18. SEMinR Lecture Series - Evaluating Formative Model | Step 3 | Indicator Weights

Formative measurement model evaluation reaches its final checkpoint by testing whether each indicator’s weight is statistically meaningful and whether the indicator truly contributes to forming the construct. In practice, that means running a bootstrap procedure to test the significance and relevance (size) of indicator weights, then using confidence intervals and indicator loadings to decide whether weak or insignificant weights should trigger indicator removal. The stakes are straightforward: formative models can’t rely on internal consistency alone, so indicator-level evidence has to guide retention or deletion.

The process starts after collinearity and convergent validity checks are already completed. For the “indicator weights” step, significance testing depends on bootstrapping. The workflow uses a SEMinR bootstrap function with a SEMinR model specified as the bootstrap target. A large number of bootstrap samples is recommended—10,000 for final reporting—though a smaller run (e.g., 1,000) can be used for preliminary estimation to save computation time. To speed things up, the procedure can automatically detect and use the maximum number of cores available on the machine (via a parallel cores option). A seed can make results reproducible, but it’s suggested to keep defaults unless strict repeatability is required.

After bootstrapping, the bootstrap output is stored in a summary object (via a summary function) that takes the bootstrap results and an alpha level. The transcript uses the default alpha = 0.05 for two-tailed testing, aligning with the convention for indicator weight significance. The resulting output provides indicator weights along with T values (and related statistics). A common rule of thumb is that, for a two-tailed 5% test, T values above 1.96 indicate statistical significance. The transcript also notes other critical thresholds for different alpha levels (e.g., 1% and 10%), but the decision framework in this run centers on 1.96.

In the example output, some formative indicators show significant weights while others fall short of the T-value threshold. That outcome alone doesn’t automatically justify deleting indicators. Instead, confidence intervals offer a second lens: if a weight’s confidence interval does not include zero, the weight is treated as significant and the indicator can be retained; if the interval includes zero, the weight is not statistically significant at the chosen alpha and the indicator becomes a candidate for removal.

When weights are insignificant, the modeler must still check absolute contribution through indicator loadings. The transcript treats loadings of 0.5 or higher as evidence of meaningful absolute contribution. Importantly, even an indicator with a lower weight can still be retained if its loading is strong and its confidence interval excludes zero. In the worked example, indicator weights are mixed—some are insignificant—but the indicator loadings are reported as consistently above 0.5, and the confidence-interval logic supports keeping the indicators. The session ends with the takeaway that indicator retention in formative models depends on both statistical significance (via T values and confidence intervals) and practical contribution (via loadings), not on weight significance alone.