Multitrait-Multimethod Matrix

Convergent validity means that different methods of measuring the same trait agree, shown by substantial correlations on the validity diagonal (same trait, different methods). Discriminant validity means that measures of different traits diverge, shown when those convergent correlations exceed the correlations among different traits — including, most stringently, different traits measured by the same method. Campbell and Fiske required both: a valid construct must converge across methods and stay distinct from other constructs. The matrix arranges all these correlations so the comparisons can be read off, and the modern confirmatory-factor version lets you test each one formally.

Method variance shows up when different traits measured by the same method correlate more than different traits measured by different methods. In matrix terms, elevated heterotrait-monomethod correlations relative to heterotrait-heteromethod correlations signal that the shared method is inflating relationships for reasons unrelated to the constructs. Campbell and Fiske built this comparison into the validation logic, and Widaman's confirmatory-factor models let you estimate the size of method factors directly and test whether they are needed. This is the same threat that later common-method-bias remedies address, making the MTMM matrix a direct ancestor of that literature.

Campbell and Fiske's criteria are inspectional: you compare the sizes of correlations in different blocks. This works when the pattern is clear but becomes ambiguous when correlations are of intermediate magnitude, and it offers no significance tests. Widaman showed how to represent the matrix with trait and method factors in a sequence of nested confirmatory factor models, so that convergent validity, discriminant validity, and method variance can be tested by comparing model fit. The model-based approach also estimates measurement error properly. Its drawback is that MTMM confirmatory models can fail to converge or yield improper solutions, especially with few traits or methods, so adequate design and sample size are important.