Factor analysis of ordinal variables: a comparative study

Abstract

The paper considers different approaches to the factor analysis (FA) for ordinal data. In some studies it is neces­sary to find a latent variable behind the observed indicators measured on an ordinal scale. Classical factor analysis cannot be applied to those indicators as it is built on the Pearson correlation coefficient which is only applicable to in­terval variables. So the researcher faces a choice: to treat the ordinal variables as the interval ones, to dichotomize ordinal variables or to use special techniques for ordinal indicators such as replacing the correlation matrix or using Categorical principal components analysis (CatP­CA). The study is based on a theoretical comparison of assumptions that under­pin the algorithms of each applications and a statistical experiment and pro­vides an answer to the question which of the above­mentioned factorization approaches is optimal for indentifying latent variables measured by ordinal in­dicators on a 3­point, 5­point or 10­point scale.