Factor Analysis of Categorical Data: Heuristic Potential of Categorical Principal Components Analysis

Abstract

The article offers analysis of factor analysis shortcomings in the analysis of categorical data (measured with ordinal scales). Three obstacles that make statistically improper use of factor analysis when processing sociological data: 1) inability of geometric interpretation of the data matrix in the case of categorical data; 2) the need for data standardization as a condition of factor analysis, which is impossible for ordinal variables, and 3) calculation of dispersion parts explained by obtained factors as the condition for selection of the optimal number of factors. The general principles of categorical principal components analysis that improve mentioned shortcomings of factor analysis, while maintaining its advantages are analyzed: quantification of ordinal variables and calculating the loss function in the obtaining factors. An empirical comparison of heuristic potential of the two methods of processing sociological data on the results of sociological survey is offered.