Mixed binary-continuous copula regression models with application to adverse birth outcomes |
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| Authors: | Nadja Klein Thomas Kneib Giampiero Marra Rosalba Radice Slawa Rokicki Mark E. McGovern |
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| Affiliation: | 1. Applied Statistics, Humboldt University of Berlin, Berlin, Germany;2. Chair of Statistics, Georg-August Universität Göttingen, Göttingen, Germany;3. Department of Statistical Science, University College London, London, UK;4. Cass Business School, City, University of London, 106 Bunhill Row, EC1Y 8TZ London, UK;5. Geary Institute for Public Policy, University College Dublin, Dublin, Ireland;6. CHARMS - Centre for Health Research at the Management School, Queen's University Belfast, Belfast, UK |
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| Abstract: | Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely, binary) whereas the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood–based approach for the resulting class of copula regression models and employ it in the context of modeling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested. |
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| Keywords: | adverse birth outcomes copula latent variable mixed discrete-continuous distributions penalized maximum likelihood penalized splines |
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