Multiple Indicator CTCMl Model

A multiple-indicator extension of the CTC(M-l) is depicted in Figure 20.3c. This model is described in detail by Eid et al. (2003). In this model there is a method factor for each combination of a trait and a nonstandard method. The method factors belonging to the same method can be correlated, thus representing the generalizability of method effects across traits. Also the method factors of different methods can be correlated, thus showing whether the nonstandard methods have more in common than can be explained by the standard method. The general version of this model, which is not depicted in Figure 20.3 but explained in detail by Eid et al. (2003), also allows correlations between the method factors belonging to one trait and the trait factors of the other traits. These correlations are heteromethod coefficients of discriminant validity, whereas the intercorrelations of the trait factors are discriminant validities with respect to the standard method. The CTC(M-l) model allows to estimate variance components that are due to trait, method, and error influences. The variance components that are due to trait (consistency) and method (specificity) influences can only be estimated for the nonstandard methods because they indicate the degree of variance that cannot be explained by the standard method. Like in the multiple-indicator CTCU model, several hypotheses concerning the method factors can be tested. For example, one can test whether the method factors belonging to the same method are identical (perfect generalizability) by specifying a model with one method factor for each method (instead of trait-specific method factors). Moreover, one can model a second-order method factor for all method factors belonging to the same method, if a measure of the general influence of one method is desired.

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