Structural Equation Modeling (SEM) in SPSS: Measurement and Structural Models

Structural Equation Modeling (SEM) is a powerful statistical technique that lets you test complex relationships between variables. It goes beyond simple regression by combining measurement models (how you measure concepts) with structural models (how those concepts relate).

In SPSS, SEM is typically run using the AMOS add-on (Analysis of Moment Structures).

Let’s break it down into the two key parts:

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1. The Measurement Model

The measurement model answers: “How well do my observed survey items represent the hidden concepts (latent variables) I want to measure?”

For example:

• Latent variable: Job Satisfaction
• Measured by Likert-scale items: pay satisfaction, promotion satisfaction, supervisor support.

Steps in AMOS/SPSS:

1. Draw your model: Create latent variables (ovals) and link them to observed items (rectangles).
2. Run Confirmatory Factor Analysis (CFA): This tests if the items really belong to their latent construct.
3. Check factor loadings: Items should load >0.50 (preferably >0.70) on their intended factor.
4. Assess validity and reliability:
   • Cronbach’s Alpha / Composite Reliability (CR) > 0.7
   • Average Variance Extracted (AVE) > 0.5
   • Discriminant Validity: Constructs should be distinct from each other.

If the measurement model fits well, you can move on. If not, you may need to remove weak items or re-specify factors.

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2. The Structural Model

The structural model answers: “How do my latent variables relate to each other?”

For example:

• Hypothesis: Job Satisfaction → Organizational Commitment → Employee Performance.
• You already know how each construct is measured (from the measurement model). Now you’re testing the causal paths between them.

Steps in AMOS/SPSS:

1. Add directional arrows between latent variables to represent hypotheses.
2. Run the SEM analysis.
3. Assess model fit indices:
   • Chi-square (χ²/df): Ideally < 3
   • RMSEA (Root Mean Square Error of Approximation): < 0.08
   • CFI (Comparative Fit Index): > 0.90
   • TLI (Tucker-Lewis Index): > 0.90
4. Check path coefficients (β): These show the strength and significance of relationships between variables.

Significant paths (p < 0.05) support your hypotheses. Non-significant paths may need to be revised or dropped.

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Putting It Together

• Measurement Model = Validation stage. Ensures your survey items measure what they’re supposed to.
• Structural Model = Testing stage. Examines the actual hypotheses and relationships between constructs.

In SEM, you must establish a solid measurement model before interpreting the structural model—otherwise your results won’t be trustworthy.

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Example Research Flow

1. Design Survey → Collect data on Likert-scale items.
2. Run CFA (Measurement Model) → Confirm constructs like job satisfaction, commitment, performance.
3. Fit Structural Model → Test hypotheses (e.g., Does satisfaction drive performance?).
4. Interpret Fit Indices & Path Coefficients → Accept/reject hypotheses.

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In short

Structural Equation Modeling in SPSS (AMOS) is like building a house:

• The measurement model is your foundation (are your variables solid?).
• The structural model is the design (how the variables connect).

Once both are strong, SEM becomes a powerful tool to validate theories and uncover insights in social sciences, business, psychology, and beyond.