In donaldRwilliams/BGGM: Bayesian Gaussian Graphical Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  dev = "png",
  dpi = 500,
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  knitr::opts_chunk$set(comment = NA)
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library(ggplot2)
library(BGGM)

Bayesian Gaussian Graphical Models

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].

Installation

To install the latest release version (2.1.1) from CRAN use

install.packages("BGGM")    

The current developmental version can be installed with

if (!requireNamespace("remotes")) { 
  install.packages("remotes")   
}   
remotes::install_github("donaldRwilliams/BGGM")

Dealing with Errors

There are automatic checks for BGGM. 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.

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

   • Confirmatory hypothesis testing

3. Comparing Gaussian graphical models [@Williams2019; @williams2020comparing]

   • Partial correlation differences

   • Posterior predictive check

   • Exploratory hypothesis testing

   • Confirmatory hypothesis testing

4. Extending inference beyond the conditional (in)dependence structure [@Williams2019]

   • Predictability

   • Posterior uncertainty intervals for the partial correlations

   • 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.

• 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).

Illustrative Examples

There are several examples in the Vignettes section.

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".

# 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

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

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

plot(summary(fit))

Graph Selection

The graph is selected and plotted with

E <- select(fit)

plot(E, node_size = 12,
     edge_magnify = 5)

The Bayes factor testing approach is readily implemented by changing estimate to explore.

References

donaldRwilliams/BGGM documentation built on April 17, 2024, 5:52 p.m.