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Modelling bivariate ordinal responses smoothly with examples from ophthalmology and genetics
R Bustami1, E Lesaffre, G Molenberghs
1Biostatistical Center, Katholieke Universiteit Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
Statistics in Medicine
|June 15, 2001
Summary
This study introduces a flexible non-parametric bivariate Dale model (BDM) for analyzing complex data. The enhanced model improves diagnostic capabilities and goodness-of-fit testing for bivariate generalized linear models.
Area of Science:
- Statistics
- Biostatistics
- Statistical Modeling
Background:
- The bivariate Dale model (BDM) is a generalized linear model for bivariate data.
- Existing BDM implementations often assume specific parametric forms for covariates and associations.
- There is a need for flexible methods to assess model fit and identify appropriate transformations.
Purpose of the Study:
- To present a non-parametric implementation of the bivariate Dale model (BDM).
- To extend the generalized additive model (GAM) framework to bivariate data.
- To provide a diagnostic tool for assessing parametric assumptions and improving model fit.
Main Methods:
- Developed a non-parametric BDM by incorporating smoothing on marginal and association levels.
- Utilized cubic smoothing spline functions for covariates.
- Estimated parameters by maximizing a penalized log-likelihood function.
Main Results:
- The non-parametric BDM serves as a diagnostic tool for identifying covariate transformations.
- It functions as a goodness-of-fit test for bivariate generalized linear models.
- Smoothing on the association level significantly improved model fit in applied studies.
Conclusions:
- The non-parametric BDM offers a flexible alternative to traditional parametric models.
- This approach enhances the ability to diagnose and improve bivariate generalized linear models.
- The method is effective in analyzing complex datasets, including epidemiological and twin studies.