ggmModSelect: Unregularized GGM model search

In qgraph: Graph Plotting Methods, Psychometric Data Visualization and Graphical Model Estimation

Unregularized GGM model search

Description

This function will search for an optimal Gaussian graphical model by minimizing the (extended) Bayesian information criterion of unregularized GGM models. Selecting unregularized GGMs according to EBIC has been shown to converge to the true model (Foygel & Drton, 2010). The algorithm starts with refitting models from the glassopath, and subsequently adds and removes edges until EBIC can no longer be improved (see details). Note, contrary to EBICglasso, the default for the EBIC hyperparameter gamma is set to 0, indicating BIC model selection.

Usage

ggmModSelect(S, n, gamma = 0, start = c("glasso", "empty", "full"), stepwise = TRUE, 
  considerPerStep = c("subset", "all"), verbose = TRUE, nCores = 1, checkPD = TRUE, 
  criterion = 'ebic', ...)

Arguments

S	A covariance or correlation matrix
n	Sample size used in computing S
gamma	EBIC tuning parameter. 0 (default) leads to BIC model selection. 0.25 or 0.5 are typical choices for more conservative model selection.
start	What model should stepwise search start from? "glasso" to first run glasso to obtain the best fitting model, "empty" for an empty network, "full" for a saturated network, or a matrix encoding the starting network.
stepwise	Logical indicating if stepwise model search should be used.
considerPerStep	"subet" to only consider changing edges that previously indicated improvement in EBIC, unless changing no edge indicated an improvement to EBIC, in which case all edges are again considered (see details). "all" will consider changing all edges at every step.
verbose	Logical, should progress reports be printed to the console?
nCores	The number of cores to use in testing models.
checkPD	If TRUE, the function will check if S is positive definite and return an error if not. It is not advised to use a non-positive definite matrix as input as (a) that can not be a covariance matrix and (b) glasso can hang if the input is not positive definite.
criterion	String indicating an output of ggmFit to be minimized
...	Arguments sent to glasso

Details

The full algorithm is as follows:

1. Run glasso to obtain 100 models

2. Refit all models without regularization

3. Choose the best according to EBIC

4. Test all possible models in which one edge is changed (added or removed)

5. If no edge can be added or changed to improve EBIC, stop here

6. Change the edge that best improved EBIC, now test all other edges that would have also lead to an increase in EBIC again

7. If no edge can be added or changed to improve EBIC, go to 4, else, go to 6.

When stepwise = FALSE, steps 4 to 7 are ignored. When considerPerStep = "all", all edges are considered at every step. Note that this algorithm is very slow in higher dimensions (e.g., above 30-40 nodes). Note that EBIC computation is slightly different as in EBICglasso and instead follows the implementation in Lavaan.

Value

A list with the following elements:

graph	The optimal partial correlation network
EBIC	EBIC corresponding to optimal network.

Author(s)

Sacha Epskamp

References

Foygel, R., & Drton, M. (2010). Extended Bayesian information criteria for Gaussian graphical models. In Advances in neural information processing systems (pp. 604-612).

Examples

## Not run: 
# Load data:
library("psych")
data(bfi)

# Compute polychoric correlations:
corMat <- cor_auto(bfi[,1:25])

# Optimize network:
Results <- ggmModSelect(corMat, nrow(bfi), gamma = 0.5, nCores = 8)

# Plot results:
qgraph(Results$graph, layout = "spring", cut = 0)

## End(Not run)

qgraph documentation built on Nov. 3, 2023, 5:07 p.m.