非随机化响应技术中logistic回归及相关问题的研究

When an investigation deals with phenomena that are considered as illegal or violation of social morality activities (such as tax evasion, drug abuse, illegal abortion and so on), it is often difficult to obtain reliable information from interviewees directly because they may feel their personal information is infringed. In order to collect reliable sensitive information, increase the degree of privacy protection of the survey, improve the accuracy and precision of the estimation of the sensitive parameters and broaden the application scope of our approaches, in this topic, we will focus on the following aspects: first, to study the relationship between the sensitive variable and other non-sensitive covariates via constructing logistic regression models based on the non-randomized parallel model is the first objective, from which we could know how the covariates would affect the sensitive variable of interest; in addition, we extend the fixed effect model to the random effect model aiming at increase the flexibility and practicability of such models; furthermore, the determination of the confounding variable(s) and the selection of valid explanatory variables will also be taken into account in order to enhance the explanatory ability of the logistic models.

当一个调查涉及到违法或违背社会道德行为时(例如逃税避税、滥用药物、非法堕胎等)，由于受访者认为他们的隐私受到侵犯，调查人员通常很难直接从受访者处获得准确有效的信息。为了提高受访者隐私被保护的程度、改进敏感参数估计的准确性和精确性并拓宽调查设计方案的应用范围，在本项目中，我们主要研究以下方面的内容：首先，通过建立基于非随机化的平行模型的logistic回归函数来研究敏感变量与其它非敏感协变量之间的依存关系从而对敏感数据进行深入分析；其次，我们将固定效应模型推广到随机效应模型以增强模型的灵活性以及实用性；更进一步，我们还将考虑logistic回归中混淆变量的识别以及有效变量的筛选，提高模型的解释能力和预测的准确性。

敏感性抽样调查设计对于协助研究人员获取特定群体有关某一敏感特征的信息方面有着突出的贡献。本项目侧重于从非随机化响应技术的角度研究二分类敏感变量与其它非敏感变量之间的依存关系以改进敏感参数估计的准确性和精确性。本项目依次：(1) 研究基于非随机化平行模型logistic回归的回归系数估计方法，并建立该回归模型与衡量一个二分类的敏感变量与另一个二分类的非敏感变量之间相关性的优势比之间的联系；(2) 提出基于非随机化变体平行模型的logistic回归中混淆变量的识别与判定的准则，并给出基于SCAD惩罚函数的变量筛选方法；(3) 给出基于非随机化平行模型logistic回归的随机效应模型中随机效应分布的参数估计的NR-EM迭代算法；(4) 研究基于泊松计数法的logistic回归模型，并给出回归系数估计的EM迭代算法及QLB迭代算法。同时，针对实际调查中可能出现的离散定量敏感特征，本项目依次：(1) 提出泊松-泊松计数模型以协助敏感信息的收集，并建立基于该模型的离散定量敏感特征均值估计的回归分析方法；(2) 针对0过剩的情况提出改进的零浮动计数模型，并证明该模型在隐私保护角度优于泊松-泊松计数模型；(3) 提出非随机化泊松扰动模型并建立基于该模型的统计分析方法。