随机效应半参数二值响应模型的估计研究

Estimation for semi-parametric binary response model with random effects

为了研究诸如在收入差距和健康关系中某些解释变量的影响效应可能依赖于其他解释变量的状况,降低可能存在的模型设定和遗漏变量偏误,本文提出了随机效应半参数二值响应模型,其中非参数的设定还可用于数据的初探性分析.随后本文探讨了模型非参数和参数部分的估计.由于似然函数中随机效应和非参数的存在加大了估计难度,为此本文采用B样条方法逼近非参数部分,同时将随机效应视为缺失数据,利用EM算法和MCMC方法建立了模型参数的估计,并研究了其一致性.模拟研究结果表明估计量在有限样本下的表现良好,最后将模型运用于收入差距与健康关系的实例研究中,结果表明数据支持收入差距弱假说.

In order to study that the marginal effect of some explanatory variables may depend on other covari- ates such as in the problem of income inequality on health, we propose a semi-parametric binary response model with random effects which can reduce both model specification and omitted variable bias. Its nonpara- metric specification can also be used to the exploratory data analysis. Then the estimation procedures are es- tablished, where the difficulties lies in the evaluation of the intractable integral caused by random effects, and the existence of nonparametric parts makes it even tougher. We solve it by using EM and MCMC algorithm to- gether with non-parametric B spline method. The estimators are shown to be consistent. Simulation studies show the good properties of the estimators. A practical application of our model supports the weak version of income inequality hypothesis.