Compute the predictive and empirical cross-validated Mahalanobis loss under the random intercept model

Use posterior predictive draws and a sampling-importance resampling (SIR) algorithm to approximate the cross-validated predictive Mahalanobis loss. The empirical Mahalanobis loss is also returned. The values are computed relative to the "best" subset according to minimum empirical Mahalanobis loss. Specifically, these quantities are computed for a collection of linear models that are fit to the Bayesian model output, where each linear model features a different subset of predictors.

Usage

pp_loss_randint(
  post_y_pred,
  post_lpd,
  post_sigma_e,
  post_sigma_u,
  XX,
  YY,
  indicators,
  post_y_pred_sum = NULL,
  K = 10,
  sir_frac = 0.5
)

Arguments

post_y_pred

S x m x n matrix of posterior predictive draws at the given XX covariate values for m replicates per subject

post_lpd

S evaluations of the log-likelihood computed at each posterior draw of the parameters

post_sigma_e

(nsave) draws from the posterior distribution of the observation error SD

post_sigma_u

(nsave) draws from the posterior distribution of the random intercept SD

XX

n x p matrix of covariates at which to evaluate

YY

m x n matrix of response variables (optional)

indicators

L x p matrix of inclusion indicators (booleans) where each row denotes a candidate subset

post_y_pred_sum

(nsave x n) matrix of the posterior predictive draws summed over the replicates within each subject (optional)

K

number of cross-validation folds

sir_frac

fraction of the posterior samples to use for SIR

Value

a list with two elements: pred_loss and emp_loss

for the predictive and empirical loss, respectively, for each subset.