The Multitrait-Multimethod Matrix

What Is the MTMM Matrix? An approach developed by Campbell, D. and Fiske, D. (1959). Convergent and Dicriminant Validation by the Multitrait-Multimethod Matrix. 56, 2, A matrix (table) of correlations arranged to facilitate the assessment of construct validity An integration of both convergent and discriminant validity

What Is the MTMM Matrix? Assumes that you measure each of several concepts (trait) by more than one method. Very restrictive -- ideally you should measure each concept by each method. Arranges the correlation matrix by concepts within methods.

PrinciplesPrinciples Convergence: Things that should be related are. Divergence/Discrimination: Things that shouldn't be related aren't.

A Hypothetical MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85)

(.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 The reliability diagonal

Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Validity diagonals

(.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 Monomethod heterotrait triangles

(.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 Heteromethod heterotrait triangles

Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Monomethod blocks

(.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Parts of the Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 Heteromethod blocks

Interpreting the MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Reliability should be highest coefficients.

Interpreting the MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Convergent validity diagonals should have strong r's.

Interpreting the MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Convergent: The same pattern of trait interrelationship should occur in all triangles (mono and heteromethod blocks).

Interpreting the MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Discriminant: A validity diagonal should be higher than the other values in its row and column within its own block (heteromethod).

Interpreting the MTMM Matrix Method 1Method 2Method 3 TraitsA 1 B 1 C 1 A 2 B 2 C 2 A 3 B 3 C 3 A 1 Method 1B 1 C 1 A 2 Method 2 B 2 C 2 A 3 Method 3 B 3 C 3 (.89).51(.89).38.37(.76) (.93) (.94) (.84) (.94) (.92) (.85) Disciminant: A variable should have higher r with another measure of the same trait than with different traits measured by the same method.

AdvantagesAdvantages l Addresses convergent and discriminant validity simultaneously l Addresses the importance of method of measurement l Provides a rigorous standard for construct validity

DisadvantagesDisadvantages l Hard to implement l No known overall statistical test for validity l Requires judgment call on interpretation