17. SPSS AMOS | Standardized Loading Greater than 1 | How to Deal with Heywood Cases

Standardized factor loadings above 1 signal a classic measurement-model problem: the model is effectively claiming an indicator is explained by more than 100% of the variance, which is not feasible in a proper standardized solution. In AMOS, this often shows up alongside a Heywood case—commonly manifested as a negative error variance estimate. The transcript links Heywood cases to practical data and model issues, especially outliers, multicollinearity, and misspecification. Risk rises when a latent construct is measured with only two indicators, since there’s less information to stabilize the estimation.

The recommended response starts before analysis: check for outliers and assess multicollinearity early, because those problems can push the model into impossible parameter territory. A structural safeguard is also suggested—use more indicators per factor (three or four rather than two) to reduce the odds of Heywood cases.

When the problem appears during modeling, several remedies are offered. One approach is to remove a covariance between indicator error terms, since correlated residuals can distort the factor structure and contribute to improper variance estimates. Another is to delete the problematic indicator, particularly if it behaves like an outlier or drives instability. If outliers are present, they should be identified and addressed. Adding an additional indicator to the latent variable can also help, though the transcript notes that this may not be feasible at the analysis stage.

Estimation choices matter too. If the default maximum likelihood estimation is producing Heywood cases, switching to generalized least squares (GLS) is presented as an alternative available in AMOS through the Analysis Properties window. There’s also a more targeted tactic: adjust constraints on regression weights. In the AMOS parameter setup, the transcript describes moving the regression weight away from the indicator that triggers standardized loadings above 1—by setting the parameter regression weight to a fixed value (e.g., 1) and removing the problematic regression weight from that indicator.

Finally, the transcript provides a workaround focused specifically on standardized loadings. If the goal is to obtain acceptable standardized factor loadings rather than perfectly “fix” the underlying unstandardized problem, AMOS can be configured to constrain the unobserved (latent) variable variance to 1. Then, by labeling the unstandardized paths from the latent construct to each indicator with the same label (such as “A”), all corresponding unstandardized estimates are forced to be equal. Under this constraint, the standardized estimates can differ across indicators and—crucially—should drop below 1, even if the unstandardized estimates remain constrained.

The transcript cautions that this constrained-variance method is not ideal as a general solution, but it can work when other fixes fail. It also emphasizes an important nuance: unstandardized loadings greater than 1 can be acceptable; the problematic behavior is mainly tied to standardized interpretations and Heywood-case diagnostics. After applying the constraint and rerunning the model, the estimates become stable, with the constrained unstandardized paths equalized while the standardized loadings reflect indicator differences without exceeding 1.