随机效应半参数logit模型的惩罚似然估计研究

 在颇具争议的收入差距和健康关系研究中，为了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logit模型，其中非参数的设定还可用于数据的初探性分析。随后本文提出了模型非参数和参数部分的估计方法。这里涉及的难点是随机效应的存在导致似然函数中的积分没有解析式，而非参数的存在更加大了估计难度。本文基于惩罚样条非参数估计方法和四阶Laplace近似方法建立了惩罚对数似然函数，其最大化采用了Newton_Raphson近似方法。文章还建立了惩罚样条中重要光滑参数的选取准则。模型在收入差距和健康实例中的估计结果表明数据支持收入差距弱假说，且非参数估计结果表明其具有U型形式，与实例估计结果的比较指出本文提出的估计方法是较准确的。

Penalized Likelihood Estimation for Semi-parametric Logit Model with Random Effects

In order to study the contestable income inequality effect on health, we propose a semi-parametric logit model with random effects which can reduce both model specification bias and omitted variable bias. Its nonparametric specification can also be used to exploratory data analysis. Then the estimation procedures are established, where the difficulty lies in evaluation of the intractable integral introduced by random effects, and the existence of nonparametric parts makes it even tougher. We solved it by the fourth order Laplace approximation together with penalized spline method, and the penalized maximum likelihood estimators are obtained by approximate Newton_Raphson algorithm. Meanwhile, we propose a selection method of smoothing parameter based on cross validation. Real application supports the weak version of income inequality hypothesis, and the nonparametric estimation results show evidence of validity of U-type function. Corresponding compares show the accuracy of our estimation method.