Bandeen-Roche et al. (1997) (see main entry in Section 4.3). Proposes a method of model assessment where (i) a latent class is assigned to each unit at random, based on the posterior class probabilities from a fitted model, and (ii) conditional independence of items of each other and of the covariates is examined, treating the assigned class as known. This is thus essentially a version of the conditional item bias methods discussed in Section 3, but using an initial latent class model to create the conditioning variable (a proxy for the true value of the latent class).
Glas (1998): Testing for (partial) DIF in general IRT models using Lagrange multiplier tests (score tests). The tests are thus similar in spirit to the “modification indices” in linear factor analysis. Illustrated by a simulation and real example.
Cheung and Rensvold (2002): discuss goodness-of-fit tests and fit statistics for testing for measurement invariance. The fit statistics are the ones used in structural equation modelling. A simulation study compares 20 of those measures of fit.
Formann (2003): In the context of a specific critique of paper by Garrett and Zeger (Biometrics, 2000), a useful overview of model identifiability and some methods of model assessment for latent class models.
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