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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.