MTMM Overview

First to give you a general overview of the "whole picture", here is a fully labeled matrix (don't distress for we will digest it piece by piece in a moment):

Correlations can be grouped into three kinds of shapes: diagonals, triangles, and blocks.

A discussion of these shapes follows.

Reliability Diagonal:

The reliability diagonal measures the same trait using the same method, therefore, it should be highly correlated. These correlations are the relationship of the measure with itself and can be referred to as monomethod monotrait correlations.

In theory this correlation would be equal to one indicating a "perfect" measurement. As there is always some amount of error, reliability correlations are estimates.

These values should be the highest in the matrix as they are essentially measuring the same item with the same method.

For example, the first reliability correlation = .89 is the correlation of agility measured by performance with agility measured by performance. These high correlation values support convergent validity.

Validity Diagonals:

Validity diagonals measure the pattern of trait interrelationship that occurs using different methods. These correlations are the relationship of the same trait measured using different methods (heteromethod monotrait diagonals).

For example the correlation of agility measured by performance vs. measured by self-rating = .57. In order to indicate convergent validity these values should be significantly different from one and highly correlated with each other.

Monomethod Heterotrait Triangles:

Monomethod heterotrait triangles are correlations of different traits that are measured by the same method.

The correlation of agility measured by performance and speed measured by performance = .51 is an example.

These correlations share methods and if the correlations are high, it indicates a strong "methods" factor. This indicates that the methods have something in common, which is not necessarily the traits.

Heteromethod Heterotrait Triangles:

The heteromethod heterotrait triangles measure different traits by different methods.

As there should be nothing in common in these measures, the correlations between them should be low, and in fact the lowest in the matrix. An example is the correlation of agility measured by performance with speed measured by self-rating = .22.

Monomethod Blocks:

Monomethod blocks are comprised of all the correlations of traits that are measured by the same method.

There are as many blocks as there are measurement methods.

Heteromethod Blocks:

Heteromethod blocks are all the correlations of traits that are measured by different methods.

O.K. that is all well and good , but what about Construct Validity???

The terminology is necessary to understand the interpretation of the MTMM.
Some basic principles for MTMM interpretation are as follows:

To support CONVERGENT VALIDITY:

Correlations in the reliability diagonal should be the highest in the matrix.

Correlations in the validity diagonals should be significantly different from zero.

To support DISCRIMINENT VALIDITY:

The validity diagonal correlations should be higher than other values in its column and row in the same heteromethod heterotrait triangle. This means that the validity diagonal variables (items comprising the correlation) have a stronger relationship then the other correlation variables that have no trait or method in common.

The validity diagonal correlations should be higher than all the other correlations in the monomethod heterotrait triangles. This means that the relationship between traits should be stronger then the relationship between methods. In our example this does not always hold by evidence of validity correlation r= .57 for agility by self-rating and agility by performance and r=.86 in the monomethod heterotrait triangle for agility by self-rating and speed by self-rating. This indicates that there may be a methods factor in our design.

The same general pattern of trait interrelationship should be seen in all the heteromethod heterotrait and monomethod heterotrait triangles. In our example notice that this criterion is met. In the heteromethod heterotrait triangles the relationship of speed is consistently nearly twice that of basketball skills (r=.22 vs. r= 11). In the monomethod heterotrait triangles the pattern is also fairly constant with speed higher correlated then basketball skills and that the correlations of basketball skills with agility and speed are almost equal.

The aforementioned items of the MTMM set up the basic guidelines for its interpretation. Much of the interpretation of the MTMM involves the use of judgment such as what is a "strong correlation". Even though some of the principles may be violated in an MTMM, you may still wind up concluding that you have fairly strong construct validity.

MTMM helps diagnose such threats to construct validity as measurement differences. In reality you probably will not get perfect adherence to the previously mentioned principles, though you may still conclude you have enough evidence to support construct validity.

The MTMM is a tool that can be used to assess construct validity.

Whew!!! I think the fitness program may have been easier then that!!!