变系数混合模型的光滑样条推断

为了拟合纵向数据和其他相关数据,本文提出了变系数混合效应模型(VCMM).该模型运用变系数线性部分来表示协变量对响应变量的影响,而用随机效应来描述纵向数据组内的相关性, 因此,该模型允许协变量和响应变量之间存在十分灵活的泛函关系.文中运用光滑样条来估计均值部分的系数函数,而用限制最大似然的方法同时估计出光滑参数和方差成分,我们还得到了所提估计的计算方法.大量的模拟研究表明对于具有各种协方差结构的变系数混合效应模型,运用本文所提出的方法都能够十分有效地估计出模型中的系数函数和方差成分.     

平衡线性混合模型方差分量几种估计的优良性

对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计.同时证明了在此条件下,似然方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子.     

异方差的线性混合模型的参数估计

本文研究既含有固定效应又含有随机效应的线性混合模型,在随机效应的方差不同即异方差情况下,即考虑方差受外界因素的影响,如温度、湿度等,我们称之为协变量,在有协变量情况下对方差建立对数线性模型,运用最大似然估计讨论了固定效应的估计和随机效应的预测,并且用约束最大似然(REML)方法研究对数线性模型中参数和随机误差中参数(离差参数)的估计,并讨论估计量的性质及离差参数估计量的渐近正态性。     

平衡线性混合模型方差分量几种估计的优良性

对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方 差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计．同时证明了在此条件下,似然 方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子．     

联合均值与方差混合专家回归模型的参数估计

在社会、经济领域中存在大量来自异质总体的异方差数据.本文针对异质总体的异方差数据,研究提出联合均值与方差混合专家回归模型,该模型同时对感兴趣的均值、方差和混合比例参数建模,可以概括和描述众多的实际问题.然后,利用EM算法和MM算法给出该模型的最大似然估计,进而通过Monte Carlo随机模拟来验证所提出的方法的有效性.最后,本文结合实际数据AQI(空气质量指数)说明模型的实用性和可行性.     

方差分量的广义谱分解估计

对于随机效应部分为一般平衡多向分类的线性混合模型,将王松桂(2002)提出的一种称之为谱分解估计的参数估计新方法推广到随机效应设计阵为任意矩阵的含两个方差分量的线性混合模型,给出了方差分量的广义谱分解估计方法,并证明了所得估计的一些统计性质。另外,还就广义谱分解估计类中某些特殊估计和对应的方差分析估计进行了比较,得到了它们相等的充分必要条件。     

线性混合效应模型的有效稳健经验似然推断

本文考虑线性混合效应模型的有效稳健经验似然统计推断问题. 通过结合众数回归方法和矩阵的QR分解技术, 提出了一种基于众数回归的正交经验似然统计推断过程. 证明提出的关于固定效应的经验对数似然比函数渐近服从中心卡方分布, 进而构造了模型固定效应的置信区间. 所提出的估计过程不需要对随机效应和模型误差的分布施加任何假定, 并且关于固定效应的估计过程不受随机效应的影响, 因此具有较好的稳健性和有效性.     

均值方差结构模型的渐近稳健推断(英文)

均值方差模型广泛应用于行为、教育、医学、社会和心理学的研究.经典的极大似然估计对于异常点和分布扰动易受影响.本文基于目标函数最小化给出稳健估计,并基于稳健偏差提出模型拟合.     

线性混合效应模型的正交经验似然推断

基于经验似然方法和QR分解技术, 对线性混合效应模型提出了一个基于正交经验似然的估计方法. 在一些正则条件下, 证明了所提出的经验对数似然比函数渐近服从卡方分布, 进而给出了模型固定效应的置信区间估计. 所提出估计过程不受模型随机效应的影响, 进而保证了所给出的估计是比较有效的. 一些数值模拟和实例分析进一步表明了所提出的估计方法是行之有效的.     

半参数广义线性混合效应模型的估计及其渐近性质

半参数广义线性混合效应模型在心理学、生物育种、医学等领域有广泛的应用. Zhang(1998)用最大惩罚似然函数的方法(MPLE)对模型的参数和非参数部分进行了估计, 而Zhang (1998) MPLE方法只适用于正态数据模型. 对于泊松等常用的模型, 常的方法是将随机效应看作缺失数据, 再引入EM算法. 本文基于McCulloch 1997)提出的MCNR算法, 此算法推广到半参数广义线性混合效应模型中并得到相应的估计算法. 于非参数部分, 本文采用P样条拟合并利用GCV方法选取光滑参数, 时证明了所得估计的相合性和渐近正态性. 最后, 过模拟和实例与其它算法作比较验证本文估计方法的有效性.     

Robust empirical likelihood inference for generalized partial linear models with longitudinal data

In this paper, we propose a robust empirical likelihood (REL) inference for the parametric component in a generalized partial linear model (GPLM) with longitudinal data. We make use of bounded scores and leverage-based weights in the auxiliary random vectors to achieve robustness against outliers in both the response and covariates. Simulation studies demonstrate the good performance of our proposed REL method, which is more accurate and efficient than the robust generalized estimating equation (GEE) method (X. He, W.K. Fung, Z.Y. Zhu, Robust estimation in generalized partial linear models for clustered data, Journal of the American Statistical Association 100 (2005) 1176-1184). The proposed robust method is also illustrated by analyzing a real data set.     

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本文综述混合效应模型参数估计方面的若干新进展. 平衡混合效应方差分析模型的协方差阵具有一定结构. 对这类模型, 文献[1]提出了参数估计的一种新方法, 称为谱分解法. 新方法的突出特点是, 能同时给出固定效应和方差分量的估计, 前者是线性的, 后者是二次的,且相互独立. 而后, 文献[2--9]证明了谱分解估计的进一步的统计性质, 同时给出了协方差阵对应的估计, 它不仅是正定阵, 而且可获得它的风险函数, 这些文献还研究了谱分解估计与方差分析估计, 极大似然估计, 限制极大似然估计以及最小范数二次无偏估计的关系. 本文综述这一方向的部分研究成果, 并提出一些待进一步研究的问题.     

部分函数线性模型的经验似然推断

本文考虑部分函数线性回归模型,研究了回归系数的经验似然推断,证明了所提出的经验对数似然比渐近于χ~2分布,此结果可以用来构造了相应兴趣参数的置信域.另外,本文也给出了系数函数的极大经验似然估计,并在适当条件下给出了所提出估计量的收敛速度.仅就置信域精度及其覆盖概率大小方面,通过模拟研究和实例分析比较了经验似然方法与最小二乘方法的优劣.     

Estimating Frailty Models via Poisson Hierarchical Generalized Linear Models

Frailty models extend proportional hazards models to multivariate survival data. Hierarchical-likelihood provides a simple unified framework for various random effect models such as hierarchical generalized linear models, frailty models, and mixed linear models with censoring. Wereview the hierarchical-likelihood estimation methods for frailty models. Hierarchical-likelihood for frailty models can be expressed as that for Poisson hierarchical generalized linear models. Frailty models can thus be fitted using Poisson hierarchical generalized linear models. Properties of the new methodology are demonstrated by simulation. The new method reduces the bias of maximum likelihood and penalized likelihood estimates.     

Jackknifed random weighting for Cox proportional hazards model

The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.     

Measurement error in proportional hazards models for survival data with long-term survivors

This work studies a proportional hazards model for survival data with "long-term survivors",in which covariates are subject to linear measurement error.It is well known that the naive estimators from both partial and full likelihood methods are inconsistent under this measurement error model.For measurement error models,methods of unbiased estimating function and corrected likelihood have been proposed in the literature.In this paper,we apply the corrected partial and full likelihood approaches to estimate the model and obtain statistical inference from survival data with long-term survivors.The asymptotic properties of the estimators are established.Simulation results illustrate that the proposed approaches provide useful tools for the models considered.     

一类零膨胀半参数混合效应模型的惩罚似然估计

本文将半参数线性混合效应模型推广应用到一类具有零膨胀的纵向数据或集群数据的研究中,提出了一类新的半参数混合效应模型,然后利用广义交叉核实法选取光滑参数,通过最大惩罚似然函数方法与EM算法给出了模型参数部分与非参数部分的估计方法,最后,通过模拟和实例说明了本文方法的有效性.     

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed two-step approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.     

Computations for the familial analysis of binary traits

For familial aggregation of a binary trait, one method that has been used is the GEE2 (generalized estimating equation) method corresponding to a multivariate logit model. We solve the complex estimating equations for the GEE2 method using an automatic differentiation software which computes the derivatives of a function numerically using the chain rule of the calculus repeatedly on the elementary operations of the function. Based on this, we are able to show in a simulation study that the GEE2 estimates are quite close to the maximum likelihood estimates assuming a multivariate logit model, and that the GEE2 method is computationally faster when the dimension or family size is larger than four.     

Fitting mixed-effects models when data are left truncated

Damage sizes, i.e. all damages occurring to a policy and not only those that are reported to an insurance company, are modelled as a linear mixed model. Only those damages that are larger than their deductibles are reported to the company, and this fact should be taken into account when analyzing such data. In statistical terms, the problem is to make inference in a linear mixed model with left truncated data. Estimation methods based on a Monte Carlo simulation of the likelihood are proposed, and extensive simulations to evaluate the quality of the methods are reported. The proposed methods are then used to analyze claimsizes for some marine insurance data, where shipowners represent random effects and technical data about the ships represent fixed effects.