As an alternative to the CTCM model, Eid (2000) proposed an MTMM model that is not affected by the identification problems of the CTCM model. Eid's model is a special variant of the CTCM model but differs from it in the number of method factors. It contains one method factor less than methods included and is, therefore, called the correlated trait/correlated method minus one [CTC(M-l)] model. The basic idea of the CTC(M-l) model is that one method has to be chosen as the comparison standard. All other methods are contrasted with this comparison standard. In this model (see Figure 20.Id), a latent trait factor is the true-score variable of the indicator that is measured by the comparison standard. A method factor is common to all variables measured by the same method. The method factor represents that part of the variance of an indicator that cannot be predicted by the trait factor (the standard method) and that is not due to random measurement error but to systematic method-
specific influences. These method-specific influences are common to all indicators measured by the same method. Hence, a method factor comprises the systematic components a method does not share with the standard method. The model is defined by two basic equations, the equation for the standard method (denoted by k = 1): YjX = ^ T. + EjV and the equation for all other methods (k 11): YJk = T. + X M, + E.,.
According to this model, the identification and interpretation problems of the CTCM model might be due to an overfactorization. The CTC(M-l) model has several advantages. One property of the model is that the trait and method factors cannot be correlated with one another (see Eid, 2000, for a proof). Therefore, the decomposition of variance into trait-specific, method-specific, and error components can be achieved as in the CTUM and CTCM models. In contrast to the CTCM model, the correlations between the method factors cannot be confounded with a general trait effect because the indicators of the standard method are not related to a method factor. Compared with the CTCU and CTUM models, the CTC(M-l) model is less restricted because method factors can be correlated. The CTC(M-l) model, however, also has its limitations. An initial limitation is that one method has to be chosen as the comparison standard. Moreover, the model is not symmetrical, which means that the fit to the same data set can differ when different methods are chosen as the comparison standard. However, in the case of structurally different methods, this might not pose a problem because one method often stands out from the others. When self-ratings are compared with different informant ratings (see Neyer, chap. 4, this volume), for example, the self-ratings might be an interesting standard method because all method factors would indicate deviations from the scores expected by the self-report.
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