Modelling bivariate ordinal responses smoothly with examples from ophthalmology and genetics.
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.
Bustami
R
R
Biostatistical Center, Katholieke Universiteit Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
Lesaffre
E
E
Molenberghs
G
G
Loos
R
R
Danckaerts
M
M
Vlietinck
R
R
D000293:Adolescent; D002648:Child; D002652:Child Behavior / Q000502:physiology / Q000523:psychology; D003930:Diabetic Retinopathy / Q000453:epidemiology; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D008297:Male; D008954:Models, Biological; D008957:Models, Genetic; D015233:Models, Statistical; D012307:Risk Factors; D018709:Statistics, Nonparametric; D018433:Twin Studies as Topic