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Multitrait-multimethod matrix
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Multitrait-multimethod matrix
The multitrait-multimethod (MTMM) matrix is an approach to examining construct validity developed by Campbell and Fiske (1959). It organizes convergent and discriminant validity evidence for comparison of how a measure relates to other measures. The conceptual approach has influenced experimental design and measurement theory in psychology, including applications in structural equation models.
Multiple traits are used in this approach to examine (a) similar or (b) dissimilar traits (constructs), in order to establish convergent and discriminant validity between traits. Similarly, multiple methods are used in this approach to examine the differential effects (or lack thereof) caused by method specific variance. Scores could be correlated because they measure similar traits, or because they are based on similar methods, or both. When variables that are supposed to measure different constructs show a high correlation because they based on similar methods, this is sometimes described as a "nuisance variance" or "method bias" problem.
There are six major considerations when examining a construct's validity through the MTMM matrix, which are as follows:
The example below provides a prototypical matrix and what the correlations between measures mean. The diagonal line is typically filled in with a reliability coefficient of the measure (e.g. alpha coefficient). Descriptions in brackets [] indicate what is expected when the validity of the construct (e.g., depression or anxiety) and the validities of the measures are all high.
In this example, the first row lists the trait being assessed (i.e., depression or anxiety) as well as the method of assessing this trait (i.e., self-reported questionnaire versus an interview). The term heteromethod indicates this cell reports the correlation between two separate methods. Monomethod indicates that the same method is being used instead (e.g., interview and interview). Heterotrait indicates that the cell refers to two supposedly different traits. Monotrait indicates the same trait supposed to be measured.
This framework makes it clear that there are at least two sources of variance that can influence observed scores on a measure: Not just the underlying trait (which is usually the goal of gathering the measurement in the first place), but also the method used to gather the measurement. The MTMM matrix uses two or more measures of each trait and two or more methods to start to tease apart the contributions of different factors. The first frame of the animated figure shows how the four measurements in the table are paired in terms of focusing on the "traits" of depression (BDI and HDRS) and anxiety (BAI and CGI-A). The second shows that they are also paired in terms of source method: two use self-report questionnaires (often referred to as "surveys"), and two are based on interview (which can incorporate direct observation of nonverbal communication and behavior, as well as the interviewee's response).
With observed data, it is possible to examine the proportion of variance shared among traits and methods to gain a sense of how much method-specific variance is induced by the measurement method, as well as provide a look at how distinct the trait is, as compared to another trait.
Ideally, the trait should matter more than the specific method chosen for measurement. For example, if a person is measured as being highly depressed by one measure, then another depression measure should also yield high scores. On the other hand, people who appear highly depressed on the Beck Depression Inventory should not necessarily get high anxiety scores on Beck's Anxiety Inventory, inasmuch as they are supposed to be measuring different constructs. Since the inventories were written by the same person, and are similar in style, there might be some correlation, but this similarity in method should not affect the scores much, so the correlations between these measures of different traits should be low.
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Multitrait-multimethod matrix
The multitrait-multimethod (MTMM) matrix is an approach to examining construct validity developed by Campbell and Fiske (1959). It organizes convergent and discriminant validity evidence for comparison of how a measure relates to other measures. The conceptual approach has influenced experimental design and measurement theory in psychology, including applications in structural equation models.
Multiple traits are used in this approach to examine (a) similar or (b) dissimilar traits (constructs), in order to establish convergent and discriminant validity between traits. Similarly, multiple methods are used in this approach to examine the differential effects (or lack thereof) caused by method specific variance. Scores could be correlated because they measure similar traits, or because they are based on similar methods, or both. When variables that are supposed to measure different constructs show a high correlation because they based on similar methods, this is sometimes described as a "nuisance variance" or "method bias" problem.
There are six major considerations when examining a construct's validity through the MTMM matrix, which are as follows:
The example below provides a prototypical matrix and what the correlations between measures mean. The diagonal line is typically filled in with a reliability coefficient of the measure (e.g. alpha coefficient). Descriptions in brackets [] indicate what is expected when the validity of the construct (e.g., depression or anxiety) and the validities of the measures are all high.
In this example, the first row lists the trait being assessed (i.e., depression or anxiety) as well as the method of assessing this trait (i.e., self-reported questionnaire versus an interview). The term heteromethod indicates this cell reports the correlation between two separate methods. Monomethod indicates that the same method is being used instead (e.g., interview and interview). Heterotrait indicates that the cell refers to two supposedly different traits. Monotrait indicates the same trait supposed to be measured.
This framework makes it clear that there are at least two sources of variance that can influence observed scores on a measure: Not just the underlying trait (which is usually the goal of gathering the measurement in the first place), but also the method used to gather the measurement. The MTMM matrix uses two or more measures of each trait and two or more methods to start to tease apart the contributions of different factors. The first frame of the animated figure shows how the four measurements in the table are paired in terms of focusing on the "traits" of depression (BDI and HDRS) and anxiety (BAI and CGI-A). The second shows that they are also paired in terms of source method: two use self-report questionnaires (often referred to as "surveys"), and two are based on interview (which can incorporate direct observation of nonverbal communication and behavior, as well as the interviewee's response).
With observed data, it is possible to examine the proportion of variance shared among traits and methods to gain a sense of how much method-specific variance is induced by the measurement method, as well as provide a look at how distinct the trait is, as compared to another trait.
Ideally, the trait should matter more than the specific method chosen for measurement. For example, if a person is measured as being highly depressed by one measure, then another depression measure should also yield high scores. On the other hand, people who appear highly depressed on the Beck Depression Inventory should not necessarily get high anxiety scores on Beck's Anxiety Inventory, inasmuch as they are supposed to be measuring different constructs. Since the inventories were written by the same person, and are similar in style, there might be some correlation, but this similarity in method should not affect the scores much, so the correlations between these measures of different traits should be low.