A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix
Filippou, P. and Kneib, T. and Marra, G. and Radice, Rosalba (2018) A Trivariate Additive Regression Model with Arbitrary Link Functions and Varying Correlation Matrix. Journal of Statistical Planning and Inference 199 , pp. 236-248. ISSN 0378-3758.
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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’ 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.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Additive predictor, Binary response, Cholesky decomposition, Penalized regression spline, Simultaneous parameter estimation, Trivariate distribution |
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Rosalba Radice |
| Date Deposited: | 11 Jul 2018 12:49 |
| Last Modified: | 02 Aug 2023 17:43 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/23112 |
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