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Estimation of a Semiparametric Recursive Bivariate Probit Model with Nonparametric Mixing
Author(s) -
Marra Giampiero,
Papageorgiou Georgios,
Radice Rosalba
Publication year - 2013
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12043
Subject(s) - mathematics , covariate , overdispersion , econometrics , statistics , probit , bivariate analysis , multinomial probit , nonparametric statistics , probit model , multivariate probit model , inference , estimator , binary data , binary number , count data , computer science , poisson distribution , arithmetic , artificial intelligence
Summary 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.