Model Criticism in Latent Space

The extended model(s) can again be subjected to criticism, and the process continues until a satisfactory model is found (O'Hagan, 2003). Model criticism is contrasted with model comparison in that model criticism assesses a single model, while model comparison deals with at least two models to decide which model is a better fit. Model comparison can be applied to compare the original and the extended model after model criticism and extension (O'Hagan, 2003, p. 2). Most work on model criticism makes use of the idea that "if the model fits, then replicated data generated under the model should look similar to observed data" (Gelman et al., 2004, p. 165). In contrast, in this paper we focus on the idea that for latent variable models, we can probabilistically pull back the data into the space of the latent variables, and carry out model criticism in that space.