11. SEM | SPSS AMOS - How to Establish Composite Reliability and Convergent Validity

Composite reliability and convergent validity come after factor loadings and model fit are checked, and they determine whether each latent construct is measured consistently and whether its indicators truly “belong together.” Construct reliability is about consistency: a measure is reliable when it produces the same results under the same conditions across occasions. In structural equation modeling, construct reliability is commonly assessed using composite reliability (often preferred in SEM) and Cronbach’s alpha. For this workflow, composite reliability is calculated from standardized factor loadings and error variances, using a formula that effectively rewards strong loadings and penalizes measurement error. The benchmark referenced is 0.7 (from Nunnally and Bernstein), where values above 0.7 indicate acceptable or modest reliability.

Composite reliability is computed per construct, not across all constructs at once. The process in AMOS starts by running the model and extracting standardized regression weights (the factor loadings) from the output estimates table. Each indicator’s standardized loading is used to compute error variance as (1 − loading), and the composite reliability is then calculated for each latent variable separately. In the example, composite reliability values for constructs such as Authentic leadership behavior, Ethical behavior, and Life satisfaction all exceed 0.7, which is treated as evidence that the measures are consistent enough to yield stable results.

Once reliability is established, the next step is construct validity, which asks whether the chosen items actually measure the intended latent construct. Construct validity is assessed through convergent validity and discriminant validity; this session focuses on convergent validity. Convergent validity checks whether multiple indicators that are supposed to measure the same construct are indeed related—meaning the indicators should converge to represent the underlying latent variable. Practically, this is linked to unidimensionality: indicators of the same construct should correlate significantly and not behave like unrelated measures.

Convergent validity is assessed using Average Variance Extracted (AVE). AVE reflects how much of the indicators’ variance is explained by the latent construct; an AVE greater than 0.50 is used as empirical evidence of convergent validity, because the latent variable accounts for more than half of the variance in its indicators. AVE is calculated by squaring each factor loading, summing those squared loadings, and dividing by the number of items for that latent variable.

In AMOS, the same factor loadings used for composite reliability feed into the AVE calculation. The example produces AVE values for Authentic leadership behavior, Ethical behavior, and Life satisfaction that are interpreted as acceptable (with values around 0.47–0.67 discussed), and the workflow notes that if an indicator’s AVE-related contribution is borderline, deletion can be considered—especially when composite reliability for the construct is above 0.7. With both composite reliability and convergent validity in place, the analysis is positioned to move next toward discriminant validity, which tests whether constructs are distinct from one another.