What PLS-SEM is and when to use it
Understand latent constructs, measurement and structural models, the difference between PLS-SEM and CB-SEM, and minimum sample sizes.
Many research questions in business and the social sciences involve concepts that cannot be measured directly: trust, satisfaction, intention, perceived usefulness. We measure each one with several survey items and want to test how the concepts influence each other. Structural equation modeling (SEM) does both at once: it estimates how well the items measure each concept and how strongly the concepts are related.
The vocabulary
- Construct (latent variable): the concept, such as behavioural intention (BI). Drawn as an oval or circle.
- Indicator (item, manifest variable): a survey question such as BI1 “I intend to use the app in the next months”. Drawn as a rectangle.
- Measurement model (outer model): the links between each construct and its indicators.
- Structural model (inner model): the paths between constructs, which represent your hypotheses.
- Exogenous constructs only send arrows (no construct explains them); endogenous constructs receive at least one arrow and get an R².
Reflective or formative?
In a reflective measurement model, the construct causes the indicators: if your trust in a website rises, your answers to all trust items rise together. The items are interchangeable and should correlate highly. Most attitude scales are reflective. In a formative model, the indicators form the construct: “socio-economic status” is made up of income, education and occupation, which need not correlate. Dropping a formative indicator changes the meaning of the construct. The type changes how you assess the measurement model, so decide it from theory before you analyse. All six constructs in this course are reflective.
PLS-SEM or CB-SEM?
There are two families of SEM. Covariance-based SEM (CB-SEM, as in AMOS, lavaan and the CB-SEM Studio on this site) estimates the model so that the implied covariance matrix matches the observed one, treats constructs as common factors, and provides global fit tests such as χ², CFI and RMSEA. Partial least squares SEM (PLS-SEM) estimates constructs as weighted composites of their indicators, maximising the explained variance of the endogenous constructs.
| Choose PLS-SEM when… | Choose CB-SEM when… |
|---|---|
| the aim is prediction and explaining variance in key outcomes, or the research is exploratory or extends existing theory | the aim is to test or confirm a well-established theory |
| the model is complex (many constructs, indicators and paths) or includes formative constructs | all constructs are reflective common factors and you need global fit indices |
| you need latent variable scores for follow-up analyses (IPMA, fsQCA, NCA) | you want to model error covariances or test strict measurement invariance |
| the sample is moderate and the data are non-normal | the sample is large enough for maximum likelihood estimation |
A small sample is not, on its own, a good justification for PLS-SEM; reviewers increasingly reject that argument. Justify your choice with the research goal (prediction, theory development), model complexity or formative measurement, and cite methodological sources such as Hair, Hult, Ringle and Sarstedt (2022) and Sarstedt et al. (2016).
How many respondents?
The old “10-times rule” (ten times the largest number of arrows pointing at a construct) is easy but often too lenient. Better options:
- The inverse square root method (Kock and Hadaya, 2018): nmin > (2.486 / |pmin|)², where pmin is the smallest path coefficient you expect to be significant at 5%. For pmin = 0.2, you need 155 respondents; for 0.15, 275; for 0.11 to 0.20 (common in practice), 155 to 511.
- A power analysis for the most complex regression in the model: the construct with the most predictors. In this course, BI has five predictors including the interaction term; for a medium effect (f² = 0.15) with 80% power, the power analysis tool gives 92 respondents, and for a small-to-medium effect (f² = 0.08), 166.
The course sample has 300 respondents, enough for paths as small as about 0.145.
The course study
The sample study in PLS-SEM Studio tests what makes people adopt a new mobile technology, following the unified theory of acceptance and use of technology (UTAUT). Performance expectancy (PE), effort expectancy (EE), social influence (SI) and trust (TR) drive behavioural intention (BI), which in turn drives actual use behaviour (UB). Effort expectancy also has a direct path to use, and trust is expected to strengthen the effect of performance expectancy on intention. You will estimate and assess this model step by step over the next eight lessons.
Key takeaways
- SEM combines a measurement model (constructs and items) with a structural model (hypotheses between constructs).
- Decide reflective versus formative measurement from theory, before the analysis.
- Justify PLS-SEM with the research goal, model complexity or formative constructs, not just a small sample.
- Plan the sample size with the inverse square root method or a power analysis.
Check your understanding
Answer each question to see the explanation. Finishing the quiz marks this lesson as complete.