A Functional Approach to Configural Frequency Analysis

Standard Configural Frequency Analysis (CFA) is a one-step procedure that determines which cells of a cross-classification contradict a base model. The results are possible types/antitypes depending on whether the observed cell frequencies are significantly lower/higher with respect to the base model. Selecting these cells out does not guarantee that the base model fits. Therefore, the role played by these cells for the base model is unclear, and interpretation of types and antitypes can be problematic. In this paper, functional CFA is proposed. This model of CFA pursues two goals simultaneously. First, cells are selected out that constitute types and antitypes. Second, the base model is fit to the data. This is done using an iterative procedure that blanks out individual cells one at a time, until the base model fits or until there are no more cells that can be blanked out. In comparison to standard CFA, functional CFA is shown to be more parsimonious, that is, fewer types and antitypes need to be selected out. The methods are illustrated and compared using data examples from the literature.