Consequences of Fitting Nonidentified Latent Class Models

Latent class models are becoming more popular in behavioral research. When models with a large number of latent classes relative to the number of manifest indicators are estimated, researchers must consider the possibility that the model is not identified. It is not enough to determine that the model has positive degrees of freedom. A well-known example is the latent class model with 4 binary indicators and 3 classes. This study shows that nonidentified latent class models can appear to be estimated normally when parameter estimates become fixed to a boundary of the parameter space. The consequences for the posterior probabilities of class membership given observed data are examined, along with the potential to bias predictions of distal outcomes contingent on class membership. Keywords: biasboundary solutionsidentificationlatent class analysisposterior probabilities Notes 1Specifically, the matrix of the partial derivatives of the likelihood function evaluated for each of the response patterns (15 nonredundant response patterns × 14 estimated model parameters) lacks full rank (rank = 13; Goodman, 1974). aFor models with 0 boundary parameters, the information matrix was always flagged as being nonpositive definite. 2For this example, of the 16 possible data patterns, 6 are deterministically mapped onto a specific latent class. aAverage maximum class bias represented the average of the largest class bias seen in each data set. The largest distal outcome bias was not always observed for the same latent class (i.e., all high, all low, high/low). aThree of these models had a nonpositive definite information matrix.