Configural Analysis in Component Space

Unless very large samples are available, the number of variables and variable categories that can be simultaneously used in categorical data analysis is small when models are estimated. In this article, an approach is proposed that can help remedy this problem. Specifically, it is proposed to perform, in a first step, principal component analysis or factor analysis. These methods help reduce the dimensionality of the data space without loss of important information. In a second step, sectors are created in the component or factor space. These sectors can, in a third step, be subjected to Configural Frequency analysis (CFA). CFA identifies those sectors that contradict a priori-specified hypotheses. It is also proposed to take into account the ordinal nature of the sectors. In addition, distributional assumptions can be considered. This is illustrated in data examples. Possible extensions of the proposed approach are discussed.