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A Monte Carlo simulation was used to determine which assumptions for orderedcategorical data, continuity vs. discrete categories, most frequentlyidentifies the underlying factor structure when a response variable has fiveordered categories. The impact of infrequently endorsed response categories wasalso examined, a condition that has not been fully explored. The typical methodfor overcoming infrequently endorsed categories in applied research is tocollapse response options with adjacent categories resulting in less responsecategories that are endorsed more frequently, but this approach may notnecessarily provide useful information. Response category endorsement issueshave been studied in Item Response Theory, but this issue has not beenaddressed in classification analyses nor has fit measure performance beenexamined under these conditions. We found that the performance of commonly usedfit statistics to identify the true number of latent class depends on thewhether continuity is assumed, sample size, and convergence. Fit statisticsperformed best when the five response options are assumed to be categorical.However, in situations with lower sample sizes and when convergence is anissue, assuming continuity and using the adjusted Lo-Mendell-Rubin likelihoodratio test may be useful.

Identifying latent classes with ordered categorical indicators