A misspecification test for finite-mixture logistic models for clustered binary and ordered responses

An alternative to using normally distributed random effects in modeling clustered binary and ordered responses is based on using a finite-mixture. This approach gives rise to a flexible class of generalized linear mixed models for item responses, multilevel data, and longitudinal data. A test of misspecification for these finite-mixture models is proposed which is based on the comparison between the Marginal and the Conditional Maximum Likelihood estimates of the fixed effects as in the Hausman’s test. The asymptotic distribution of the test statistic is derived; it is of chi-squared type with a number of degrees of freedom equal to the number of covariates that vary within the cluster. It turns out that the test is simple to perform and may also be used to select the number of components of the finite-mixture, when this number is unknown. The approach is illustrated by a series of simulations and three empirical examples covering the main fields of application.