Patterns › Dimension reduction

PLS-SEM (partial least squares)

PLS-SEM estimates a structural equation model from composites rather than covariances, maximising explained variance with bootstrap inference — the variance-based counterpart to covariance-based SEM.

What is PLS-SEM (partial least squares)?

Where covariance-based SEM reproduces the covariance matrix under a latent-variable model, PLS builds each construct as a weighted composite of its indicators and maximizes explained variance in the dependent constructs. No distributional assumptions, no convergence problems, and it tolerates small samples and many indicators — at the cost of biased-toward-zero structural paths (consistent PLS corrections exist but are not in v1).

Inference is by bootstrap (200 resamples): path SEs, t-values, and percentile CIs. Reliability: composite reliability ρC and ρA, AVE (convergent validity, want ≥ 0.5), alongside α.

When should I use PLS-SEM (partial least squares)?

Prediction-oriented structural models, especially in business/psychology survey research.
Small samples or formative-leaning measurement where ML-SEM struggles.
Exploratory structural modeling before committing to a confirmatory model.

What data does it need?

Numeric indicator columns + a model: composites as 'F =~ i1 + i2', paths as 'Y ~ X1 + X2'.

What does it report?

Bootstrapped structural paths (estimate, SE, t, 95% CI), R² per endogenous construct, reliability table (α, ρC, AVE, ρA), indicator loadings with bootstrap t.

What does it assume?

Indicators assigned to the right blocks; composites are formed, not 'discovered'.
Bootstrap assumes rows are independent.

How do I interpret the result?

Judge paths by their bootstrap CIs. AVE < 0.5 (amber) means less than half the indicator variance reaches the construct — reconsider the block.

References

Hair, Hult, Ringle & Sarstedt (2022). A Primer on PLS-SEM, 3rd ed.
Ray, Danks & Calero Valdez (2022). seminr: Domain-specific language for PLS-SEM. JSS.