Reflective Measurement Model Assessment

The four criteria every reviewer checks

When you submit a paper using PLS-SEM with reflective constructs, there are four things every reviewer will evaluate before looking at your hypotheses:

1. Indicator reliability — does each item carry enough of its construct’s variance?
2. Internal consistency reliability — do the items on a construct agree with each other?
3. Convergent validity — does the construct explain at least half the indicator variance?
4. Discriminant validity — are the constructs distinguishable from each other?

SEMinR gives you all four from a single summary() call. Here’s the end-to-end workflow using the corporate reputation example from Chapter 4.

The corporate reputation model

library(seminr)
library(seminrExtras)

corp_rep_data <- corp_rep_data

# Measurement model
corp_rep_mm <- constructs(
  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)))

# Structural model
corp_rep_sm <- relationships(
  paths(from = c("COMP", "LIKE"), to = c("CUSA", "CUSL")),
  paths(from = c("CUSA"),         to = c("CUSL")))

# Estimate
corp_rep_pls_model <- estimate_pls(
  data              = corp_rep_data,
  measurement_model = corp_rep_mm,
  structural_model  = corp_rep_sm,
  missing           = mean_replacement,
  missing_value     = "-99")

summary_corp_rep <- summary(corp_rep_pls_model)

Note on composite(): In SEMinR, composite() is the estimation mode, not a statement about whether your construct is reflectively or formatively measured. Reflective vs. formative is a question about how you assess the construct, which is what this video is about. We’ll return to this distinction in the formative measurement video.

1. Indicator reliability

summary_corp_rep$loadings
summary_corp_rep$loadings^2

Squaring the loading gives indicator reliability — the proportion of an item’s variance explained by its construct. The conventional threshold is 0.708 (which squares to 0.50). Items between 0.40 and 0.708 should be deleted only if removing them raises composite reliability or AVE above threshold. Below 0.40: drop them.

2. Internal consistency reliability

summary_corp_rep$reliability
plot(summary_corp_rep$reliability)

SEMinR reports Cronbach’s alpha, rho_A, and composite reliability (rho_C). Report rho_A as the primary measure — Dijkstra and Henseler showed it’s the consistent reliability estimator for PLS. It sits between alpha (lower bound) and rho_C (upper bound).

3. Convergent validity

AVE is in the same $reliability table. The floor is 0.50: more than half of the indicator variance should be accounted for by the construct.

4. Discriminant validity with HTMT

summary_corp_rep$validity$htmt

Fornell-Larcker is out. HTMT is in. Henseler, Ringle, and Sarstedt (2015) showed HTMT has much better detection rates for discriminant validity problems. Thresholds: < 0.85 for conceptually distinct constructs, < 0.90 for conceptually similar ones.

Bootstrapped HTMT — the inferential test

set.seed(123)
boot_corp_rep     <- bootstrap_model(corp_rep_pls_model, nboot = 1000)
sum_boot_corp_rep <- summary(boot_corp_rep, alpha = 0.10)
sum_boot_corp_rep$bootstrapped_HTMT

The stricter test: the upper bound of the 90% bootstrap CI on HTMT should not include 1. This is what reviewers increasingly expect in 2026.

R practice #3 — Seed your bootstraps. set.seed(123) immediately before bootstrap_model() is a one-line insurance policy. Without it, every run produces slightly different CIs and your Table 3 becomes unreproducible. Do it every time.

Bonus — the congruence coefficient

congruence_test(corp_rep_pls_model, alpha = 0.10)$results

The congruence coefficient (Franke, Sarstedt, Danks, 2021) is a more stringent test of whether two construct scores capture the same underlying latent variable. Chapter 4 covers the theory.

Going further

Full theoretical treatment is in Chapter 4 of Hair et al. (2026). The next video in this series covers formative measurement — same workflow, completely different rules.