Modelling bivariate ordinal responses smoothly with examples from ophthalmology and genetics
Research output: Contribution to journal › Journal article › Research › peer-review
A non-parametric implementation of the bivariate Dale model (BDM) is presented as an extension of the generalized additive model (GAM) of Hastie and Tibshirani. The original BDM is an example of a bivariate generalized linear model. In this paper smoothing is introduced on the marginal as well as on the association level. Our non-parametric procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in the linear BDM, hence it also provides a kind of goodness-of-fit test for a bivariate generalized linear model. Cubic smoothing spline functions for the covariates are estimated by maximizing a penalized version of the log-likelihood. The method is applied to two studies. The first study is the classical Wisconsin Epidemiologic Study of Diabetic Retinopathy. The second study is a twin study, where the association between the elements of twin pairs is of primary interest. The results show that smoothing on the association level can give a significant improvement to the model fit.
Original language | English |
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Journal | Statistics in Medicine |
Volume | 20 |
Issue number | 12 |
Pages (from-to) | 1825-42 |
Number of pages | 18 |
ISSN | 0277-6715 |
DOIs | |
Publication status | Published - 30 Jun 2001 |
Externally published | Yes |
- Adolescent, Child, Child Behavior/physiology, Diabetic Retinopathy/epidemiology, Female, Humans, Likelihood Functions, Logistic Models, Male, Models, Biological, Models, Genetic, Models, Statistical, Risk Factors, Statistics, Nonparametric, Twin Studies as Topic
Research areas
ID: 258040802