SmartPLS | Convergent Validity - Discriminant Validity (Fornell and Larcker Criterion)

TL;DR

Compute AVE as the average of squared outer loadings: AVE = (Σ(loading²))/n.

Briefing Cornell Notes

Briefing

When items show very low outer loadings in SmartPLS, the practical fix is not to ignore them—it’s to re-check convergent validity (via AVE) and then confirm discriminant validity using the Fornell–Larcker criterion. The key takeaway is that low loadings can drag down Average Variance Extracted (AVE) and reliability, but stepwise deletion of problematic indicators can restore acceptable measurement quality, after which discriminant validity must still be tested.

The lecture first addresses why low loadings can appear in the first place. If a dataset comes from a multi-dimensional scale and items are “clubbed together” into a single construct, loadings often drop because indicators no longer align cleanly with one latent dimension. To demonstrate a remedy, a new model is built where “internal communication” is set as a factor influencing “knowledge sharing.” In that revised setup, construct reliability and validity come out strong, and outer loadings are all above 0.60—suggesting the indicators fit the construct well.

Next comes the mechanics of computing AVE (labeled “a” in the transcript). The formula is the sum of squared outer loadings divided by the number of items: AVE = (Σ(loading²))/n. The instructor illustrates the workflow in SmartPLS by exporting outer loadings to Excel, squaring each loading, summing them, and dividing by the number of indicators. In the example, the calculated AVE is about 0.591, which matches the SmartPLS-reported value after rounding (0.592). The rule of thumb emphasized is that AVE should exceed 0.50. The reasoning given is mathematical: if loadings fall below the recommended threshold, AVE trends downward; with a target loading around 0.70, the implied AVE stabilizes near 0.50 because 0.70² = 0.49.

The lecture then shifts to what to do when loadings are genuinely problematic. A separate model examining “task conflict” on “team performance” produces low alpha, low composite reliability, and low AVE. The outer loadings reveal weak indicators—TC1 is negative and TC3 is only 0.026. The response is stepwise deletion: remove the worst indicator, rerun the model, and check whether reliability/validity improve. After deleting additional low-loading items, the model’s AVE and “team performance” reliability/validity become acceptable, establishing convergent validity.

Finally, discriminant validity is tested with the Fornell–Larcker criterion. For each construct, the square root of AVE (the “top value”) must be greater than the correlations between that construct and other constructs (the “underneath values”). In the demonstrated case, only one correlation is relevant (task conflict with team performance), so the square root of AVE for task conflict (given as 0.841) is compared against the correlation value. With the top value exceeding the underneath correlation, discriminant validity is considered established.

Cornell Notes

The transcript explains how to handle low outer loadings in SmartPLS by restoring convergent validity and then verifying discriminant validity. AVE is computed as the sum of squared outer loadings divided by the number of indicators, and it should be above 0.50. When reliability and AVE are low, the recommended move is stepwise deletion of the worst indicators (e.g., those with negative or near-zero loadings), rerunning the model after each deletion. After convergent validity improves, discriminant validity is checked using the Fornell–Larcker criterion: the square root of AVE for a construct must exceed its correlations with other constructs. In the example, task conflict’s √AVE (0.841) is greater than its correlation with team performance, satisfying the criterion.

How is AVE (labeled “a” in the transcript) calculated from SmartPLS outer loadings?

AVE is computed as the sum of squared outer loadings divided by the number of items: AVE = (Σ(loading²))/n. The workflow described is to export outer loadings from SmartPLS (via an Excel-format option), square each loading in Excel (using a power function), sum those squared values, and divide by the count of indicators. The transcript’s example yields AVE ≈ 0.591, matching SmartPLS’s rounded value of 0.592.

Why is AVE expected to be above 0.50, and how does the 0.70 loading rule connect to it?

The transcript links the 0.50 threshold to how AVE behaves mathematically. If loadings are around 0.70, squaring them gives 0.49, which keeps AVE near or above 0.50 when averaged across indicators. If loadings drop below that level, the squared terms shrink and AVE falls toward (or below) 0.50, which is why the recommended loading threshold is stated as >0.70.

What should be done when reliability and AVE are low in a SmartPLS model?

The first step is to inspect outer loadings and identify problematic indicators. In the task conflict → team performance example, TC1 has a very low (negative) loading and TC3 is about 0.026. The transcript recommends stepwise deletion: remove one weak indicator, rerun the model, and check whether alpha, composite reliability, and AVE improve. If improvement is still insufficient, delete the next worst indicator and repeat.

What does it mean that convergent validity is established after indicator deletion?

Convergent validity is treated as achieved once AVE and reliability measures become acceptable after removing low-loading items. In the example, deleting TC1 and then TC3 leads to a model where AVE and the relevant reliability/validity outputs for the constructs are no longer low. At that point, the transcript explicitly notes that convergent validity is established, but discriminant validity still needs separate testing.

How does the Fornell–Larcker criterion test discriminant validity?

Fornell–Larcker requires that the square root of AVE for each construct (the “top value”) be greater than the correlations between that construct and other constructs (the “underneath values”). The transcript frames it as: √AVE (top) > correlation(s) (under). In the task conflict case, √AVE for task conflict is given as 0.841, and it is compared against the correlation between task conflict and team performance. Because the top value exceeds the correlation, discriminant validity is considered satisfied.

Review Questions

In SmartPLS, how would you compute AVE from a list of outer loadings, and what threshold is used to judge it?
Why does deleting low-loading indicators help with convergent validity, and what is the stepwise deletion process?
What inequality must hold under the Fornell–Larcker criterion for discriminant validity, and how is √AVE used in that test?

Key Points

1
Compute AVE as the average of squared outer loadings: AVE = (Σ(loading²))/n.
2
Use AVE > 0.50 as the benchmark for convergent validity, and understand how low loadings mathematically pull AVE down.
3
If alpha, composite reliability, and AVE are low, inspect outer loadings to find indicators with negative or near-zero values.
4
Apply stepwise deletion: remove the worst indicator, rerun the model, and re-check reliability/validity before deleting more.
5
After convergent validity improves, discriminant validity still requires a separate test using the Fornell–Larcker criterion.
6
Under Fornell–Larcker, the square root of AVE for a construct must exceed its correlations with other constructs.

Highlights

AVE is calculated directly from outer loadings by squaring each loading, summing them, and dividing by the number of indicators.

A loading around 0.70 is tied to the AVE > 0.50 rule because 0.70² ≈ 0.49, keeping the average variance extracted near the cutoff.

Stepwise deletion is the recommended response to low loadings: delete one weak indicator, rerun, and only continue if metrics remain poor.

Discriminant validity via Fornell–Larcker uses √AVE as the “top value,” which must be larger than the construct’s correlation(s).

In the example, task conflict’s √AVE is 0.841 and exceeds its correlation with team performance, satisfying the criterion. 