prior_belief_var function

Prior Belief Graphical VAR

prior_belief_var(
  Y,
  prior_temporal = NULL,
  post_odds_cut = 3,
  est_ggm = TRUE,
  prior_ggm = NULL,
  progress = TRUE,
  ...
)

Arguments

• Y: Matrix (or data frame) of dimensions n

  (observations) by p (variables/nodes).

• prior_temporal: Matrix of dimensions p by p, encoding the prior odds for including each relation in the temporal graph (see 'Details'). If null a matrix of 1's is used, resulting in equal prior odds.

• post_odds_cut: Numeric. Threshold for including an edge (defaults to 3). Note post_odds refers to posterior odds.

• est_ggm: Logical. Should the contemporaneous network be estimated (defaults to TRUE)?

• prior_ggm: Matrix of dimensions p by p, encoding the prior odds for including each relation in the graph (see 'Details'). If null a matrix of 1's is used, resulting in equal prior odds.

• progress: Logical. Should a progress bar be included (defaults to TRUE) ?

• ...: Additional arguments passed to explore. Ignored if prior_ggm = FALSE.

Returns

An object including (est_ggm = FALSE):

• adj: Adjacency matrix
• post_prob: Posterior probability for the alternative hypothesis.

An object including (est_ggm = TRUE):

• adj_temporal: Adjacency matrix for the temporal network.
• post_prob_temporal: Posterior probability for the alternative hypothesis (temporal edge)
• adj_ggm: Adjacency matrix for the contemporaneous network (ggm).
• post_prob_ggm: Posterior probability for the alternative hypothesis (contemporaneous edge)

Details

Technically, the prior odds is not for including an edge in the graph, but for (H1)/p(H0), where H1 captures the hypothesized edge size and H0 is the null model \insertCite @see Williams2019_bfBGGM. Accordingly, setting an entry in prior_ggm to, say, 10, encodes a prior belief that H1 is 10 times more likely than H0. Further, setting an entry in prior_ggm or prior_var to 1 results in equal prior odds (the default in select.explore).

Note

The returned matrices are formatted with the rows indicating the outcome and the columns the predictor. Hence, adj_temporal[1,4] is the temporal relation of node 4 predicting node 1. This follows the convention of the vars package (i.e., Acoef).

Further, in order to compute the Bayes factor the data is standardized (mean = 0 and standard deviation = 1).

Examples

# affect data from 1 person
# (real data)
y <- na.omit(subset(ifit, id == 1)[,2:7])
p <- ncol(y)

# random prior graph
# (dont do this in practice!!)
prior_var = matrix(sample(c(1,10),
                   size = p^2, replace = TRUE),
                   nrow = p, ncol = p)

# fit model
fit <- prior_belief_var(y,
                        prior_temporal = prior_var,
                        post_odds_cut = 3)