15. SPSS AMOS - Reporting Fit Indices | Measurement Model (Confirmatory Factor Analysis) - P1
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Report CFA measurement model quality first using a set of fit indices (Chi-square/CMIN/DF, CFI, TLI, GFI, RMSEA, SRMR/RMSR) against stated acceptance thresholds.
Briefing
A confirmatory factor analysis (CFA) measurement model can be reported in a structured way by pairing fit statistics with item-level decisions and clearly stated acceptance thresholds. In this walkthrough, the model’s overall goodness of fit is treated as the first priority: multiple fit indices (including Chi-square, CMIN/DF, CFI, TLI, GFI, RMSEA, and SRMR/RMSR) are used to judge whether the proposed factor structure is statistically acceptable. The key practical takeaway is that even when the initial model fit looks “very good,” a single weak indicator can drag down the measurement quality, and removing it can improve fit enough to justify reporting the final model.
The process begins with running the CFA in IBM SPSS AMOS and ensuring the output includes the needed components: standardized estimates, squared multiple correlations, residuals, modification indices, and covariance/correlation outputs. After calculating estimates, the model fit results are checked against common benchmarks. The walkthrough emphasizes that the Chi-square p-value often becomes significant with large samples, so it should not be the sole decision rule. Instead, attention shifts to indices such as CMIN/DF (recommended between 3 and 5), CFI and TLI (both above 0.90), GFI (above 0.90), and SRMR/RMSR (below 0.08). In the reported case, the model fit is ultimately considered acceptable, with values such as CMIN/DF around 2.599, GFI about 0.915, CFI about 0.958, TLI about 0.949, SRMR about 0.04, and RMSR about 0.06.
A central decision point is the evaluation of factor loadings. One item, labeled LS5, shows a standardized regression weight (loading) of about 0.463—below the commonly used 0.50 threshold. Because LS5 fails to represent its intended construct adequately, it is removed from the model. The model is then re-run to confirm whether fit improves. Fit improves slightly after deletion, and the revised model is used for reporting.
The final reporting text ties these steps together: the CFA is run in AMOS to test the measurement model; factor loadings are assessed for each item; LS5 is removed due to low loading; and the resulting fit indices fall within accepted levels. The model is described as a three-factor structure—Authentic Leadership, Ethical Leadership, and Life Satisfaction—each treated as a distinct latent construct in the CFA. The walkthrough also instructs how to present results in a table format, including the corrected CMIN/DF value and the specific fit index values.
Finally, the workflow sets up the next stage: once model fit is reported, the subsequent session will focus on construct reliability and validity—specifically convergent validity and discriminant validity—using reliability and validity metrics rather than fit indices.
Cornell Notes
The CFA measurement model is reported by first demonstrating acceptable model fit using multiple indices and then documenting item-level decisions. Fit is judged with benchmarks such as CMIN/DF between 3 and 5, CFI and TLI above 0.90, GFI above 0.90, and SRMR/RMSR below 0.08; the Chi-square p-value may be significant in large samples and is not treated as the only criterion. In the example, the initial model is improved by removing LS5, whose standardized loading is about 0.463 (below the 0.50 threshold). After re-running the model, fit indices such as GFI ≈ 0.915, CFI ≈ 0.958, TLI ≈ 0.949, SRMR ≈ 0.04, and RMSR ≈ 0.06 support reporting the final three-factor structure (Authentic Leadership, Ethical Leadership, Life Satisfaction).
Why isn’t the Chi-square p-value treated as the main decision rule in CFA reporting?
What does CMIN/DF (Chi-square divided by degrees of freedom) represent, and what range is recommended?
How does the model decide whether an indicator should stay in the CFA?
Which fit indices are explicitly recommended for reporting, and what are their acceptance thresholds?
What is the final factor structure being reported, and how is it described?
Review Questions
- What specific fit indices and cutoff values would you include in a CFA measurement model report, and which one is least reliable when sample size is large?
- If an indicator’s standardized loading is 0.45, what decision rule would you apply based on the walkthrough, and what would you do next in AMOS?
- How would you describe the reporting sequence from model fit to construct reliability/validity in a measurement model write-up?
Key Points
- 1
Report CFA measurement model quality first using a set of fit indices (Chi-square/CMIN/DF, CFI, TLI, GFI, RMSEA, SRMR/RMSR) against stated acceptance thresholds.
- 2
Do not rely solely on the Chi-square p-value for model adequacy when sample size is large; prioritize indices like CMIN/DF, CFI/TLI, GFI, and SRMR/RMSR.
- 3
Use standardized factor loadings to evaluate indicators; apply the 0.50 threshold to decide whether an item should be removed.
- 4
If an item such as LS5 has a standardized loading below 0.50 (about 0.463 in the example), delete it and re-run the CFA to confirm fit remains acceptable.
- 5
Present fit results in a table with the corrected CMIN/DF value and the obtained values for CFI, TLI, GFI, SRMR, and RMSR.
- 6
After finalizing model fit and item retention, move to construct reliability and validity (convergent and discriminant validity) in the next reporting stage.