13. SEMinR Series - Reflective Model | Reliability and Convergent Validity

Reflective measurement model checks hinge on three linked quality tests: internal consistency reliability, convergent validity, and (later) discriminant validity. In this step, reliability is assessed first using composite reliability (often labeled “rho C”), with Cronbach’s alpha as a more conservative alternative and “rho A” as a middle-ground coefficient. Composite reliability values above 0.70 are typically treated as reliable; 0.60–0.70 is acceptable in exploratory work; and 0.70–0.90 is generally satisfactory to good. Values above 0.90—especially above 0.95—raise a red flag: they can indicate redundant indicators, which can reduce construct validity. Extremely high reliability may also reflect undesirable response patterns such as straight-lining, where respondents choose the same response option across items, inflating correlations among indicator error terms.

Because Cronbach’s alpha and composite reliability rely on different assumptions, the reliability picture can shift. Cronbach’s alpha assumes “tau-equivalence,” meaning all indicator loadings are equal in the population; when that assumption fails, alpha tends to produce lower reliability estimates. Composite reliability (rho C) can be too liberal under the same circumstances. To balance these extremes, rho A is introduced as a coefficient that usually falls between Cronbach’s alpha and composite reliability. A practical rule of thumb used here is that rho C, rho A, and Cronbach’s alpha should exceed 0.70 (with rho A and alpha often expected to exceed 0.50), and rho A should sit between alpha and rho C. In the worked example, the reliability outputs for multiple constructs clear the 0.70 threshold across the three measures, indicating the indicators within each construct are internally consistent.

After reliability, convergent validity checks whether items intended to measure the same construct actually converge on that underlying concept. Convergent validity is quantified using Average Variance Extracted (AVE), computed as the grand mean of squared indicator loadings: square each loading, sum them, then divide by the number of indicators. AVE is interpreted as the proportion of variance in the indicators captured by the construct; the minimum acceptable level is 0.50. In the example, all constructs show AVE values above 0.50, so the indicators are judged to represent their intended constructs well enough to establish convergent validity.

Finally, there’s guidance on reporting results: present the measurement model, then report factor (indicator) loadings, construct reliability (including composite reliability and the reliability coefficients), and AVE for convergent validity. The transcript also notes how to extract these metrics in R (via a reliability summary object) and how to visualize reliability with a plot that includes Cronbach’s alpha, rho A, and rho C. With reliability and convergent validity established, the next phase moves to discriminant validity for reflective measurement models.