Formative Measurement Model Assessment

Everything you learned last video now does not apply

Reflective assessment asks whether your indicators agree with each other. Formative assessment cannot ask that, because formative indicators have no obligation to correlate at all.

If quality, performance, social responsibility, and attractiveness make up a firm’s reputation drivers, then dropping one does not lose a redundant symptom — it changes what the construct means. That single fact invalidates Cronbach’s alpha, rho_A, rho_C, AVE, and HTMT for these constructs.

Three criteria replace them: redundancy analysis, collinearity, and significance and relevance of weights.

Specifying formative constructs: weights = mode_B

library(seminr)

corp_rep_mm_ext <- constructs(
  composite("QUAL", multi_items("qual_", 1:8), weights = mode_B),
  composite("PERF", multi_items("perf_", 1:5), weights = mode_B),
  composite("CSOR", multi_items("csor_", 1:5), weights = mode_B),
  composite("ATTR", multi_items("attr_", 1:3), weights = mode_B),
  composite("COMP", multi_items("comp_", 1:3)),
  composite("LIKE", multi_items("like_", 1:3)),
  composite("CUSA", single_item("cusa")),
  composite("CUSL", multi_items("cusl_", 1:3)))

The distinction that trips everyone up. In the reflective lesson we said composite() is about estimation, and reflective-vs-formative is about assessment. Here is the estimation half: mode_B computes regression weights, mode_A (the default) computes correlation weights. Only the four drivers are mode B — the rest of the model is unchanged. One model, two measurement philosophies, one constructs() call.

1. Convergent validity — redundancy analysis

Can your formative indicators, taken together, reproduce a direct global measure of the same concept? You test this by regressing each formative construct on a single-item global measure of itself:

ATTR_redundancy_mm <- constructs(
  composite("ATTR_F", multi_items("attr_", 1:3), weights = mode_B),
  composite("ATTR_G", single_item("attr_global")))

ATTR_redundancy_sm <- relationships(paths(from = "ATTR_F", to = "ATTR_G"))

ATTR_redundancy_pls_model <- estimate_pls(
  data = corp_rep_data,
  measurement_model = ATTR_redundancy_mm,
  structural_model  = ATTR_redundancy_sm,
  missing = mean_replacement, missing_value = "-99")

summary(ATTR_redundancy_pls_model)$paths

The path should reach 0.708 — the same “half the variance” logic as indicator reliability. In the corporate reputation data all four pass: QUAL 0.805, PERF 0.811, CSOR 0.857, ATTR 0.874.

This requires that you collected a global item for each formative construct. If you did not, you cannot run this test — which is why it belongs in your questionnaire design, not your analysis plan.

2. Collinearity — VIF

corp_rep_summary_ext$validity$vif_items

Formative weights are regression coefficients, so collinear indicators destabilise them and can flip their signs. Below 3 is comfortable; 5 is the hard ceiling. Across all 21 formative indicators here the highest is qual_3 at 2.27 — no action needed.

3. Significance and relevance of weights

set.seed(123)
corp_rep_boot_ext <- bootstrap_model(corp_rep_pls_model_ext, nboot = 1000)
corp_rep_boot_ext_summary <- summary(corp_rep_boot_ext, alpha = 0.05)

corp_rep_boot_ext_summary$bootstrapped_weights
corp_rep_boot_ext_summary$bootstrapped_loadings

Five weights have confidence intervals covering zero: qual_2, qual_3, qual_4, csor_2, csor_4. This is not the disaster it looks like.

With eight indicators on QUAL, weights are mathematically compressed — the more indicators a formative construct has, the smaller the average weight, regardless of quality. That is exactly why the decision rule falls back on loadings:

All five flagged indicators here clear the loading test, so all five stay. Formative indicator removal is a content decision, not a statistical reflex — deleting one changes what your construct means.

R practice — comment the why, never the what. Look at the comment above estimate_pls() in the script: it does not say “estimate the model”, because the code already says that. It says why missing_value = "-99" — that value is a sentinel for a skipped answer, not a real response. Code records what; comments record decisions.

What never to report

Cronbach’s alpha, rho_A, rho_C, AVE, and HTMT for a formative construct. All of them assume interchangeable indicators. Reporting them is the fastest way to signal you have not understood formative measurement — and reviewers do notice.

Going further

Chapter 5 of Hair et al. (2026) has the full treatment, including questionnaire design for redundancy analysis. Next: the structural model — path coefficients, R², effect sizes, and out-of-sample prediction.