Current Approaches for Assessing Convergent and Discriminant Validity with SEM: Issues and Solutions

Since Campbell and Fiske (1959) defined convergent validity and discriminant validity, the tests for convergent validity and discriminant validity have evolved from checking the “high” and “low” correlation coefficients in the multitrait-multimethod context to specific rules of thumbs suggested by Fornell and Larcker (1981) in a multitrait-monomethod context. In this study, a simulation was conducted to first evaluate the effectiveness of (a) the Fornell-Larcker criterion for convergent validity, which requires the Average Variance Extracted (AVE) greater than 0.5 and (b) the Hair et al. criteria for convergent validity, which require the AVE greater than 0.5, standardized factor loading of all items not less than 0.5, and composite reliability not less than 0.7. We also evaluate the effectiveness of (c) the Forell-Larcker criterion for discriminant validity, which requires the AVE of both constructs greater than square correlation between the two constructs, (d) the Bagozzi et al. criterion which requires the correlation between two constructs significantly less than unity, and (e) the Kline criterion for discriminant validity, which requires the correlation between two constructs less than 0.85. Results show that all these criteria are not very effective in evaluating convergent validity and discriminant validity and most of them have ignored sampling errors such that the conclusion cannot be inferred to the population of interest. Finally, we recommend (a) concluding convergent validity if AVE is not significantly smaller than 0.5 and standardized factor loadings of all items are not significantly less than 0.5. and (b) concluding discriminant validity if correlation between two constructs is not significantly larger than 0.7.