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This study has a didactic purpose to help applied investigators and practitioners to understand the roles of observed categorical data (OCD) in structural equation modeling (SEM) and the appropriate ways of analyzing such data under SPSS AMOS. To that end, the study reviews types of OCD (nominal, ordinal, dichotomous, and polytomous) and their incorporation into SEM under AMOS to play different roles. The study presents two applications from the health and retirement study where Bayesian statistical inference is used to analyze one set of OCD variables serving as endogenous variables with/without groups created by another OCD variable. Besides, the study demonstrates the typical ways of summarizing, reporting, and interpreting the results from Bayesian statistics. The study concludes with summaries of the findings for its intended audience.