Accuracy of Parameter Estimates and Confidence Intervals in Moderated Mediation Models

TLDR

The regression approach is the most popular method for testing moderated mediation, but measurement errors bias both regression coefficient estimates and the confidence intervals they produce. The study extends the latent moderated structural equations (LMS) method to analyze moderated mediation among latent variables. Simulations compared the regression approach with the LMS approach to assess their performance. The LMS method produced accurate effect estimates and confidence intervals, whereas regression substantially underestimated effects and yielded inaccurate intervals, suggesting that prior significant findings may be biased.

Abstract

Currently, the most popular analytical method for testing moderated mediation is the regression approach, which is based on observed variables and assumes no measurement error. It is generally acknowledged that measurement errors result in biased estimates of regression coefficients. What has drawn relatively less attention is that the confidence intervals produced by regression are also biased when the variables are measured with errors. Therefore, we extend the latent moderated structural equations (LMS) method—which corrects for measurement errors when estimating latent interaction effects—to the study of the moderated mediation of latent variables. Simulations were conducted to compare the regression approach and the LMS approach. The results show that the LMS method produces accurate estimated effects and confidence intervals. By contrast, regression not only substantially underestimates the effects but also produces inaccurate confidence intervals. It is likely that the statistically significant moderated mediation effects that have been reported in previous studies using regression include biased estimated effects and confidence intervals that do not include the true values.