Confirmatory Factor Analysis of Multitrait Multimethod Matrices.

Campbell and Fiske (1959) argue that the demonstration of construct validity requires both convergent validity and discriminant validity; that is, multiple indicators of the same construct should be substantially correlated with each other, but less correlated with indicators of other constructs. They propose collecting measures of more than one trait, each of which is assessed by more than one method. Convergent validity is inferred from agreement between measures of the same trait assessed by different methods. Discriminant or divergent validity refers to the distinctiveness of the different traits, and is inferred from the relative lack of correlation between different traits. Support for these characteristics is based upon inspection or analysis of a multitrait-multimethod (MTMM) matrix. MTMM matrices have been analyzed by a variety of different procedures (Althauser & Heberlein, 1970; Alwin, 1974; Joreskog, 1974; Kavanagh, MacKinney, & Wolins, 1971; Kenny, 1979; Lomax & Algina, 1979; Schmitt, 1978; Schmitt, Coyle, & Saari, 1977; Werts & Linn, 1970). The most frequently employed procedures have been the original Campbell-Fiske criteria (Campbell & Fiske, 1959) and an ANOVA model (Kavanagh et al., 1971; Stanley, 1961). More recently, applications of confirmatory factor analysis have been applied to MTMM matrices, though the approach has been described under a variety of different labels: restricted factor analysis.(Boruch & Wolins, 1970), confirmatory factor analysis (Kenny, 1976; Werts, Jireskog, & Linn, 1972), path analysis (Schmitt, 1978; Schmitt et al., 1977), and exploratory factor analysis (Lomax & Algina, 1979). Most of the other procedures, though not necessarily described in terms of confirmatory factor analysis, do involve applications that are special cases of the more general approach described in this paper (see Alwin, 1974; Avison, 1978). This paper provides a pedagogical exposition of the confirmatory factor analysis of MTMM matrices, and compares this approach with the application of the CampbellFiske criteria and the ANOVA model. These analyses will be performed on the MTMM matrix presented in Table 1. Although the methodology and content relevance of the study are not emphasized here, these details are elaborated elsewhere (Marsh, 1982; Marsh & Overall, 1979). Briefly, university instructors in 329 college classes were asked to evaluate their own teaching effectiveness on the same nine-trait (35 items) instrument that was completed by their students. The definition and calculation of these nine traits are described in the earlier research (Marsh & Overall, 1979). The names of the trait factors of both teacher (A1, A2, etc.) and student (B,, B2, etc.) responses are presented in Table 1. Table 1 also includes correlations that are corrected for attenuation due to measurement error. These are indicated below the main diagonal of the entire 18 x 18