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.
posterior_predictive(object, new_X = NULL)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.
object of class "poisreg" (usually, the result of a call to sample_bpr).
(optional) a data frame in which to look for variables with which to predict.
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.