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A general algorithm for error-in-variables regression modelling using Monte Carlo expectation maximization.

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This study introduces a new algorithm to correct regression models for measurement errors in predictor variables. The method, implemented in the R package refitME, makes complex statistical modeling accessible to applied researchers.

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Computational Statistics

Background:

  • Regression modeling frequently requires addressing measurement error in covariates.
  • Existing methods for measurement error models lack general algorithms and user-friendly software for applied researchers.
  • Advanced statistical expertise is often needed to implement current measurement error correction techniques.

Purpose of the Study:

  • To develop a novel, general algorithm for measurement error modeling applicable to various regression types.
  • To extend existing maximum likelihood and penalized likelihood regression models to incorporate covariate uncertainty.
  • To provide accessible software for applied researchers to implement measurement error correction.

Main Methods:

  • Developed a novel algorithm based on the Monte Carlo Expectation-Maximization (MCEM) algorithm.
  • Algorithm exploits MCEM's property of being an iteratively reweighted maximization of complete data likelihoods.
  • The method nests existing regression models within the proposed iteratively reweighted MCEM algorithm to handle covariate uncertainty.

Main Results:

  • Demonstrated the algorithm's application on generalized linear models, point process models, generalized additive models, and capture-recapture models.
  • The maximum (penalized) likelihood approach ensures advantageous optimality and inferential properties, supported by simulation studies.
  • Investigated the robustness of the model to violations of predictor distributional assumptions.

Conclusions:

  • The novel algorithm effectively extends various regression models to account for measurement error in covariates.
  • The developed method provides a computationally efficient and statistically sound approach for applied researchers.
  • The refitME R package offers a user-friendly tool for implementing measurement error correction in regression analysis.