grad-pls-sem

Overview

PLS-SEM (Wold, 1982; Hair et al., 2017) is a variance-based approach to structural equation modeling that estimates composite-based path models. Unlike CB-SEM, it maximizes explained variance in endogenous constructs and readily handles both reflective and formative measurement models.

When to Use

• Formative measurement models are part of the research design
• Sample size is small (PLS works with N ≥ 10× the largest number of paths pointing to any construct)
• Research goal is prediction and variance explanation rather than theory confirmation
• The structural model is complex with many constructs and indicators

When NOT to Use

• Research goal is strict theory testing and model fit assessment
• All constructs are reflective and sample size is adequate for CB-SEM
• You need global model fit indices (chi-square, CFI, RMSEA)
• Circular relationships (non-recursive models) are hypothesized

Assumptions

IRON LAW: PLS-SEM maximizes VARIANCE EXPLAINED, not model fit — it does NOT
test overall model fit like CB-SEM. A high R² does not mean the model
structure is correct.

Key assumptions:

1. Predictor specification — each construct must be correctly specified as reflective or formative
2. No circular (non-recursive) relationships in the structural model
3. Observations are independent (no nested structure without extensions)
4. Data need not be normally distributed (PLS is distribution-free)

Methodology

Step 1 — Specify Measurement Models

Classify each construct as reflective (arrows from construct to indicators) or formative (arrows from indicators to construct). Formative constructs require at minimum two indicators and a theoretical rationale.

Step 2 — Assess Reflective Measurement

Evaluate indicator reliability (loadings ≥ 0.70), internal consistency (CR ≥ 0.70), convergent validity (AVE ≥ 0.50), and discriminant validity (HTMT < 0.90).

Step 3 — Assess Formative Measurement

Check indicator weights for significance via bootstrapping. Examine VIF among indicators (VIF < 5.0). Assess content validity — dropping a formative indicator changes the construct meaning.

Step 4 — Evaluate Structural Model

Report path coefficients, R², f² effect sizes, Q² predictive relevance (via blindfolding), and bootstrapped confidence intervals. See references/ for algorithm details.

Output Format

## PLS-SEM Analysis: [Study Title]

### Reflective Measurement Assessment
| Construct | Indicator | Loading | CR | AVE | HTMT |
|-----------|-----------|---------|-----|-----|------|
| [name] | [item] | x.xx | x.xx | x.xx | x.xx |

### Formative Measurement Assessment
| Construct | Indicator | Weight | VIF | p-value |
|-----------|-----------|--------|-----|---------|
| [name] | [item] | x.xx | x.xx | x.xx |

### Structural Model
| Path | β | t-value | p-value | f² | Supported? |
|------|---|---------|---------|-----|------------|
| X → Y | x.xx | x.xx | x.xx | x.xx | [Yes/No] |

### Model Quality
| Endogenous Construct | R² | Q² |
|---------------------|-----|-----|
| [name] | x.xx | x.xx |

### Limitations
- [Note any assumption violations]

Gotchas

• PLS-SEM is NOT a silver bullet for small samples — it still requires adequate statistical power
• Misspecifying reflective as formative (or vice versa) fundamentally changes results
• HTMT is preferred over Fornell-Larcker for discriminant validity in PLS-SEM
• PLS overestimates loadings and underestimates path coefficients (consistency at large corrects this)
• Blindfolding Q² > 0 shows predictive relevance but does not validate the model structure
• Reporting PLS results using CB-SEM criteria (CFI, RMSEA) is methodologically incorrect

References

• Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (2nd ed.). Sage.
• Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity. Journal of the Academy of Marketing Science, 43(1), 115-135.
• Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report PLS-SEM. European Business Review, 31(1), 2-24.