We will illustrate the five models by applying them to data from an MTMM study exploring the relations between self- and peer-rated frequency of negative emotions. The traits were/ear, anger, and sadness. The three methods were self-ratings, ratings by a good friend, and ratings by an acquaintance. The sample consisted of 172 triples of self- and peer raters. This sample was a subgroup of individuals from a larger MTMM study (see Eid et al., 2003; Trierweiler, Eid, & Lischetzke, 2002). While seated separately, all participants rated the frequency with which the target individual usually experienced different negative emotions using a four-category scale (from not at all to very often). Three scales, consisting of four emotion terms each, assessed fear, anger, and sadness. For the MTMM analyses, the scales were divided into two test halves comprising two items each. The applications of the single-indicator models were based on the first test halves for instructive reasons only. Both test halves will be analyzed conjointly in the next section. The covari-ance and correlation matrix is given in Table 20.1. The CT model had to be rejected (x2 = 94.56, df = 24, p < .01, CFI = .67, RMSEA = .13), demonstrating that there are systematic method-specific influences. The CTCU model and the CTUM model fitted the data equally well (%2 = 19.94, df = 15, p = .17, CFI = .98, RMSEA = .04) because they are data equivalent in the case of three traits (i.e., three loadings on each factor). However, in the CTUM model, one residual variance had a negative value. The estimation of the CTCM model did not converge. The CTC(M-l) model fitted the data well ("/2 = 24.57, df= 17, p = .10, CFI = .96, RMSEA = .05). For the CTUM model and the CTC(M-l) model, the estimated loading parameters and variances of the factors are given in Figure 20.2. The CTCU model is not depicted in this figure because the trait part of the CTUM model is identical to the trait part of the CTCU model in this application. The error variances and correlations (CTCU model) as well as the reliability, consistency, and method specificity coefficients are given in Table 20.2. The reliability coefficient is computed as the degree of variance of an observed variable that is explained by the factors of the model. The consistency coefficient is the degree of true variance of an observed variable that is explained by the respective trait factor; the method specificity coefficient indicates the degree of true variance of an observed variable that is due to the respective method factor. Consistency and specificity coefficients together add up to 1.
The trait parameters of the CTCU and the CTUM models (see Figure 20.2) showed that the three methods differed in their trait loadings. For the first trait the friend rating had the highest loading, for the second trait the self-rating had the highest loading, and for the third trait the acquaintance rating showed the highest loading. According to this result, the trait influences were not consistent across the different traits, and sometimes one method was "better" in terms of "explained variance by the common trait" than other methods. Moreover, the correlations of the residuals in the CTCU model (see Table 20.2) were rather different for one rater, indicating that method influences did
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