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Weighted cumulative sum tests for random effect models with binary responses.

Antonia K Korre¹, Vassilis Gs Vasdekis¹

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

Statistical Methods in Medical Research

|November 14, 2019

Summary

This study introduces weighted cumulative sum tests for random effects logistic regression models. These new methods offer improved performance for assessing model fit in medical and other research areas.

Keywords:

Binary correlated data cumulative sums generalized linear mixed models goodness-of-fit tests h-likelihood supremum statistics

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Area of Science:

Statistics
Biostatistics
Econometrics

Background:

Correlated binary responses are frequent in medical studies and other fields.
Assessing the adequacy of fitted models using goodness-of-fit tests is crucial.
Existing methods may not fully capture the complexities of random effects logistic regression.

Purpose of the Study:

To develop weighted modifications of cumulative sum (or moving cumulative sum) of residuals tests.
To specifically address goodness-of-fit testing for random effects logistic regression models.
To evaluate the performance of these novel weighted tests.

Main Methods:

Proposed weighted modifications of cumulative sums of residuals.
Weights are derived from a weighted linear regression of an omitted covariate.
Null distribution of supremum statistics is determined through simulation.
Comparison of weighted versus unweighted supremum statistics performance.

Main Results:

Weighted supremum statistics demonstrated superior performance compared to unweighted versions.
Simulation results indicate enhanced power for the proposed weighted tests.
The methodology provides a robust approach for model adequacy assessment.

Conclusions:

The developed weighted tests are effective for goodness-of-fit in random effects logistic regression.
These methods offer a valuable enhancement over existing unweighted approaches.
The study illustrates practical application with a real-world data example.