[The copyright line for this article was changed on 21 July 2014 after original online publication.]
Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing
Article first published online: 20 OCT 2013
© 2013 The Authors. Australia and New Zealand Journal of Statistics published by Wiley Publishing Asia Pty Ltd on behalf of Statistical Society of Australia.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Australian & New Zealand Journal of Statistics
Volume 55, Issue 3, pages 321–342, September 2013
How to Cite
Marra, G., Papageorgiou, G. and Radice, R. (2013), Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing. Australian & New Zealand Journal of Statistics, 55: 321–342. doi: 10.1111/anzs.12043
- Issue published online: 20 OCT 2013
- Article first published online: 20 OCT 2013
- nonparametric maximum likelihood estimation;
- penalised regression spline;
- recursive bivariate probit model;
- unobserved confounding
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.