posterior_predictive {bpr}

Compute Posterior Predictive Distribution

Description

This function is a method for class poisreg. Compute the posterior predictive distribution and summary statistics for posterior check of the model; optionally, it also computes the predictive distribution with new values of the explanatory variables.

Usage

posterior_predictive(object, new_X = NULL)

Arguments

object

object of class "poisreg" (usually, the result of a call to sample_bpr).

new_X

(optional) a data frame in which to look for variables with which to predict.

Value

The call to this function returns an object of S3 class posterior_check. The object is a list with the following elements:

data : the component from object (list with covariates X and response variable y).

y_pred : matrix of dimension [n, iter] (with n sample size), each column is a draw from the posterior predictive distribution.

y_MAP_pred : vector of length n containing a draw from the posterior distribution obtained using the maximum a posteriori estimates (MAP) of the parameters.

diagnostics : list containing 2 elements: CPO, i.e. the Conditional Predictive Ordinate (Gelfand et al. 1992); and LPML, i.e. the logarithm of the pseudo-marginal likelihood (Ibrahim et al. 2014).

newdata : if the matrix new_X of new values of the covariates is provided, list of three elements:

• new_X : the provided matrix of explanatory variables;

• y_newdata : a matrix of dimension [nrow(new_X), iter], each column is a draw from the posterior predictive distribution using new_X;

• y_MAP_newdata : vector of length nrow(new_X) containing a draw from the posterior distribution obtained using the MAP estimate of the parameters, computed on the new data new_X.

perc_burnin : the component from object.

References

Gelfand, A., Dey, D. and Chang, H. (1992), Model determination using predictive distributions with implementation via sampling-based-methods (with discussion), in ‘Bayesian Statistics 4’, University Press.

Ibrahim, J. G., Chen, M.H. and Sinha, D. (2014), Bayesian Survival Analysis, American Cancer Society.