Structural Equation Modeling (SEM) for Dissertation Research
By Dr. Lisa H., PhD in Sociology. Reviewed by Dr. Patricia N.. 2025-09-25.
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Key takeaways
- SEM tests complex theoretical models with both measurement and structural components
- Plan for adequate sample size: minimum 200 cases, ideally 10-20 per parameter
- Specify models based on theory, SEM is confirmatory, not exploratory
- Report multiple fit indices: χ², CFI, TLI, RMSEA, and SRMR
- Only modify models with theoretical justification, not just statistical criteria
- Present path diagrams with standardized coefficients and R² values
Worked Example: Testing a Mediation Model
Suppose you test whether job autonomy predicts burnout through work engagement, using survey data from 412 nurses. Step 1: run a confirmatory factor analysis (CFA) for the three latent constructs and check loadings (ideally above .50), composite reliability (above .70), and average variance extracted (above .50). Step 2: fit the structural model with autonomy to engagement, engagement to burnout, and the direct path from autonomy to burnout. Step 3: test the indirect effect with bias-corrected bootstrapping (for example, 5,000 resamples) and report the 95% confidence interval. If the interval excludes zero, the indirect effect is supported.
How to Report SEM Results in APA Style
Report, in this order: software and estimator (for example, lavaan with MLR), sample size and missing data handling (for example, FIML), measurement model fit, then structural model fit and standardized paths.
Commonly reported fit indices and conventional cutoffs (Hu and Bentler, 1999): chi-square with df and p, CFI and TLI at or above .95 (.90 acceptable), RMSEA at or below .06 with its 90% CI, and SRMR at or below .08.
Example sentence: The structural model showed good fit, chi-square(87) = 164.21, p < .001, CFI = .96, TLI = .95, RMSEA = .046, 90% CI [.035, .057], SRMR = .041. Autonomy positively predicted engagement (beta = .42, p < .001), and engagement negatively predicted burnout (beta = -.51, p < .001). The indirect effect was significant (beta = -.21, 95% CI [-.29, -.14]).
Include a path diagram with standardized coefficients and a table of loadings. Numbers in these examples are illustrative.
What Is Structural Equation Modeling?
Structural equation modeling (SEM) is a multivariate statistical technique that combines factor analysis and path analysis to test complex theoretical models. It allows you to examine relationships among multiple observed and latent variables simultaneously, making it ideal for testing theoretical frameworks in dissertation research.
Unlike simpler techniques like regression, SEM can model measurement error, test indirect effects (mediation), and evaluate overall model fit. This makes it particularly powerful for social science, psychology, education, and business dissertations where you're testing theoretically derived models.
SEM has two main components: the measurement model (how observed variables relate to latent constructs, tested via confirmatory factor analysis) and the structural model (the hypothesized causal relationships among constructs). You typically test the measurement model first to ensure your constructs are adequately measured before testing structural relationships.
Planning Your SEM Analysis
Sample size is critical in SEM. The general rule of thumb is 10-20 cases per estimated parameter, with a minimum of 200 cases. Complex models with many parameters require larger samples. Inadequate sample sizes lead to unstable solutions and unreliable fit indices.
Specify your model based on theory, not data. SEM is a confirmatory technique, you should have a theoretically justified model before you begin analysis. Data-driven model modification (adding or removing paths based solely on modification indices) capitalizes on sample-specific characteristics and reduces generalizability.
Choose appropriate software: AMOS (user-friendly, graphical interface), Mplus (powerful, flexible syntax), LISREL (classic SEM software), or R packages like lavaan (free, growing capabilities). Your choice may depend on your university's available licenses and your advisor's expertise.
Assess data assumptions: multivariate normality (SEM assumes this, though robust methods exist for violations), absence of excessive multicollinearity, and adequate sample size. Missing data handling is important, full information maximum likelihood (FIML) is generally preferred over listwise deletion.
Evaluating and Reporting Model Fit
Report multiple fit indices, no single index tells the whole story. Standard reporting includes: Chi-square (χ²) with degrees of freedom and p-value, CFI (Comparative Fit Index, ≥.95 good), TLI (Tucker-Lewis Index, ≥.95 good), RMSEA (Root Mean Square Error of Approximation, ≤.06 good) with 90% confidence interval, and SRMR (Standardized Root Mean Square Residual, ≤.08 good).
If your initial model doesn't fit well, resist the temptation to make atheoretical modifications. Review modification indices, but only make changes you can justify theoretically. Each modification should be documented and justified in your methodology chapter. Report both your original model and any modified model.
Present results with a path diagram showing standardized coefficients, significance levels, and R² values for endogenous variables. Include a table of all parameter estimates (unstandardized and standardized), standard errors, and p-values. For mediation analyses, report indirect effects with bootstrapped confidence intervals.
Compare alternative models when theoretically justified. Report fit indices for all compared models and use chi-square difference tests (for nested models) or information criteria (AIC, BIC for non-nested models) to determine which model best represents your data.