The `R`

package **BGGM** provides tools for making Bayesian inference in
Gaussian graphical models (GGM). The methods are organized around two general approaches for
Bayesian inference: (1) estimation \insertCiteWilliams2019BGGM and (2) hypothesis testing
\insertCiteWilliams2019_bfBGGM. The key distinction is that the former focuses on either the
posterior or posterior predictive distribution, whereas the latter focuses on model comparison
with the Bayes factor.

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:

Bayesian estimation with the novel matrix-F prior distribution \insertCiteMulder2018BGGM.

Estimation

`estimate`

.

Bayesian hypothesis testing with the novel matrix-F prior distribution \insertCiteMulder2018BGGM.

Exploratory hypothesis testing

`explore`

.Confirmatory hypothesis testing

`confirm`

.

Comparing GGMs \insertCitewilliams2020comparingBGGM

Partial correlation differences

`ggm_compare_estimate`

.Posterior predictive check

`ggm_compare_ppc`

.Exploratory hypothesis testing

`ggm_compare_explore`

.Confirmatory hypothesis testing

`ggm_compare_confirm`

.

Extending inference beyond the conditional (in)dependence structure

Predictability with Bayesian variance explained \insertCitegelman_r2_2019BGGM

`predictability`

.Posterior uncertainty in the partial correlations

`estimate`

.Custom Network Statistics

`roll_your_own`

.

Furthermore, the computationally intensive tasks are written in `c++`

via the `R`

package **Rcpp** \insertCiteeddelbuettel2011rcppBGGM and the `c++`

library **Armadillo** \insertCitesanderson2016armadilloBGGM, there are plotting functions
for each method, control variables can be included in the model, and there is support for
missing values `bggm_missing`

.

**Supported Data Types**:

Continuous: The continuous method was described \insertCite@in @Williams2019_bf;textualBGGM.

Binary: The binary method builds directly upon \insertCite@in @talhouk2012efficient;textualBGGM, that, in turn, built upon the approaches of \insertCitelawrence2008bayesian;textualBGGM and \insertCitewebb2008bayesian;textualBGGM (to name a few).

Ordinal: Ordinal data requires sampling thresholds. There are two approach included in

**BGGM**: (1) the customary approach described in \insertCite@in @albert1993bayesian;textualBGGM (the default) and the 'Cowles' algorithm described in \insertCite@in @cowles1996accelerating;textualBGGM.Mixed: The mixed data (a combination of discrete and continuous) method was introduced \insertCite@in @hoff2007extending;textualBGGM. This is a semi-parametric copula model (i.e., a copula GGM) based on the ranked likelihood. Note that this can be used for data consisting entirely of ordinal data.

**Additional Features**:

The primary focus of `BGGM`

is Gaussian graphical modeling (the inverse covariance matrix).
The residue is a suite of useful methods not explicitly for GGMs:

Bivariate correlations for binary (tetrachoric), ordinal (polychoric), mixed (rank based), and continous (Pearson's) data

`zero_order_cors`

.Multivariate regression for binary (probit), ordinal (probit), mixed (rank likelihood), and continous data (

`estimate`

).Multiple regression for binary (probit), ordinal (probit), mixed (rank likelihood), and continous data (e.g.,

`coef.estimate`

).

**Note on Conditional (In)dependence Models for Latent Data**:

All of the data types (besides continuous) model latent data. That is, unoboserved data that is
assumed to be Gaussian distributed. For example, a tetrachoric correlation (binary data) is a
special case of a polychoric correlation (ordinal data). Both relations are between "theorized
normally distributed continuous **latent** variables"
(Wikipedia). In both instances,
the correpsonding partial correlation between observed variables is conditioned
on the remaining variables in the *latent* space. This implies that interpration
is similar to continuous data, but with respect to latent variables. We refer interested users
to \insertCite@page 2364, section 2.2, in @webb2008bayesian;textualBGGM.

**High Dimensional Data?**

**BGGM** was builit specificially for social-behvarioal scientists. Of course, the methods
can be used by all researchers. However, there is *not* support for high-dimensonal data
(i.e., more variables than observations) that are common place in the genetics literature.
These data are rare in the social-behavioral sciences. In the future, support for high-dimensional
data may be added to **BGGM**.

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