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Pairwise residuals and diagnostic tests for misspecified dependence structures in models for binary longitudinal

Nina Breinegaard1, Sophia Rabe-Hesketh2, Anders Skrondal3

  • 1Section of Biostatistics, University of Copenhagen, Copenhagen, Denmark.

Statistics in Medicine
|October 31, 2017
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Summary

New diagnostic tests improve the analysis of binary longitudinal data by detecting misspecified dependence structures. These methods use pairwise concordance residuals for robust model checking.

Keywords:
diagnosticsmisspecificationresidualsserial dependence

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Maximum likelihood estimation for binary longitudinal data can be inconsistent if the dependence structure is misspecified.
  • Existing diagnostic tools for detecting such misspecifications are limited.

Purpose of the Study:

  • To develop novel residuals and diagnostic tests for identifying misspecified dependence structures in binary longitudinal data models.
  • To provide robust methods for model checking in the presence of complex covariate patterns.

Main Methods:

  • Developed residuals and diagnostic tests by comparing observed and expected frequencies of response patterns over time.
  • Utilized lower-order marginal tables, specifically two-way tables aggregated over covariate patterns, to address data sparseness.
  • Proposed pairwise concordance residuals for exploratory diagnostics and constructing generic and targeted dependence structure tests.

Main Results:

  • The proposed pairwise concordance residuals effectively detect misspecified dependence structures.
  • The methods are adaptable for generic tests of overall dependence and targeted tests for excess serial dependence.
  • The diagnostic tests are straightforward to implement and perform well across various scenarios.

Conclusions:

  • The developed methods offer valuable tools for assessing the adequacy of dependence structures in binary longitudinal data models.
  • These diagnostics are broadly applicable, irrespective of the number of time points or the complexity of covariates.
  • The pairwise concordance approach enhances the reliability of statistical modeling for longitudinal binary outcomes.