Correlated Trait Correlated Method Model

The restriction of uncorrelated methods is removed by admitting correlations between the method factors in the correlated trait/correlated method (CTCM) model (Marsh & Grayson, 1995; Widaman, 1985). This model looks like the CTUM model depicted in Figure 20.1c but with correlations between all method factors. That means that the CTUM model is also a restrictive version of the CTCM model. Although the CTCM model seems to be an attractive model because it overcomes some of the strong limitations of the previously described MTMM models, it is also afflicted by several problems that question its applicability. One of its major problems is that it is not globally identified (Grayson & Marsh, 1994). This means that there are data structures for which the parameters of the model cannot be estimated. These data structures, however, are not unusual, and they are often even desired. For example, in the case of perfectly homogeneous indicators (that all have the same loading parameters on the trait and method factors), the model is not identified and, therefore, not applicable. Hence, in addition to not being globally identifiable, another serious problem of the model is that it is not globally applicable. Moreover, applications of this model often reveal improper estimations such as negative variances. Beyond these more technical problems, there are also more substantive interpretation problems that exist when all of the method factors are correlated. In this case, the method factor correlations indicate a portion of the shared variance of all variables that might not be indicative of method-specific influences but are more likely to be indica tive of a general trait influence or associations between the traits (Marsh, 1989). Hence, it is unclear whether the correlations between the trait factors are valid estimators of discriminant validity because the different indicators are also related via the correlated method factors. Furthermore, the condition under which it is reasonable to assume that the trait and the method factors are uncorrected is unclear because there is also a variant of the model that has correlated trait and method factors (Schmitt & Stults, 1986). The assumption of the uncorrelatedness of the trait and method factors is adhered to mainly to avoid technical problems and to make the decomposition of variances possible. Note that the question of whether trait and method factors should be uncorrelated or not is also relevant for the CTUM model.

Finally, the CTCM model, like the CTCU model, assumes that the method effect is due to one method that generalizes homogeneously across the different traits because the covariances of the indicators belonging to the same method are explained by one method factor. Consequently, the application of the CTCM model is restricted in strong ways.

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