A Functional Approach to Configural Frequency Analysis

Alexander von Eye, Patrick Mair

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung


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
Seiten (von - bis)161 - 173
FachzeitschriftAustrian Journal of Statistics
PublikationsstatusVeröffentlicht - 1 Nov. 2008