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The Multitrait-Multimethod Matrix

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, 81-105.

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The Multitrait-Multimethod Matrix

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  1. The Multitrait-Multimethod Matrix

  2. 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, 81-105. • A matrix (table) of correlations arranged to facilitate the assessment of construct validity • An integration of both convergent and discriminant validity

  3. 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.

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

  5. A Hypothetical MTMM Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85)

  6. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) The reliability diagonal

  7. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Validity diagonals

  8. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Monomethod heterotrait triangles

  9. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Heteromethod heterotrait triangles

  10. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Monomethod blocks

  11. Parts of the Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Heteromethod blocks

  12. Interpreting the MTMM Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Reliability should be highest coefficients.

  13. Interpreting the MTMM Matrix Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85) Convergent validity diagonals should have strong r's.

  14. Interpreting the MTMM Matrix Convergent: The same pattern of trait interrelationship should occur in all triangles (mono and heteromethod blocks). Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85)

  15. Interpreting the MTMM Matrix Discriminant: A validity diagonal should be higher than the other values in its row and column within its own block (heteromethod). Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85)

  16. Interpreting the MTMM Matrix Disciminant: A variable should have higher r with another measure of the same trait than with different traits measured by the same method. Method 1 Method 2 Method 3 Traits A1 B1 C1 A2 B2 C2 A3 B3 C3 A1 Method 1 B1 C1 A2 Method 2 B2 C2 A3 Method 3 B3 C3 (.89) .51 (.89) .38 .37 (.76) .57 .22 .09 (.93) .22 .57 .10 .68 (.94) .11 .11 .46 .59 .58 (.84) .56 .22 .11 .67 .42 .33 (.94) .23 .58 .12 .43 .66 .34 .67 (.92) .11 .11 .45 .34 .32 .58 .58 .60 (.85)

  17. Advantages • Addresses convergent and discriminant validity simultaneously • Addresses the importance of method of measurement • Provides a rigorous standard for construct validity

  18. Disadvantages • Hard to implement • No known overall statistical test for validity • Requires judgment call on interpretation

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