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Often times with longitudinal data, the outcome variable may be categorical rather than continuous, such as the Likert-scale measures or certain occurrences of life events like divorce, job loss, or pregnancy. The discrete nature of binary or ordinal variables leads to a violation of distributional assumption, and standard estimation methods may not be appropriate. This study investigates the performance LGM with binary and ordinal indicators under different estimation methods and model misspecifications. Results revealed larger sample size, more time points, and larger number of categories were associated with lower bias, better model fit, and fewer improper solutions for all estimation methods. The performance of WLS and DWLS were relatively more robust to model misspecification than MML.