Describe the assessment of discriminant validity in a measurement model

Question

What will be an ideal response?

Answer 1

In order to establish discriminant validity, we must show that the construct is distinct from other constructs and thus makes a unique contribution. First, individual observed variables should load on only one latent construct. Cross-loadings indicate lack of distinctiveness and present potential problems in establishing discriminant validity.
One formal way to show distinctiveness is to set the correlation between any two constructs as equal to one, i.e., we are specifying that observed variables measuring the two constructs might as well be represented by only one construct. Evidence of discriminant validity is obtained if the fit of the two-construct model is significantly better than the fit of the one-construct model. However, this actually turns out to be a weak test as significant fit differences may be obtained even when the correlations between the two constructs are very high.

An alternative test of discriminant validity is based on the logic that a construct should explain its observed variables better than it explains any other construct. This test is conducted by showing that the average variance extracted is greater than the square of the correlations. Equivalently, discriminant validity is achieved if the square root of the average variance extracted is larger than correlation coefficients.