Some remarks on the application of factor analysis to ordered categorical data

Abstract

The purpose of this paper is to clarify the conditions of data, under which the direct application of factor analysis to ordered categorical data may not be appropriate. For this purpose, we conducted two simulation studies, in which the numbers of observations, items, categories and factors were systematically changed, and in which two methods for estimating correlations were used. In these simulations, we examined the effects of the various conditions of data on the reproducibility of the true factor loadings and true number of factors, and on the frequency of improper solutions. Based on the results, several practical suggestions were provided to prevent inappropriate uses of factor analysis for the ordered categorical date; e.g., at least five categories are needed for sound applications of factor analysis.