Testing Hypotheses About Methods, Traits, and Communalities in the Direct-Product Model

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Abstract
The direct-product model has been suggested as a procedure for estimating multiplicative effects of traits and methods in multitrait-multimethod matrices. Research on the direct-product model is extended in two ways. First, hierarchically nested models are derived for explicitly testing the overall and specific patterns of method and trait factors. Second, formal tests are developed for the pattern of communalities. These procedures are illustrated with data from Lawler (1967). Index terms: direct-product model, method factors, multiplicative model, multitrait-multimethod matrix, trait factors