Configural Frequency Analysis Under Multinormality in Incomplete Tables

Configural Frequency Analysis (CFA) allows researchers to identify those cells in a cross-classification that contain more or fewer cases than expected under a suitably specified base model. In most applications, the expected cell frequencies are estimated using log-linear models. These models are applied to cross-classifications of categorical variables. For logical, ethical, or design-related reasons, cross-classifications can contain structural zeros, that is, cells that cannot contain cases by definition. In the present chapter, three issues are discussed. The first concerns the presence of structural zeros. The application of existing methods of dealing with structural zeros is illustrated. The second issue concerns the case in which the cross-classification is spanned by variables that result from categorization of normally distributed variables. For this case, as well, methods exist to take the information into account that comes from a multinormal distribution. The third issue, new to the method of CFA, involves joint application of methods for log-linear modeling of normally distributed variables in cross-classifications with structural zeros. This application is illustrated in a real-world data example.