4 - Global models of CFA: applications and examples

Summary

Zero order CFA

Zero order CFA (Lienert and von Eye 1984a, 1985; von Eye and Lienert, in press) is applied to determine if there are effects in a given data set. To answer this question, expected frequencies are estimated under the following assumptions:

1. (1) There are no main effects; the variables under study are distributed according to a joint uniform sampling distribution.

2. (2) There are no interactions; the variables under study are totally independent.

In other words, zero order CFA assumes no effects whatsoever in the contingency table under study. Deviations from an overall uniform distribution are assumed random in nature. Therefore, zero order CFA can be viewed as an omnibus test sensitive to any kind of effect. Types in zero order CFA indicate that main effects, interactions, or both have led to agglomerations of cases in certain configurations. These agglomerations are similar to clusters of cases that are identified with, for example, Ward's (1963) method. Both CFA and Ward's method define clusters as spatially close cases. Both methods identify agglomerations of cases without reference to underlying main effects or interactions of variables. Because of this, zero order CFA is also called configural cluster analysis, and zero order types are called clusters. Accordingly, anticlusters indicate relatively sparsely frequented sectors of the data space that are due also to main effects or interactions.