Journal
EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT
Volume 79, Issue 1, Pages 19-39Publisher
SAGE PUBLICATIONS INC
DOI: 10.1177/0013164417752008
Keywords
categorical omega; Bayesian estimation; factor analysis; small sample size; prior specification
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When item scores are ordered categorical, categorical omega can be computed based on the parameter estimates from a factor analysis model using frequentist estimators such as diagonally weighted least squares. When the sample size is relatively small and thresholds are different across items, using diagonally weighted least squares can yield a substantially biased estimate of categorical omega. In this study, we applied Bayesian estimation methods for computing categorical omega. The simulation study investigated the performance of categorical omega under a variety of conditions through manipulating the scale length, number of response categories, distributions of the categorical variable, heterogeneities of thresholds across items, and prior distributions for model parameters. The Bayes estimator appears to be a promising method for estimating categorical omega. Mplus and SAS codes for computing categorical omega were provided.
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