Bayesian Posterior Predictive Checks for Complex Models

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Bayesian Estimation and Inference (2015, methodology): “However, small PPP values (e.g., .05) indicate poor model fit because this means that the observed data fit better than generated data very infrequently (e.g., less than 5% of the time), prompting model respecification (Lynch & Western, 2004).”
7. Multivariate Decomposition for Hazard Rate Models (2009, methodology): “Under this approach, the decomposition is carried out M times, resulting in a posterior predictive distribution for each quantity in the decomposition (e.g., see Lynch and Western 2004).”
Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables (2009, methodology): “Specifically, the observed item associations were compared to what is predicted by the model (for a general description, see Gelman, Carlin, Stern, & Rubin, 1995; Gelman, Meng, & Stern, 1996; Lynch & Western, 2004 ).”