The Impact of Unmodeled Error Covariance on Measurement Models in Structural Equation Modeling

Abstract

Subject responses to observed variables are affected by both the underlying construct(s) of interest as well as the observed variables’ measurement error. In practice, method effects can cause some observed variables to share error, violating the assumption of linear independence if the error covariance is not directly modeled. The current study evaluated the impact of failing to account for error covariance under varied, real-world conditions. Data from a 2-factor, 4-indicator per factor confirmatory factor analysis (CFA) model were simulated to have one correlated error term between two items that load onto the first factor. Levels of within-factor error correlation, sample sizes, loading magnitudes, and factor-factor correlations were varied, with N = 100,000 simulations per condition. All conditions were analyzed using a 2-factor model that assumed no error covariance, leaving the assumption of linear independence intact. The results were evaluated for the effect of the misspecification of the correlated error term on estimate bias as well as 95% confidence interval coverage. Overall, the findings showed that the failure to account for correlated error terms caused bias in parameter estimates that was exacerbated by the magnitude of the covariance between error terms. Greater shared error variance between items led to larger bias and poorer confidence interval coverage, while larger factor loadings decreased the amount of bias and improved confidence interval coverage. Relative bias in the factor loadings was not affected by sample size, though confidence interval coverage worsened with larger samples. Discussion of results and recommendations for applied analysts are given.