9. SEM | SPSS AMOS - Understanding, Assessing, and Improving Model Fit in AMOS

Model fit in AMOS is ultimately about whether the proposed measurement and structural relationships reproduce the covariance patterns seen in the data—and the practical workflow is a cycle of diagnosing misfit, making theory-consistent adjustments, and re-running the model until fit indices land in acceptable ranges. After building a model from theory, researchers specify how constructs are measured, collect data, and then use AMOS to estimate parameters and compute overall fit statistics plus standardized parameter estimates. When fit is poor, the fix is not guesswork: it starts with checking indicator quality (outer loadings), then using modification indices and residual diagnostics to target specific sources of discrepancy.

The transcript lays out commonly used fit thresholds for AMOS/SEM. For the chi-square test, the p-value should exceed 0.05, but the guidance is tempered by sensitivity to sample size. Several incremental and absolute fit indices are given: GFI should be above 0.95 and AGFI above 0.90; NFI and NNFI above 0.95; CFI above 0.90 (the session uses a “more liberal” cutoff of 0.90 for CFI and TLI); RMSEA should be below 0.08; and SRMR below 0.08. Convergent validity is also monitored via Average Variance Extracted, with a target above 0.5.

When the model fails these benchmarks, the first diagnostic step is outer loadings: indicators with loadings below 0.50 are candidates for removal. After each deletion, the model must be re-estimated and re-evaluated. If misfit persists, modification indices become the next lever. The key constraint is conceptual and statistical: AMOS suggestions should not be used to correlate error terms across different constructs. Acceptable covariance additions are limited to error terms within the same construct (or otherwise theoretically justified redundancy among indicators), because correlating errors can explain shared unexplained variance without changing the latent structure.

The transcript also emphasizes standardized residual covariances. These values reflect gaps between the model-implied covariance matrix and what the data actually show. Large standardized residual covariances—often flagged when they exceed 2—signal specific indicator relationships that the model fails to reproduce. Deleting items based on residuals can improve fit, but it must be done cautiously to avoid damaging content validity and the operational definition of constructs. A practical process is proposed: clean the dataset (inconsistent values, missingness, imputation), build the model, remove low-loading indicators, apply modification indices only when theoretically defensible, then address residual covariances, and finally report the revised model.

A worked AMOS example demonstrates the loop. Initial fit is weak: CMIN/chi-square is significant, CFI/TLI are below target, and RMSEA is high. The analyst then adds covariances suggested by modification indices (e.g., between specific error terms like E11 and E12), re-runs the model, and observes incremental improvement. Residual diagnostics identify problematic indicators within constructs (notably items labeled SL3, SL6, and FP5). After deleting those indicators, an AMOS “reference point” issue is resolved by fixing a parameter to 1. The final re-run produces substantially improved fit (including CFI/TLI near acceptable levels and SRMR around 0.03), though RMSEA remains comparatively poor. The takeaway is that model improvement is iterative and diagnostic-driven: each adjustment is justified by fit statistics and theory, then validated by re-estimation.