Higher-Order Configural Frequency Analysis of Groups of Variables: Dependencies in Test Data

In person-oriented research, Configural Frequency Analysis (CFA) is usually employed to identify those sectors of the data space that contradict a priori hypotheses concerning the structure of variables. In this chapter, the distinction is made between two groups of variables that, in standard CFA, are hypothesized to be completely independent of each other. An approach is presented in which first- and higher-order interactions among variables from the two variable groups are taken into account. Local deviations from such a model suggest that interactions exist higher than the ones taken into account. The interpretation of these deviations can be performed with the aid of functional CFA, that is, based on a search for interactions that make the local deviations disappear. In a data example, it is shown that, in scales that result from factor analysis, there can still be dependencies at levels higher than specified by covariances. The issues of the roles played by the variable groups and of type/antitype patterns are discussed.