Convergent and Discriminant Validity in SEM

Measurement validity is considered one of the most critical requirements that must be met by measuring instruments, and it is also one of the essential criteria for test quality. Validity has also been deemed an attribute related to the test results, not the test itself. There is no test characterized by lack of validity or complete validity, as the procedures for the validity of any measuring instrument start from building that instrument. Validity is a comprehensive concept achieved by examining each step for that test.

Convergent Validity

Convergent validity refers to how closely the items of a construct(variable) are correlated to each other. When the items converge on a particular scale depicting a specific construct, it is considered convergent validity. We use Average Variance Extracted (AVE) to designate convergent validity; it is the average squared factor loading for each indicator in the construct. When (AVE) > 0.50, the construct’s items converge. Likewise, when (AVE) >0.50 for all constructs in the measuring instrument, it can be said that convergent validity is established.

Discriminant Validity

Discriminant validity refers to the distinctiveness of the constructs from each other. Each construct has its unique identity and is not significantly related to the other constructs in the measurement scale. In confirmatory factor analysis, there are two general approaches:

  • Fornell and Larcker Criterion: Discriminant validity is established if the Sq. root of (AVE) for a particular construct is greater than its correlation with all other constructs. Thresholds are 0.850 for strict and 0.900 for liberal discriminant validity.
  • Cross-Loadings: When the cross-loading of an item on its parent construct is higher than on other constructs, this is an indication of discriminant validity. If the factor loading of a given item in its original construct is high, at the same time, high in another construct, this means that there is a problem with discriminant validity. A loading difference of less than 0.10 indicates that the item is cross-loading onto the other construct; thus, it could threaten discriminant validity.
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