Two Kinds of Factor Analysis For Ordered Categorical Variables

In factor analysis of variables with ordered categories, latent response variables are assumed. These latent response variables may be either discrete or continuous. Different assumptions regarding the latent response variables lead to different kinds of factor models. A convenient assumption is to postulate that the latent response variables are continuous and normally distributed. In this paper the relationship between two kinds of factor analysis is discussed. It is shown, mathematically, that factor analysis of data with integer values only (the category numbers) is very sensitive to the skewness of the manifest variables and the size of the factor loadings. This was also shown by Olsson (1979b) by a simulation study with "perfect" data. Further, in the paper we propose a simple estimation procedure for the factor model of categorical variables, in which it is assumed that the latent response variables are normally distributed.