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Goodness of fit tests for random effect models with binary responses.

Antonia K Korre1, Vassilis G S Vasdekis1

  • 1Department of Statistics, Athens University of Economics and Business, Athens, Greece.

Statistics in Medicine
|August 21, 2018
PubMed
Summary

New goodness-of-fit score statistics were developed for random effects models analyzing correlated binary data. Weighted statistics, particularly those partitioning covariate space, showed superior performance in simulations for longitudinal studies.

Keywords:
binary correlated datageneralized linear mixed modelsgoodness-of-fit testsh-likelihoodscore statistics

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Statistical Modeling

Background:

  • Correlated binary responses are prevalent in longitudinal and repeated measures studies.
  • Random effects models are frequently employed for analyzing such data.
  • The h-likelihood procedure is a key inferential tool for these models.

Purpose of the Study:

  • To introduce novel goodness-of-fit score statistics for the fixed component of random effects models.
  • To evaluate the performance of these statistics, including weighted versions.
  • To assess different grouping strategies for the proposed statistics.

Main Methods:

  • Development of goodness-of-fit score statistics based on partitioning observations into mutually exclusive groups.
  • Introduction of weighted statistics utilizing the correlation between adjusted covariates and model residuals.
  • A simulation study to compare the performance of unweighted and weighted statistics under various grouping procedures.

Main Results:

  • Weighted goodness-of-fit statistics demonstrated superior performance compared to their unweighted counterparts.
  • Statistics based on partitioning the covariate space exhibited slightly better performance than other grouping methods.
  • The utility of the proposed statistics was validated through application to a real-world dataset.

Conclusions:

  • The developed goodness-of-fit score statistics provide a valuable tool for assessing model fit in longitudinal correlated binary data.
  • Weighted statistics and covariate space partitioning offer improved performance for model evaluation.
  • These methods enhance the reliability of inferences drawn from random effects models in complex study designs.