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Updated: Mar 27, 2026

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A Comparison of Bias and Mean Squared Error in Parameter Estimates of Interaction Effects: Moderated Multiple

L E Anderson, E F Stone-Romero, J Tisak

    Multivariate Behavioral Research
    |January 12, 2016
    PubMed

    Insights

    Errors-in-variables regression (EIVR) offers less biased estimates than moderated multiple regression (MMR) when predictor reliability and sample size are high. MMR is preferable for low reliability or small sample sizes in moderator analysis.

    Area of Science:

    • Statistics
    • Psychometrics
    • Social Sciences

    Background:

    • Moderated multiple regression (MMR) results are sensitive to unreliability in predictor variables.
    • Errors-in-variables regression (EIVR) can correct for measurement error, potentially yielding less biased estimates.
    • The performance of EIVR in moderator analysis contexts is not well understood.

    Purpose of the Study:

    • To compare the effectiveness of MMR and EIVR in detecting moderator variables.
    • To investigate the bias and mean squared error of MMR and EIVR estimators under various conditions.

    Main Methods:

    • The study employed simulation methods to evaluate MMR and EIVR.
    • Evaluated estimator bias and mean squared error.
    • Varied sample size, predictor reliability, and intercorrelations among predictors.

    Main Results:

    • EIVR provided superior estimates to MMR when sample size was large (≥250) and predictor reliabilities were high (≥.65).
    • MMR demonstrated better performance with low predictor reliabilities or small sample sizes.
    • The choice between MMR and EIVR depends on data characteristics.

    Conclusions:

    • EIVR is a valuable alternative to MMR for moderator analysis, especially with high-quality data.
    • MMR remains a suitable choice when dealing with measurement error or limited sample sizes.
    • Researchers should consider data reliability and sample size when selecting a regression strategy for moderator analysis.

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