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index.Rmd
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---
output: github_document
bibliography: inst/REFERENCES.bib
---
```{r, echo = FALSE, message=F}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.path = "man/figures/README-",
dev = "png",
dpi = 500,
fig.align = "center",
knitr::opts_chunk$set(comment = NA)
)
library(ggplot2)
library(BGGM)
```
# Bayesian Gaussian Graphical Models <img src="man/figures/logo.png" align="right" alt="" width="150" />
<!-- badges: start -->
[](https://cran.r-project.org/package=BGGM)
[](https://cran.r-project.org/package=BGGM)
[](https://travis-ci.org/donaldRwilliams/BGGM)
<!-- badges: end -->
The `R` package **BGGM** provides tools for making Bayesian inference in
Gaussian graphical models [GGM, @williams2020bggm]. The methods are organized around
two general approaches for Bayesian inference: (1) estimation and (2) hypothesis
testing. The key distinction is that the former focuses on either the posterior or posterior
predictive distribution [@Gelman1996a; see section 5 in @rubin1984bayesianly], whereas the
latter focuses on model comparison with the Bayes factor [@Jeffreys1961; @Kass1995].
## <i class="fas fa-cog"></i> Installation
To install the latest release version (`2.1.1`) from CRAN use
```{r gh-installation, eval = FALSE}
install.packages("BGGM")
```
The current developmental version can be installed with
```{r, eval = FALSE}
if (!requireNamespace("remotes")) {
install.packages("remotes")
}
remotes::install_github("donaldRwilliams/BGGM")
```
### <i class="fas fa-skull-crossbones"></i> Dealing with Errors
There are automatic checks for [**BGGM**](https://travis-ci.org/github/donaldRwilliams/BGGM/branches). However, that only checks for Linux and **BGGM** is built on Windows.
The most common installation errors occur on OSX. An evolving guide to address these
issues is provided in the [Troubleshoot Section](https://donaldrwilliams.github.io/BGGM/articles/installation.html).
## <i class="fas fa-clipboard-list"></i> Overview
The methods in **BGGM** build upon existing algorithms that are well-known in the literature.
The central contribution of **BGGM** is to extend those approaches:
1. Bayesian estimation with the novel matrix-F prior distribution [@Mulder2018]
+ Estimation [@Williams2019]
2. Bayesian hypothesis testing with the matrix-F prior distribution [@Williams2019_bf]
+ [Exploratory hypothesis testing](https://github.com/donaldRwilliams/BGGM#Exploratory)
+ [Confirmatory hypothesis testing](https://github.com/donaldRwilliams/BGGM#confirmatory)
3. Comparing Gaussian graphical models [@Williams2019; @williams2020comparing]
+ [Partial correlation differences](https://github.com/donaldRwilliams/BGGM#partial-correlation-differences)
+ [Posterior predictive check](https://github.com/donaldRwilliams/BGGM#posterior-predictive-check)
+ [Exploratory hypothesis testing](https://github.com/donaldRwilliams/BGGM#exploratory-groups)
+ [Confirmatory hypothesis testing](https://github.com/donaldRwilliams/BGGM#confirmatory-groups)
4. Extending inference beyond the conditional (in)dependence structure [@Williams2019]
+ [Predictability](https://github.com/donaldRwilliams/BGGM#predictability)
+ [Posterior uncertainty intervals](https://github.com/donaldRwilliams/BGGM#posterior-uncertainty) for the
partial correlations
+ [Custom Network Statistics](https://github.com/donaldRwilliams/BGGM#custom-network-statistics)
The computationally intensive tasks are written in `c++` via the `R` package **Rcpp** [@eddelbuettel2011rcpp] and the `c++` library **Armadillo** [@sanderson2016armadillo]. The Bayes factors are computed with the `R` package **BFpack** [@mulder2019bfpack]. Furthermore, there are plotting functions
for each method, control variables can be included in the model (e.g., `~ gender`),
and there is support for missing values (see `bggm_missing`).
## Supported Data Types
* **Continuous**: The continuous method was described in @Williams2019. Note that
this is based on the customary [Wishart distribution](https://en.wikipedia.org/wiki/Wishart_distribution).
* **Binary**: The binary method builds directly upon @talhouk2012efficient
that, in turn, built upon the approaches of @lawrence2008bayesian and
@webb2008bayesian (to name a few).
* **Ordinal**: The ordinal methods require sampling thresholds. There are two approach
included in **BGGM**. The customary approach described in @albert1993bayesian
(the default) and the 'Cowles' algorithm described in @cowles1996accelerating.
* **Mixed**: The mixed data (a combination of discrete and continuous) method was introduced
in @hoff2007extending. This is a semi-parametric copula model
(i.e., a copula GGM) based on the ranked likelihood. Note that this can be used for
*only* ordinal data (not restricted to "mixed" data).
## <i class="fas fa-folder-open"></i> Illustrative Examples
There are several examples in the [Vignettes](https://donaldrwilliams.github.io/BGGM/articles/) section.
## <i class="fas fa-play-circle"></i> Basic Usage
It is common to have some combination of continuous and discrete (e.g., ordinal, binary, etc.) variables. **BGGM** (as of version `2.0.0`) can readily be used for these kinds of data. In this example, a model is fitted for the `gss` data in **BGGM**.
### Visualize
The data are first visualized with the **psych** package, which readily shows the data are "mixed".
```r
# dev version
library(BGGM)
library(psych)
# data
Y <- gss
# histogram for each node
psych::multi.hist(Y, density = FALSE)
```
### Fit Model
A Gaussian copula graphical model is estimated as follows
```r
fit <- estimate(Y, type = "mixed")
```
`type` can be `continuous`, `binary`, `ordinal`, or `mixed`. Note that `type` is a misnomer, as the data can consist of *only* ordinal variables (for example).
### Summarize Relations
The estimated relations are summarized with
```r
summary(fit)
#> BGGM: Bayesian Gaussian Graphical Models
#> ---
#> Type: mixed
#> Analytic: FALSE
#> Formula:
#> Posterior Samples: 5000
#> Observations (n): 464
#> Nodes (p): 7
#> Relations: 21
#> ---
#> Call:
#> estimate(Y = Y, type = "mixed")
#> ---
#> Estimates:
#> Relation Post.mean Post.sd Cred.lb Cred.ub
#> INC--DEG 0.463 0.042 0.377 0.544
#> INC--CHI 0.148 0.053 0.047 0.251
#> DEG--CHI -0.133 0.058 -0.244 -0.018
#> INC--PIN 0.087 0.054 -0.019 0.196
#> DEG--PIN -0.050 0.058 -0.165 0.062
#> CHI--PIN -0.045 0.057 -0.155 0.067
#> INC--PDE 0.061 0.057 -0.050 0.175
#> DEG--PDE 0.326 0.056 0.221 0.438
#> CHI--PDE -0.043 0.062 -0.162 0.078
#> PIN--PDE 0.345 0.059 0.239 0.468
#> INC--PCH 0.052 0.052 -0.052 0.150
#> DEG--PCH -0.121 0.056 -0.228 -0.012
#> CHI--PCH 0.113 0.056 0.007 0.224
#> PIN--PCH -0.080 0.059 -0.185 0.052
#> PDE--PCH -0.200 0.058 -0.305 -0.082
#> INC--AGE 0.211 0.050 0.107 0.306
#> DEG--AGE 0.046 0.055 -0.061 0.156
#> CHI--AGE 0.522 0.039 0.442 0.594
#> PIN--AGE -0.020 0.054 -0.122 0.085
#> PDE--AGE -0.141 0.057 -0.251 -0.030
#> PCH--AGE -0.033 0.051 -0.132 0.063
#> ---
```
The summary can also be plotted
```r
plot(summary(fit))
```
### Graph Selection
The graph is selected and plotted with
```r
E <- select(fit)
plot(E, node_size = 12,
edge_magnify = 5)
```
The Bayes factor testing approach is readily implemented by changing `estimate` to `explore`.
## <i class="fas fa-pen-square"></i> References