select.explore: Graph selection for 'explore' Objects
In BGGM: Bayesian Gaussian Graphical Models

select.explore

R Documentation

Graph selection for `explore` Objects

Description

Provides the selected graph based on the Bayes factor \insertCiteWilliams2019_bfBGGM.

Usage

## S3 method for class 'explore'
select(
  object,
  method = c("BF_cut", "BMA"),
  BF_cut = 3,
  prior.prob.H0 = 0.5,
  alternative = "two.sided",
  ...
)

Arguments

`object`	An object of class `explore.default`
`method`	Character string specifying the edge selection method. Options include: `"BF_cut"`: Select edges based on a Bayes factor threshold. This is the original approach described in \insertCiteWilliams2019_bfBGGM. `"BMA"`: Bayesian model averaging based on posterior model probabilities. For each edge, the posterior is a mixture distribution placing mass at zero under the null model and using the posterior under the alternative model otherwise. Reported edges are based on the median of this mixture.
`BF_cut`	Numeric. Evidence threshold for including an edge when `method = "BF_cut"` (defaults to 3). An edge is selected when the posterior probability of the hypothesis exceeds `BF_cut / (BF_cut + 1)`. With the default `prior.prob.H0 = 0.5` this is equivalent to a Bayes factor of `BF_cut` against the competing hypothesis; for other values of `prior.prob.H0` it is a cutoff on the posterior probability.
`prior.prob.H0`	Numeric between 0 and 1. Prior probability assigned to the null hypothesis for each edge (defaults to `0.5`). It is used for the posterior hypothesis probabilities and the edge inclusion probabilities under both `method = "BF_cut"` and `method = "BMA"`. For `alternative = "exhaustive"` the remaining `1 - prior.prob.H0` is split equally over the positive and the negative hypothesis, so that splitting the alternative by sign leaves `P(H_0 \mid Y)` unchanged.
`alternative`	A character string specifying the alternative hypothesis. It must be one of "two.sided" (default), "greater", "less", or "exhaustive". See note for further details.
`...`	Currently ignored.

Details

Exhaustive provides the posterior hypothesis probabilities for a positive, negative, or null relation \insertCite@see Table 3 in @Williams2019_bfBGGM.

method = "BF_cut" selects an edge when its posterior inclusion probability exceeds BF_cut / (BF_cut + 1) (0.75 for BF_cut = 3), and calls an edge null when the posterior probability of the null hypothesis exceeds that same cutoff. With the default prior.prob.H0 = 0.5 this is the Bayes factor threshold of \insertCiteWilliams2019_bfBGGM: BF_cut = 3 selects the edges with a Bayes factor larger than 3. For alternative = "exhaustive" the inclusion probability is 1 - P(H_0 \mid Y) = P(H_+ \mid Y) + P(H_- \mid Y), which equals the inclusion probability of alternative = "two.sided", so both give the same selected edges; a selected edge is labelled positive or negative according to the larger of the two directional probabilities, which are reported in addition. An edge can be assigned to none of the three hypotheses.

method = "BMA" does not use BF_cut: an edge is selected when the median of the model-averaged mixture is nonzero, which corresponds to an inclusion probability above 0.5, so it selects more edges than method = "BF_cut" with the default BF_cut = 3.

method = "BMA" performs Bayesian model averaging using a spike-and-slab style mixture distribution for each edge. The spike corresponds to the null hypothesis (exactly zero partial correlation), whereas the slab corresponds to the posterior under the alternative hypothesis, approximated by a normal distribution for the Fisher-z transformed partial correlation (truncated to the positive or negative half-line for one-sided hypotheses). Posterior model probabilities are computed from the Bayes factors and prior.prob.H0. The selected network is based on the median of this mixture, which is computed exactly (no simulation), so the result is deterministic. For alternative = "exhaustive" the mixture has three states – a spike at zero (H_0), a positive slab (H_+), and a negative slab (H_-) – mixed by the posterior hypothesis probabilities. The model-averaged partial correlations are returned in pcor_mat_zero, and pos_mat/neg_mat/null_mat classify each edge by the sign of that model-averaged median.

Value

The returned object of class select.explore contains a lot of information that is used for printing and plotting the results. For users of BGGM, the following are the useful objects:

alternative = "two.sided"

pcor_mat_zero Selected partial correlation matrix (weighted adjacency).
pcor_mat Partial correlation matrix (posterior mean).
Adj_10 Adjacency matrix for the selected edges.
Adj_01 Adjacency matrix for which there was evidence for the null hypothesis.
incl_prob Matrix of posterior edge inclusion probabilities, P(H_1 \mid Y), based on BF_10 and prior inclusion probability 1 - prior.prob.H0.

alternative = "greater" and "less"

pcor_mat_zero Selected partial correlation matrix (weighted adjacency).
pcor_mat Partial correlation matrix (posterior mean).
Adj_20 Adjacency matrix for the selected edges.
Adj_02 Adjacency matrix for which there was evidence for the null hypothesis (see note).
incl_prob Matrix of posterior probabilities of the one-sided hypothesis against the null, based on BF_20 and prior probability 1 - prior.prob.H0.

alternative = "exhaustive"

post_prob A data frame of the posterior hypothesis probabilities P(H_0 \mid Y), P(H_+ \mid Y), and P(H_- \mid Y) for each relation (a null, positive, or negative partial correlation).

For method = "BF_cut" the following are hard hypothesis assignments; for method = "BMA" they classify the sign of the model-averaged posterior median (pcor_mat_zero), not the most probable hypothesis:
pos_mat Adjacency matrix for positive edges.
neg_mat Adjacency matrix for negative edges.
null_mat Adjacency matrix for null edges (see note).
incl_prob Matrix of posterior edge inclusion probabilities, 1 - P(H_0 \mid Y).
pcor_mat Partial correlation matrix (posterior mean). The weighted adjacency matrices can be computed by multiplying pcor_mat with an adjacency matrix.
pcor_mat_zero Selected partial correlation matrix (weighted adjacency). For method = "BF_cut" this is the posterior mean of the selected edges and zero elsewhere; for method = "BMA" it is the model-averaged matrix, i.e. for each edge the posterior median of the three-state mixture over the null, positive, and negative hypotheses.

Note

Care must be taken with the options alternative = "less" and alternative = "greater". This is because the full parameter space is not included, such, for alternative = "greater", there can be evidence for the "null" when the relation is negative. This inference is correct: the null model better predicted the data than the positive model. But note this is relative and does not provide absolute evidence for the null hypothesis.

References

\insertAllCited

Examples



#################
### example 1 ###
#################

#  data
Y <- bfi[,1:10]

# fit model
fit <- explore(Y, progress = FALSE)

# edge set (Bayes factor threshold)
E <- select(fit,
            alternative = "exhaustive")

# edge set (Bayesian model averaging), with prior P(H0) = 0.5
E <- select(fit,
            method = "BMA",
            alternative = "exhaustive")

BGGM documentation built on Sept. 24, 2026, 9:06 a.m.