Analysis of The MTMM Matrix
A variety of statistical approaches have been used to analyze the data from the MTMM matrix. The standard method from Campbell and Fiske can be implemented using the MTMM.EXE program available at: http://gim.med.ucla.edu/FacultyPages/Hays/util.htm One can also use confirmatory factor analysis due to the complexities in considering all of the data in the matrix. The Sawilowsky I test, however, considers all of the data in the matrix with a distribution-free statistical test for trend.
The test is conducted by reducing the heterotrait-heteromethod and heterotrait-monomethod triangles, and the validity and reliability diagonals, into a matrix of four levels. Each level consists of the minimum, median, and maximum value. The null hypothesis is these values are unordered, which is tested against the alternative hypothesis of an increasing ordered trend. The test statistic is found by counting the number of inversions (I). The critical value for alpha = 0.05 is 10, and for alpha = .01 is 14.
Read more about this topic: Multitrait-multimethod Matrix
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