot diagnostics\nplot(b, which = \"resid\")\n\n\n\n\n\n\n\n## predict parameters\npar <- predict(b)\n\n## predict quantiles\npq <- sapply(c(0.05, 0.5, 0.95), function(q) family(b)$q(q, par))\n\n## visualize\nplot(y ~ x, data = abdom, pch = 19,\n col = rgb(0.1, 0.1, 0.1, alpha = 0.3))\nmatplot(abdom$x, pq, type = \"l\", lwd = 2,\n lty = 1, col = 4, add = TRUE)\n\n\n\n\n\n\n\n## use of starting values\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10))\n\nGAMLSS-RS iteration 1: Global Deviance = 4789.7797 eps = 0.556012 \nGAMLSS-RS iteration 2: Global Deviance = 4774.5657 eps = 0.003176 \nGAMLSS-RS iteration 3: Global Deviance = 4771.4193 eps = 0.000658 \nGAMLSS-RS iteration 4: Global Deviance = 4769.9947 eps = 0.000298 \nGAMLSS-RS iteration 5: Global Deviance = 4769.9556 eps = 0.000008 \n\n## fix some parameters\nm <- gamlss2(f, data = abdom, family = BCT,\n start = c(mu = 200, sigma = 0.1, nu = 0, tau = 10),\n fixed = c(nu = TRUE, tau = TRUE))\n\nGAMLSS-RS iteration 1: Global Deviance = 4799.422 eps = 0.555118 \nGAMLSS-RS iteration 2: Global Deviance = 4795.2807 eps = 0.000862 \nGAMLSS-RS iteration 3: Global Deviance = 4795.2668 eps = 0.000002 \n\n## estimated coefficients (intercepts)\ncoef(m)\n\n mu.p.(Intercept) sigma.p.(Intercept) nu.p.(Intercept) tau.p.(Intercept) \n 226.347632 -2.922923 0.000000 2.302585 \n\n## starting values using full predictors\nm <- gamlss2(f, data = abdom, family = BCT,\n start = fitted(m))\n\nGAMLSS-RS iteration 1: Global Deviance = 4902.0767 eps = 0.372276 \nGAMLSS-RS iteration 2: Global Deviance = 4775.8465 eps = 0.025750 \nGAMLSS-RS iteration 3: Global Deviance = 4775.0302 eps = 0.000170 \nGAMLSS-RS iteration 4: Global Deviance = 4774.9582 eps = 0.000015 \nGAMLSS-RS iteration 5: Global Deviance = 4774.9519 eps = 0.000001 \n\n## same with\nm <- gamlss2(f, data = abdom, family = BCT,\n start = m)\n\nGAMLSS-RS iteration 1: Global Deviance = 4774.4683 eps = 0.534345 \nGAMLSS-RS iteration 2: Global Deviance = 4770.229 eps = 0.000887 \nGAMLSS-RS iteration 3: Global Deviance = 4770.1663 eps = 0.000013 \nGAMLSS-RS iteration 4: Global Deviance = 4770.1554 eps = 0.000002", "crumbs": [ "Reference", "gamlss2"