SHOULD WE CONSTRAIN THE THRESHOLDS IN FACTOR ANALYSIS OF RATING SCALE RESPONSES?

In factor analysis of ordinal variables, category thresholds determine the values of a hypothetical latent response at which a transition to a higher response option occurs. In general, category thresholds are estimated as free parameters. In the Rasch measurement theory framework, the rating -scale model has been proposed that prescribes equal sets of distances between category thresholds for all items. As a factor analytic parallel, I propose a model with a constrained threshold structure (FACTS). The application of the model is illustrated with a real data example. A simulation study showed that the thresholds are estimated more accurately with the FACTS model than with the standard unconstrained model for different sample sizes, test lengths, and number of response categories. In addition, the likelihood ratio test generally showed good power in comparing the two models. Because the FACTS model performs well and provides a meaningful interpretation of category thresholds, it may be used routinely in factor analysis of categorical item responses.