Testing Nested Additive, Multiplicative, and General Multitrait-Multimethod Models

Abstract

The article gives alternatives to Campbell and O'Connell's (1967) definitions of additive and multiplicative method effects in multitrait-multimethod (MTMM) data. The alternative definitions can be formulated by means of constraints in the parameters of the correlated uniqueness (CU) model (Marsh, 1989), which is first reviewed. The definitions have 2 major advantages. First, they allow the researcher to test for additive and multiplicative method effects in a straightforward manner by simply testing the appropriate constraints. An illustration of these tests is given. Second, the alternative definitions are closely linked to other currently used models. The article shows that CU models with additive constraints are equivalent to constrained versions of the confirmatory factor analysis model for MTMM data (Althauser, Heberlein, & Scott, 1971; Werts & Linn, 1970). In addition, Coenders and Saris (1998) showed that, for designs with 3 methods, a CU model with multiplicative constraints is equivalent to the direct product model (Browne, 1984).