predictability {BGGM}

Predictability: Bayesian Variance Explained (R2)

Description

Compute nodewise predictability or Bayesian variance explained (R2 Gelman et al. 2019). In the context of GGMs, this method was described in Williams (2018).

Usage

predictability(
  object,
  select = FALSE,
  cred = 0.95,
  BF_cut = 3,
  iter = NULL,
  progress = TRUE,
  ...
)

Arguments

object

object of class estimate or explore

select

logical. Should the graph be selected ? The default is currently FALSE.

cred

numeric. credible interval between 0 and 1 (default is 0.95) that is used for selecting the graph.

BF_cut

numeric. evidentiary threshold (default is 3).

iter

interger. iterations (posterior samples) used for computing R2.

progress

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

...

currently ignored.

Value

An object of classes bayes_R2 and metric, including

• scores A list containing the posterior samples of R2. The is one element

  for each node.

Note

Binary and Ordinal Data:

R2 is computed from the latent data.

Mixed Data:

The mixed data approach is somewhat ad-hoc see for example p. 277 in Hoff (2007). This is becaue uncertainty in the ranks is not incorporated, which means that variance explained is computed from the 'empirical' CDF.

Model Selection:

Currently the default to include all nodes in the model when computing R2. This can be changed (i.e., select = TRUE), which then sets those edges not detected to zero. This is accomplished by subsetting the correlation matrix according to each neighborhood of relations.

References

Gelman A, Goodrich B, Gabry J, Vehtari A (2019). “R-squared for Bayesian Regression Models.” American Statistician, 73(3), 307–309. ISSN 15372731.

Hoff PD (2007). “Extending the rank likelihood for semiparametric copula estimation.” The Annals of Applied Statistics, 1(1), 265–283. doi:10.1214/07-AOAS107.

Williams DR (2018). “Bayesian Estimation for Gaussian Graphical Models: Structure Learning, Predictability, and Network Comparisons.” arXiv. doi:10.31234/OSF.IO/X8DPR.

Examples

# data
Y <- ptsd[,1:5]

fit <- estimate(Y, iter = 250, progress = FALSE)

r2 <- predictability(fit, select = TRUE,
                     iter = 250, progress = FALSE)

# summary
r2