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Estimation Methods for Mixed Logistic Models with Few Clusters.

Daniel McNeish1

  • 1a Utrecht University ; University of Maryland , College Park.

Multivariate Behavioral Research
|November 2, 2016
PubMed
Summary
This summary is machine-generated.

For mixed-effects models with few clusters, linearization methods are preferred over likelihood approximations for binary outcomes. This approach allows for restricted maximum likelihood and Kenward-Roger corrections, yielding less biased estimates in small samples.

Keywords:
Mutilevel logistic regressionhierarchical generalized linear modelsmall sample

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Mixed-effects models with few clusters often produce biased estimates, especially for variance components and standard errors.
  • Linear mixed models commonly use restricted maximum likelihood (REML) and Kenward-Roger corrections to mitigate small sample bias.
  • Binary outcomes lack direct analogs to REML and Kenward-Roger corrections, posing a challenge for small sample bias reduction.

Purpose of the Study:

  • To investigate the trade-off between approximating a biased function versus approximating an unbiased function in mixed models for binary outcomes with few clusters.
  • To determine the preferable estimation strategy when dealing with small sample sizes in mixed-effects modeling for binary data.

Main Methods:

  • The study employed simulation and an empirical analysis to compare different estimation methods.
  • Methods compared include likelihood approximation techniques (adaptive Gaussian quadrature, Laplace approximation) and linearization methods.
  • The focus was on evaluating bias in variance components and standard errors under small cluster conditions.

Main Results:

  • Likelihood approximation methods (adaptive Gaussian quadrature, Laplace) approximate the full likelihood, which is known to be biased with few clusters.
  • Linearization methods approximate the model linearly, enabling the application of restricted maximum likelihood (REML) and Kenward-Roger corrections.
  • The simulation and empirical analysis directly address whether a better approximation of a biased function is preferable to a worse approximation of an unbiased function.

Conclusions:

  • The findings provide guidance on selecting appropriate statistical methods for mixed-effects models with binary outcomes and limited clusters.
  • The study contributes to understanding small sample bias in mixed-effects modeling for binary data.
  • Results inform practitioners on balancing approximation accuracy with the bias properties of estimation techniques.