Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing |
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Authors: | Giampiero Marra Georgios Papageorgiou Rosalba Radice |
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Institution: | 1. Department of Statistical Science, University College London, , London, WC1E 6BT UK;2. Department of Epidemiology and Biostatistics, Imperial College London, , London, W2 1PG UK;3. Department of Economics, Mathematics and Statistics, Birkbeck, University of London, , London, WC1E 7HX UK |
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Abstract: | We consider an extension of the recursive bivariate probit model for estimating the effect of a binary variable on a binary outcome in the presence of unobserved confounders, nonlinear covariate effects and overdispersion. Specifically, the model consists of a system of two binary outcomes with a binary endogenous regressor which includes smooth functions of covariates, hence allowing for flexible functional dependence of the responses on the continuous regressors, and arbitrary random intercepts to deal with overdispersion arising from correlated observations on clusters or from the omission of non‐confounding covariates. We fit the model by maximizing a penalized likelihood using an Expectation‐Maximisation algorithm. The issues of automatic multiple smoothing parameter selection and inference are also addressed. The empirical properties of the proposed algorithm are examined in a simulation study. The method is then illustrated using data from a survey on health, aging and wealth. |
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Keywords: | nonparametric maximum likelihood estimation penalised regression spline recursive bivariate probit model unobserved confounding |
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