Latent class model diagnostics - a review and some proposals

This contribution has two purposes. First, to review established methods for latent class model diagnostics and, second, to present and discuss less well-known methods. To the first group belong: (a) overall goodness-of-fit tests using, for large samples, the asymptotic chi-square approximation (Pearson, likelihood ratio, Read-Cressie power divergence statistic) and, for sparse data, resampling techniques such as parametric bootstrap; (b) residual analysis of the pattern frequencies for which also bootstrapping their reference distributions in the presence of smaller samples is recommended. Less well-known are (a) a chi-square goodness-of-fit test not being based on the full information provided by the pattern frequencies but rather using partial information available from lower-order marginals of the contingency table formed by the items, (b) a simple test for the odds ratios of pairs of items, (c) the Rudas-Clogg-Lindsay index of lack of fit of which (d) a new variant is considered, too. The methods are applied to both generated and empirical data to demonstrate their usefulness in latent class model diagnosis.