#SmartPLS4 Series 8 - How to Assess Convergent Validity?

Convergent validity in SmartPLS is judged largely through Average Variance Extracted (AVE): if each construct’s AVE is at least 0.50, the indicators are sufficiently “converging” to represent the underlying latent variable. In a simple SmartPLS model, the AVE values reported for two constructs were 0.618 and 0.742—both above the 0.50 cutoff—so the items were treated as adequately measuring their constructs. The same logic is reinforced by indicator loadings: when individual outer loadings are strong (often referenced around 0.70), they contribute to a construct’s AVE and support the claim that the items share enough variance with the latent construct.

When AVE falls short, the fix is not automatic item deletion; it’s targeted removal based on how each item affects AVE and Composite Reliability (CR). The workflow starts with checking the “graphical output” and identifying any outer loadings below 0.70, because those weaker items are the most likely to drag down AVE. AVE itself is computed by squaring each item’s loading for a construct, summing those squared loadings, and dividing by the number of items. SmartPLS reports AVE in the quality criteria section (under construct reliability and validity), and the transcript demonstrates verifying the reported AVE by copying the loadings from the report, squaring them, and applying the formula.

The decision rules for deletion are staged. If an item’s loading is between 0.40 and 0.70, it is not removed just because it is below 0.70; it is removed only if deleting it increases AVE (and, by extension, supports the construct’s reliability) beyond the recommended thresholds. If AVE is still inadequate after removing the weakest contributors, the deletion threshold can be tightened. The guidance given is: first remove items with loadings below 0.40; if AVE remains low, consider removing items with loadings below 0.50; if the problem persists, move toward removing items below 0.60 and then below 0.70—but only when those deletions improve CR and AVE enough to clear the cutoffs.

A key nuance is that items can be kept even when some loadings are under 0.70, as long as the overall AVE remains above 0.50 and CR is adequate (the transcript references CR above 0.70 as a supporting condition). Conversely, very low loadings (e.g., around 0.35) are treated as clear candidates for removal because they are unlikely to contribute meaningfully to AVE.

The approach is summarized as a practical, iterative cleanup: delete only the items that improve AVE/CR, and stop once convergent validity is established. A referenced paper supports the same principle—outer loadings between 0.40 and 0.70 are considered for removal only if deletion increases CR and AVE above recommended values. After convergent validity is secured via AVE, attention shifts to discriminant validity in the next session.