Two Studies of Specification Error in Models for Categorical Latent Variables

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities. Keywords: entropyinformation matrixlatent class analysislatent Markov modelspecification error Notes 1Tables for the 500 and 1,000 sample size conditions are available from the authors on request. 2The number of random starts for the models used in this study were 100. The number of final stage optimization steps was 10. These settings were used to ensure that estimates were not the result of problems with local maxima. 3In the Mplus program, this column is labeled as “% Sig” giving the proportion over the number of replications in which the null hypothesis is rejected when it is true (Muthén & Muthén, 1998–2007).