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Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using

Oliver Lüdtke1,2, Alexander Robitzsch1,2, Stephen G West3

  • 1Leibniz Institute for Science and Mathematics Education.

Multivariate Behavioral Research
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This study introduces a new factored regression modeling approach to accurately estimate complex regression models with missing data. This method provides valid estimates for nonlinear and interaction effects, improving statistical analysis.

Keywords:
Multiple regressioninteraction effectsmaximum likelihood estimationmissing data

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Estimating multiple regression models with incomplete predictor variables requires specifying a joint distribution.
  • Multivariate normal distribution is a common but often misspecified assumption when predictors have nonlinear or interaction effects.

Purpose of the Study:

  • To introduce a novel factored regression modeling approach for handling missing data in regression models.
  • To address the limitations of the multivariate normal distribution assumption in the presence of nonlinear and interaction effects.

Main Methods:

  • The proposed approach utilizes maximum likelihood estimation.
  • The model likelihood is factorized into components related to the model of interest and the incomplete predictors.
  • Developed the R package 'mdmb' for user-friendly application.

Main Results:

  • Factored regression modeling produced valid estimates of interaction and nonlinear effects.
  • Demonstrated effectiveness across various conditions with categorical and continuous predictor variables.
  • Simulation studies confirmed the approach's validity.

Conclusions:

  • The factored regression modeling approach offers a robust method for regression with missing data.
  • The 'mdmb' R package provides a flexible tool for implementing this advanced statistical technique.
  • This method improves the accuracy of estimating complex effects in the presence of missing predictor variables.