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Generalized linear mixed quantile regression with panel data.

Xiaoming Lu¹, Zhaozhi Fan¹

¹Department of Mathematics and Statistics, Memorial University of Newfoundland, Newfoundland, Canada.

|August 12, 2020

Summary

This summary is machine-generated.

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A novel generalized linear mixed quantile model for panel data offers consistent regression coefficient estimates. This method utilizes smoothed generalized estimating equations (GEE) and best linear unbiased predictors (BLUP) for robust statistical analysis.

Area of Science:

Statistics
Biostatistics
Econometrics

Background:

Panel data analysis requires robust models that can handle complex data structures and distributional assumptions.
Existing methods may not adequately address quantile estimation in the presence of random effects and smoothed estimating functions.
The Tweedie distribution offers a flexible framework for modeling various data types within a generalized linear model.

Purpose of the Study:

To introduce a new generalized linear mixed quantile model specifically designed for panel data.
To develop an estimation procedure that ensures consistent and asymptotically normal parameter estimates.
To demonstrate the model's utility and performance through simulation studies and a real-world data application.

Main Methods:

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Application of generalized estimating equations (GEE) with smoothed estimating functions for coefficient estimation.

Prediction of random effects using best linear unbiased predictors (BLUP) based on Tweedie exponential dispersion distributions.

Linearization of random effects via Taylor expansion of the quantile estimating function, with parameter estimation via Newton-Raphson iteration.

Main Results:

The proposed quantile mixed model yields consistent parameter estimates with asymptotic normal distributions.
Simulation studies confirm the model's good performance in small sample scenarios.
The method is successfully applied to analyze epilepsy data, showcasing its practical applicability.

Conclusions:

The developed generalized linear mixed quantile model provides a powerful tool for analyzing panel data.
The approach effectively handles various distributional assumptions through the Tweedie family.
The method offers a statistically sound and computationally feasible approach for quantile regression with random effects.