Factor analysis of ordinal variables: a comparative study
Keywords:latent variables, factor analysis, ordinal variables, Principal component analysis, Categorical Principal Components Analysis
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.