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Regression models involving nonlinear effects with missing data: A sequential modeling approach using Bayesian

Oliver Lüdtke1, Alexander Robitzsch1, Stephen G West2

  • 1Department of Educational Measurement, Leibniz Institute for Science and Mathematics Education.

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This study introduces a sequential modeling approach for handling missing data in regression. It accurately estimates nonlinear effects even with complex data structures, offering a robust alternative to standard methods.

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Area of Science:

  • Statistics
  • Data Science
  • Psychometrics

Background:

  • Estimating regression models with missing predictor variables requires specifying a joint distribution.
  • The common assumption of a joint normal distribution is often misspecified when predictors have nonlinear effects or interactions.

Purpose of the Study:

  • To present a sequential modeling approach for decomposing joint distributions of predictor variables.
  • To implement a multiple imputation strategy using Bayesian estimation for complex regression models with missing data.
  • To develop a user-friendly R package (mdmb) for applying this approach.

Main Methods:

  • Sequential modeling to decompose joint distributions into model-of-interest and incomplete-predictor parts.
  • Bayesian estimation techniques for multiple imputation.
  • Simulation studies to evaluate performance with continuous, categorical, and skewed predictors.
  • Assessment of robustness against distributional misspecifications.

Main Results:

  • The sequential modeling approach effectively estimates nonlinear effects in regression models with missing data.
  • The method performs well across various predictor types and under different conditions.
  • The approach demonstrates robustness against distributional misspecifications.

Conclusions:

  • Sequential modeling provides a flexible and accurate strategy for handling missing data in complex regression analyses.
  • The developed R package, mdmb, facilitates practical application of this advanced imputation technique.