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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Copula-based regression models for a bivariate mixed discrete and continuous outcome.

A R de Leon¹, B Wu

¹Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4. adeleon@math.ucalgary.ca

Statistics in Medicine

|October 22, 2010

Summary

This study introduces a novel regression model using copulas for mixed discrete and continuous outcomes. The method offers interpretable parameters and a margin-free association measure, validated through simulations and burn injury data analysis.

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Area of Science:

Statistics
Biostatistics
Epidemiology

Background:

Correlated mixed discrete and continuous outcomes present analytical challenges in regression modeling.
Existing methods may lack interpretability or flexibility in handling outcome associations.

Purpose of the Study:

To develop a robust regression framework for joint modeling of mixed discrete and continuous outcomes.
To enhance the interpretability of regression parameters and association measures.
To provide a flexible approach for analyzing correlated outcomes in various fields.

Main Methods:

Utilizing copula functions, specifically the Gaussian copula, to model the dependence structure between outcomes.
Specifying marginal regression models (e.g., generalized linear models) for individual outcome types.
Employing a latent variable framework for discrete outcomes to ensure unique joint distribution determination.

Main Results:

The proposed copula-based regression model provides marginally meaningful regression parameters.
The association between outcomes is characterized independently by the copula, offering a 'margin-free' interpretation.
Simulation studies demonstrated the bias and efficiency of likelihood-based estimation methods.

Conclusions:

The copula approach offers a powerful and interpretable method for analyzing correlated mixed discrete and continuous outcomes.
The model is applicable to real-world data, as shown by the burn injury case study.
This framework advances statistical modeling for complex data structures.