  A Monte Carlo simulation was used to determine which assumptions for ordered
categorical data, continuity vs. discrete categories, most frequently
identifies the underlying factor structure when a response variable has five
ordered categories. The impact of infrequently endorsed response categories was
also examined, a condition that has not been fully explored. The typical method
for overcoming infrequently endorsed categories in applied research is to
collapse response options with adjacent categories resulting in less response
categories that are endorsed more frequently, but this approach may not
necessarily provide useful information. Response category endorsement issues
have been studied in Item Response Theory, but this issue has not been
addressed in classification analyses nor has fit measure performance been
examined under these conditions. We found that the performance of commonly used
fit statistics to identify the true number of latent class depends on the
whether continuity is assumed, sample size, and convergence. Fit statistics
performed best when the five response options are assumed to be categorical.
However, in situations with lower sample sizes and when convergence is an
issue, assuming continuity and using the adjusted Lo-Mendell-Rubin likelihood
ratio test may be useful.
