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. (C) 2002 Elsevier Science B.V. All rights reserved.