Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing

Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing

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Article ID: iaor201524969
Volume: 55
Issue: 3
Start Page Number: 321
End Page Number: 342
Publication Date: Sep 2013
Journal: Australian & New Zealand Journal of Statistics
Authors: , ,
Keywords: optimization
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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