City Research Online

Abstract

In many empirical situations, modelling simultaneously three or more outcomes as well as their dependence structure can be of considerable relevance. Copulae provide a powerful framework to build multivariate distributions and allow one to view the specification of the marginal responses’ equations and their dependence as separate but related issues. We propose a generalizationof the trivariate additive probit model where the link functions can in principle be derived from any parametric distribution and the parameters describing the residual association between the responses can be made dependent on several types of covariate effects (such as linear, nonlinear, random, and spatial effects). All the coefficients of the model are estimated simultaneously within a penalized likelihood framework that uses a trust region algorithm with integrated automatic multiple smoothing parameter selection. The effectiveness of the model is assessed in simulation as well as empirically by modelling jointly three adverse birth binary outcomes in North Carolina. The approach can be easily employed via the gjrm() function in the R package GJRM.

Publication Type:	Article
Additional Information:	© 2018 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Additive predictor, Binary response, Cholesky decomposition, Penalized regression spline, Simultaneous parameter estimation, Trivariate distribution
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Departments:	Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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