Factor Analysis for Categorical Data

Summary The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is restricted to the case of ordered categories where the latent variables are continuous. It is argued that the choice of model should be made from a restricted set which includes two existing models as special cases. A new method is proposed together with a simple approximate technique of fitting for the one-factor model. The paper concludes with an evaluation of existing methods and makes some suggestions about the direction which future research should take.