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Moderation analysis with missing data in the predictors.

Qian Zhang1, Lijuan Wang2

  • 1Department of Educational Psychology and Learning Systems, College of Education, Florida State University.

Psychological Methods
|November 8, 2016
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Bayesian estimation (BE) is the most effective method for handling missing data in moderated multiple regression (MMR) models, outperforming normal-distribution-based methods under missing at random conditions.

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Moderated multiple regression (MMR) is a key statistical model for analyzing moderation effects.
  • Missing data in predictor variables present significant challenges in MMR due to the nonlinear nature of interaction terms.

Purpose of the Study:

  • To evaluate methods for estimating and testing moderation effects in MMR models with missing data in the focal predictor.
  • To compare Normal-distribution-based Maximum Likelihood (NML), Normal-distribution-based Multiple Imputation (NMI), and Bayesian Estimation (BE) under missing completely at random (MCAR) and missing at random (MAR) mechanisms.

Main Methods:

  • Simulation studies were conducted to compare NML, NMI, and BE.
  • The focus was on a simple MMR model with a focal predictor (X) moderated by a variable (U).
  • Missing data mechanisms considered were MCAR and MAR.

Main Results:

  • NML and NMI yielded biased moderation effect estimates under MAR missingness.
  • BE demonstrated superior performance compared to NMI and NML when predictor distributions were correctly specified.
  • BE's advantage was observed when missingness depended on the moderator or auxiliary variables.

Conclusions:

  • Bayesian estimation is recommended for MMR models with missing data in the focal predictor, especially under MAR.
  • Further research is needed to develop more robust BE methods that address potential issues with distribution mis-specification.