Structural Equation Modelling

Client Context

A psychology researcher at a Russell Group university was investigating whether self-efficacy mediates the relationship between perceived social support and academic achievement in first-year undergraduates. She had collected survey data from 480 students across three measurement waves and needed a structural equation model (SEM) to test her hypothesised mediation pathway.

The Challenge

The measurement model involved three latent constructs, each with four to six indicators. Initial confirmatory factor analysis showed poor fit (CFI = 0.82, RMSEA = 0.11), and several indicator cross-loadings were suspected. The researcher also needed to test for measurement invariance across gender groups and handle 8% missing data under a MAR assumption. The analysis required AMOS expertise and alignment with APA reporting standards.

Our Approach

We first refined the measurement model by removing two weak indicators and allowing one theoretically justified cross-loading, achieving acceptable fit (CFI = 0.96, RMSEA = 0.04). We then estimated the structural model using full-information maximum likelihood to handle missing data. Bootstrapped confidence intervals (5,000 resamples) were used to test the indirect effect of social support on achievement through self-efficacy. Measurement invariance was tested sequentially: configural, metric, and scalar. All analyses were conducted in AMOS with R verification, and results were reported following the APA SEM reporting guidelines.

Results

The mediation model showed a significant indirect effect (standardised indirect effect = 0.19, 95% bootstrapped CI: 0.10 to 0.29). Scalar invariance was supported across gender, confirming that group comparisons were valid. The direct effect of social support on achievement remained significant, indicating partial mediation. The manuscript was accepted by the British Journal of Educational Psychology on first submission.

Client Testimonial

"I had struggled with SEM for months. AnalyticsScholar not only solved the measurement issues but explained every decision so clearly that I could defend the analysis in my viva with confidence."

— Dr. Amira H., Lecturer in Educational Psychology

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