If you read quantitative research in management, psychology, education, marketing, information systems or public health, you will often see diagrams with ovals, rectangles and arrows, accompanied by fit indices such as CFI and RMSEA. These are signs of structural equation modelling (SEM). Many PhD students feel they must use SEM to produce “serious” quantitative research. Others are unsure whether their study really needs it, or whether regression would be enough.
This post explains what SEM is, its main components, the difference between covariance-based SEM and PLS-SEM, when SEM is the right choice, what you need before using it, and how to report it clearly in your thesis.
What is structural equation modelling?
Structural equation modelling is a family of statistical techniques that allows you to test complex relationships among multiple variables at the same time. It combines two ideas:
- Factor analysis: measuring latent constructs (such as motivation or trust) using several observed indicators (questionnaire items).
- Path analysis / regression: testing relationships among constructs, including direct and indirect effects.
In one integrated model, SEM estimates how well your items measure your constructs and how your constructs relate to each other.
Key components of SEM
Latent variables
Latent variables are constructs that cannot be observed directly, such as job satisfaction or self-efficacy. In diagrams, they are usually drawn as ovals or circles.
Observed (manifest) variables
These are the measured indicators, such as individual questionnaire items. They are drawn as rectangles.
The measurement model
The measurement model specifies how observed indicators relate to latent variables. It is essentially a confirmatory factor analysis (CFA). It allows you to assess reliability and validity of your constructs.
The structural model
The structural model specifies the hypothesised relationships among latent variables, such as “Leadership → Psychological safety → Engagement”. These are shown as single-headed arrows between ovals.
Error terms
SEM explicitly models measurement error for each indicator and unexplained variance (disturbance) for each endogenous (predicted) latent variable.
Exogenous and endogenous variables
- Exogenous variables are not predicted by other variables in the model (similar to independent variables).
- Endogenous variables are predicted by at least one other variable (similar to dependent variables, and including mediators).
Why use SEM instead of regression?
SEM offers several advantages over running a series of separate regressions:
- It accounts for measurement error. Regression typically uses averaged scale scores, which assume perfect measurement. SEM models measurement error explicitly, which can give less biased estimates of relationships between constructs.
- It tests the whole model at once. Multiple dependent variables and mediators can be estimated simultaneously.
- It provides model fit indices. You can assess how well your overall theoretical model reproduces the observed data, and compare alternative models.
- It handles complex models. Mediation, moderation (with some methods), multiple-group comparisons and longitudinal models can all be tested within SEM.
- It tests measurement invariance. You can check whether constructs are measured equivalently across groups before comparing them.
When is SEM needed?
SEM is a good choice when:
- Your model includes several latent constructs measured by multiple items.
- You want to test a network of relationships, including mediators, in one model.
- You want to account for measurement error.
- You need to compare competing theoretical models.
- You want to compare models across groups, such as countries or genders, with measurement invariance testing.
- You have a strong theoretical basis for the model.
When SEM may not be necessary
- Your model is simple, such as one predictor and one outcome, or a few predictors of one outcome, and your scales are reliable. Multiple regression may be sufficient and easier to communicate.
- Your sample size is small, which can make covariance-based SEM unstable.
- Your research is exploratory with little theory to specify the model.
Using SEM when a simpler method would answer your question can make your thesis harder to follow without adding value. Choose the method that fits your research questions, not the method that seems most advanced.
Two main approaches: CB-SEM and PLS-SEM
Covariance-based SEM (CB-SEM)
CB-SEM estimates model parameters so that the model-implied covariance matrix is as close as possible to the observed covariance matrix. It is typically estimated with maximum likelihood.
- Emphasises theory testing and confirmation.
- Provides global fit indices (χ², CFI, TLI, RMSEA, SRMR).
- Generally requires larger samples and assumes approximately multivariate normal data (though robust estimators exist).
- Software: AMOS, Mplus, lavaan (R), LISREL, Stata.
Partial least squares SEM (PLS-SEM)
PLS-SEM uses a variance-based approach that maximises the explained variance of endogenous constructs.
- Often described as prediction-oriented.
- Often used with smaller samples, complex models, non-normal data and formative constructs.
- Assessment focuses on reliability, validity, R², effect sizes and predictive relevance rather than traditional global fit.
- Software: SmartPLS, and packages such as seminr in R.
There is an ongoing methodological debate about when PLS-SEM is appropriate. Critics argue it is sometimes chosen merely to avoid the demands of CB-SEM, while proponents highlight its usefulness for prediction-oriented research. Whichever you choose, justify the choice based on your research aims, data and constructs, and cite methodological sources.
What you need before running SEM
1. A clear theoretical model
Every path should be justified by theory or prior research. Draw your conceptual model before collecting data.
2. Good measurement
Use validated multi-item scales, ideally with at least three indicators per construct.
3. Adequate sample size
Sample size requirements depend on model complexity, number of indicators, strength of loadings and estimation method. Older rules such as “at least 200” or “10 cases per parameter” are rough guides. Simulation studies show that requirements vary widely. Power analysis tools and Monte Carlo simulation can provide better estimates. Cite guidance appropriate to your method.
4. Clean data
Check missing data, outliers, normality and multicollinearity before analysis.
The two-step approach
A widely recommended strategy, associated with Anderson and Gerbing (1988), is to test the model in two steps:
- Measurement model: run a CFA to check that indicators load well on their constructs, assess reliability, convergent validity and discriminant validity, and confirm acceptable model fit.
- Structural model: once the measurement model is satisfactory, test the hypothesised relationships among constructs.
This separates measurement problems from structural problems and makes interpretation clearer.
Assessing and reporting CB-SEM results
- Model fit: report several indices, such as χ² (with df and p), CFI, TLI, RMSEA (with 90% CI) and SRMR, and cite the cut-off guidelines you use (for example, Hu and Bentler, 1999), treating them as guidelines rather than rigid rules.
- Measurement model: standardised loadings, composite reliability, average variance extracted and discriminant validity evidence.
- Structural paths: standardised coefficients, standard errors or confidence intervals, and p-values.
- Explained variance: R² for each endogenous construct.
- Indirect effects: with bootstrapped confidence intervals if testing mediation.
- Model diagram: showing the final model with standardised estimates.
A worked example of an SEM study
Suppose your research question is: “Does perceived organisational support influence employees' innovative behaviour through work engagement, and does this differ between public and private sector employees?”
- Constructs: perceived organisational support (6 items), work engagement (9 items across three dimensions), and innovative behaviour (6 items), all measured with established scales.
- Model: perceived support → engagement → innovative behaviour, with a direct path from support to innovative behaviour as well.
- Why SEM? The model has three latent constructs, a mediator, and a planned comparison across two sectors. SEM allows you to model measurement error, test the indirect effect with bootstrapping, and test whether constructs are measured equivalently in both sectors before comparing paths.
- Step 1, measurement model: A CFA shows acceptable fit after one item with a low loading is removed (with justification). Composite reliability and AVE support convergent validity, and discriminant validity is supported.
- Step 2, measurement invariance: Configural, metric and scalar invariance are tested across sectors. Metric invariance holds, allowing meaningful comparison of structural paths.
- Step 3, structural model: The structural model shows acceptable fit. The indirect effect of support on innovative behaviour through engagement is significant, with a bootstrapped confidence interval excluding zero.
- Step 4, multi-group comparison: The path from engagement to innovative behaviour is stronger in the private sector than in the public sector.
Each step answers a specific part of the research question. This is the kind of logical sequence that makes an SEM chapter easy for examiners to follow.
Explaining SEM results in plain language
Examiners appreciate when you translate statistical output into clear statements. After presenting fit indices and path coefficients, add sentences such as: “In practical terms, employees who felt more supported by their organisation reported higher engagement, and more engaged employees reported more innovative behaviour. About 40% of the variance in innovative behaviour was explained by the model.” (Illustrative figure.) Plain-language summaries like this show that you understand what your model means, not just how to run it.
Common mistakes to avoid
- Using SEM without a clear theoretical model.
- Skipping the measurement model and going straight to structural paths.
- Reporting only favourable fit indices.
- Making many modification-index-based changes without justification.
- Claiming causality from cross-sectional SEM. SEM tests whether data are consistent with a causal model; it does not prove causation.
- Choosing PLS-SEM or CB-SEM without justification.
- Presenting large tables of output without explaining what they mean for the hypotheses.
Final thoughts
Structural equation modelling is a powerful tool for testing theory-driven models with multiple constructs, mediators and measurement error. It is most valuable when your model is complex, your constructs are latent, and your theory is well developed. It is not automatically better than regression, and it demands careful preparation, adequate samples and transparent reporting. Choose SEM because your research questions need it, follow the two-step approach, and explain your results in plain language alongside the statistics.
Are you deciding between regression and SEM for your thesis? Describe your model in the comments and we can help you think it through.