Testing Thurstonian Case V ranking models using posterior predictive checks

This paper presents the results of a Monte Carlo study which investigates the validity of the method of posterior predictive checks (PPC) for testing the fit of a Thurstonian Case V ranking model. The PPC method is employed as an alternative to standard goodness-of-fit tests which are of limited use even when the number of items to be ranked is small. Several test quantities are formed to assess the fit of the Case V ranking model to data for various sample sizes and for two types of violations of the Case V assumptions: heterogeneous stimulus variances and rankers from different populations. The study concludes that the PPC method is useful in detecting local and global misfits of a Thurstonian Case V model, even when the ranking data are sparse.