The pp_validate function is based on the methods described in
Cook, Gelman, and Rubin (2006) for validating software developed to fit
particular Bayesian models. Here we take the perspective that models
themselves are software and thus it is useful to apply this validation
approach to individual models.
pp_validate(object, nreps = 20, seed = 12345, ...)A fitted model object returned by one of the
rstanarm modeling functions. See stanreg-objects.
The number of replications to be performed. nreps must be
sufficiently large so that the statistics described below in Details are
meaningful. Depending on the model and the size of the data, running
pp_validate may be slow. See also the Note section below for advice
on avoiding numerical issues.
A seed passed to Stan to use when refitting the model.
Currently ignored.
A ggplot object that can be further customized using the ggplot2 package.
We repeat nreps times the process of simulating parameters and data
from the model and refitting the model to this simulated data. For each of
the nreps replications we do the following:
Refit the model but without conditioning on the data (setting
prior_PD=TRUE), obtaining draws \(\theta^{true}\)
from the prior distribution of the model parameters.
Given \(\theta^{true}\), simulate data \(y^\ast\)
from the prior predictive distribution (calling
posterior_predict on the fitted model object obtained in step
1).
Fit the model to the simulated outcome \(y^\ast\), obtaining parameters \(\theta^{post}\).
For any individual parameter, the quantile of the "true" parameter value with respect to its posterior distribution should be uniformly distributed. The validation procedure entails looking for deviations from uniformity by computing statistics for a test that the quantiles are uniformly distributed. The absolute values of the computed test statistics are plotted for batches of parameters (e.g., non-varying coefficients are grouped into a batch called "beta", parameters that vary by group level are in batches named for the grouping variable, etc.). See Cook, Gelman, and Rubin (2006) for more details on the validation procedure.
Cook, S., Gelman, A., and Rubin, D. (2006). Validation of software for Bayesian models using posterior quantiles. Journal of Computational and Graphical Statistics. 15(3), 675--692.
pp_check for graphical posterior predictive checks and
posterior_predict to draw from the posterior predictive
distribution.
color_scheme_set to change the color scheme of the
plot.
# NOT RUN {
if (!exists("example_model")) example(example_model)
try(pp_validate(example_model)) # fails with default seed / priors
# }
# NOT RUN {
# }
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