Multitrait–Multimethod Matrix

Monomethod Blocks

The monomethod blocks contain the correlations between variables that belong to the same method. In Table 1 there are three monomethod blocks, one for each method. Each monomethod block consists of two parts. The first part (reliability diagonals) contains the reliabilities of the measures. The second part (the heterotrait– monomethod triangles) include the correlations between different traits that are measured by the same methods. The reliabilities can be considered as monotrait–monomethod correlations.

Heteromethod Blocks

The heteromethod blocks comprise the correlations between traits that were measured by different methods. Table 1 contains three heteromethod blocks, one for each combination of the three methods. A heteromethod block consists of two parts. The validity diagonal (monotrait–heteromethod correlations) contains the correlations of the same traits measured by different methods. The hetero-trait–heteromethod triangles cover the correlations of different traits measured by different methods.

Limitations of These Rules

These four requirements have been developed by Campbell and Fiske because they are easy-to-apply rules for evaluating an MTMM matrix with respect to its convergent and discriminant validity. They are, however, restricted in several ways. The application of these criteria is difficult if the different measures differ in their reliabilities. In this case the correlations, which are correlations of observed variables, can be distorted by measurement error in different ways, and differences between correlations could only be due to differences in reliabilities. Moreover, there is no statistical test of whether these criteria are fulfilled in a specific application. Finally, the MTMM matrix is not explained by a statistical model allowing the separation of different sources of variance that are due to trait, method, and error influences. Modern psychometric approaches complete these criteria and circumvent some of these problems.

...