Posterior predictive p-values are described by Lee & Song (2003, Appendix C). A posterior predictive p-value should be near near .5 for a correct model, with values toward the extremes of 0 or 1 indicating that a model is not plausible. Gelman, et al. (2013) have a useful discussion of the interpretation of posterior predictive p-values. See also Lee (2007, pages 128-129).