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A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix

Filippou, P; Kneib, T; Marra, G; Radice, R; (2019) A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix. Journal of Statistical Planning and Inference , 119 pp. 236-248. 10.1016/j.jspi.2018.07.002. Green open access

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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 and their dependence as separate but related issues. We propose a generalisation of the trivariate additive probit model where the link functions can in principle be derived from any parametric distribution and the parameters describing the 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.

Type: Article
Title: A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jspi.2018.07.002
Publisher version: https://doi.org/10.1016/j.jspi.2018.07.002
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Additive predictor; Binary response; Cholesky decomposition; Penalized regression spline; Simultaneous parameter estimation; Trivariate distribution
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10052122
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