43. SPSS AMOS - How to Improve Model Fit using CB-SEM (Confirmatory Factor Analysis)

Improving a weak confirmatory factor analysis (CFA) model fit in AMOS hinges on a disciplined loop: clean the data, then adjust the measurement model using only defensible changes, and finally re-check fit indices after each modification. The workflow starts with data quality—screening for incorrect or inconsistent values, assessing missingness, and applying data imputation—because poor data can masquerade as model problems.

Once the dataset is ready, the process shifts to AMOS model diagnostics. The first pass checks whether the measurement model is structurally sound: low factor loadings (with a practical cutoff around standardized regression weights below 0.5) and problematic residuals or modification indices. If fit is poor—often signaled by a significant chi-square and weak comparative/absolute fit statistics such as CMIN above 5, GFI/AGFI below .90, CFI/TLI below .90, and RMSEA far above .08—the modeler then targets specific, localized issues rather than making broad changes.

The transcript’s core method is iterative model refinement using modification indices and residual diagnostics. Large modification indices (the example uses a threshold around 4, with the option to raise it) guide where correlated error terms might be added. In the walkthrough, adding a covariance between error terms E11 and E12 produces only limited improvement, but subsequent targeted covariances—such as between E10 and E11 (when allowed), E4 and E5, and E1 and E2 (and E1 and E5 when feasible)—gradually push fit closer to acceptable ranges. Even when fit indices improve, the transcript stresses that changes should be constrained: covariances are drawn only between error terms of indicators belonging to the same construct.

After modification indices are exhausted, the next diagnostic layer is standardized residual covariances. Values exceeding about 2 flag indicators that still misbehave. In the example, the indicator sl3 within “servant leadership” is identified as problematic and removed, which improves several fit measures. A second pass checks standardized regression weights again; a low-loading indicator is removed if needed. However, removing an indicator can break the model’s reference scaling, which is why the transcript highlights a critical fix: after deleting an indicator, the remaining factor must be re-referenced by fixing a parameter to 1 (so the model has a stable metric).

The final stage compares fit indices holistically. After the last adjustments, the model fit becomes “very good” on most metrics—close to the desired threshold for chi-square/CMIN and improved SRMR after running the standardized RMR plugin (the example reports SRMR around 0.3, described as very good). RMSEA remains poor in the example, but with SRMR and other fit indicators acceptable, the model is treated as having a reasonable overall fit for reporting. The takeaway is that model fit improvement in AMOS is less about chasing a single statistic and more about a controlled sequence of data checks, targeted error covariances, and indicator removal guided by residuals—while maintaining proper factor scaling.