Latent variables (LVs)
The constructs you actually care about - customer satisfaction, trust, perceived usefulness. Cannot be measured directly.
PLS-SEM explained
What is PLS-SEM?
Partial Least Squares Structural Equation Modeling is a variance-based method for estimating models with latent constructs - things you cannot measure directly, only through observable indicators. This page explains what PLS-SEM is, when to use it, and how it differs from covariance-based SEM.
What PLS-SEM actually does, in plain English
Some things researchers care about - customer satisfaction, brand trust, intention to use a technology - can't be measured with a single number. There is no "satisfaction meter" you can put on someone. So researchers ask several survey questions that circle around the concept ("I'm satisfied with X", "I'd recommend X", "X met my expectations") and use those answers as clues to what's going on underneath.
PLS-SEM is the math that turns those clues into a testable model. It asks: does satisfaction actually cause loyalty, and if so how strongly? It gives you numbers you can report - for example, "a 1-point increase in satisfaction corresponds to a 0.6-point increase in loyalty, and this effect is statistically reliable". Marketing researchers, HR researchers, information-systems researchers, health-services researchers use it every day.
The four building blocks
Indicators (manifest variables)
Observable dataset columns that stand in for each latent construct - survey items, ratings, sensor readings.
Measurement model (outer model)
How the indicators relate to their latent variable. Reflective (LV causes indicators, e.g. satisfaction → sat1..sat4) or formative (indicators cause the LV, e.g. income + education → SES).
Structural model (inner model)
The hypothesized relationships between latent variables. These are the causal paths you are testing.
Quality criteria that matter
Reviewers expect the following criteria to be reported for a defensible PLS-SEM analysis.
- R² per endogenous LV
- How much variance the model explains. Chin (1998) tiers: 0.19 weak, 0.33 moderate, 0.67 substantial.
- Path coefficients with p-values
- Bootstrapped significance tests on the structural paths. Publication standard is 5 000+ resamples.
- HTMT for discriminant validity
- Heterotrait-Monotrait Ratio (Henseler 2015). Threshold 0.85 conservative, 0.90 liberal. HTMT2 (Roemer 2021) refines this.
- Reliability: Cronbach's α, ρ_A, ρ_c
- Convergent validity indicators; ≥ 0.70 is the standard threshold for confirmatory research.
- SRMR model fit
- Standardized Root Mean Square Residual. < 0.08 is considered a good fit (Hu & Bentler 1999).
- Sample size guidance
- The 10-times rule: sample size at least ten times the largest number of paths pointing at any single latent variable.
PLS-SEM vs CB-SEM
PLS-SEM is not a strict substitute for covariance-based SEM (CB-SEM). Both are structural equation modeling techniques but they optimize for different goals.
| Aspect | PLS-SEM | CB-SEM |
|---|---|---|
| Estimation goal | Prediction, exploration | Confirmation of established theory |
| Assumptions | No distributional requirements | Multivariate normality |
| Sample size | Works with small samples (n < 100 possible) | Typically n ≥ 200 |
| Formative indicators | Native support | Awkward, requires workarounds |
| Model complexity | Handles complex models with many LVs and paths well | Struggles with high complexity |
| Fit indices | SRMR, dULS, dG | χ², CFI, TLI, RMSEA (comprehensive) |
| Popular tools | OpenPLS, SmartPLS, seminr, cSEM | lavaan, Mplus, AMOS, LISREL |
When to use PLS-SEM
- Your research is prediction- or exploration-oriented rather than confirming a well-established theory.
- You have a small sample or non-normal data.
- Your model has formative constructs (indicators causing the LV).
- Your model is structurally complex (many LVs, many hypothesized paths).
- You need to work with composite variables rather than common factors.
When NOT to use PLS-SEM
- You are confirming a well-established measurement theory and need traditional fit indices (χ², CFI, RMSEA) - use CB-SEM.
- Your indicators are purely reflective and you want to model measurement error rigorously - use CB-SEM.
- You need latent-variable scores that are strict common factors (not composites) - use CB-SEM.
- You are doing pure exploratory factor analysis without a structural model - use classical EFA / PCA instead.
A minimal example
A customer-satisfaction study asks: does perceived quality drive satisfaction, and does satisfaction drive loyalty? Three latent variables (Quality, Satisfaction, Loyalty), each measured by 3-5 survey items on a 7-point Likert scale. Two hypothesized paths (Quality → Satisfaction, Satisfaction → Loyalty). PLS-SEM estimates the path coefficients, checks whether the indicators reliably measure each construct (via loadings and HTMT), and computes bootstrapped p-values for the two paths.
Run a PLS-SEM analysis in your browser
OpenPLS is an open-source PLS-SEM tool that runs entirely in the browser. Visual path-diagram editor, full quality-criteria panel, advanced methods (MGA, IPMA, PLSpredict, FIMIX). Validated against SmartPLS 4 in a published working paper.
Further reading
The canonical practitioner reference is Hair, Hult, Ringle & Sarstedt (2021), A Primer on Partial Least Squares Structural Equation Modeling, 3rd ed. (Sage). For methodological guidance on when to use PLS-SEM vs alternatives, see Hair et al. (2019), When to use and how to report the results of PLS-SEM (European Business Review, 31(1), 2–24).