单个协变量带有测量误差的多维结构回归模型

给出可交换条件下单个协变量的带有测量误差的多维结构回归模型,利用该模型研究总体平均处理效应的估计,给出当暴露组和对照组的协变量测量误差同分布时总体平均处理效应的拟极大似然估计及其性质.     

多维协变量具有测量误差的结构回归模型

提出具有测量误差的结构回归模型,研究可交换条件下多维协变量的测量误差对平均处理效应估计的影响,在没有其它的附加条件下,尽管大多数模型参数不可识别,平均处理效应仍可识别,由于平均处理效应的极大似然估计求解困难,建议在实际中使用拟极大似然估计作为替代。     

可交换条件下多维结构回归模型总体平均处理效应的估计

在可交换条件下，当响应变量为多维时，利用结构回归模型研究总体平均处理效应的估计。     

响应变量为多维时因果推断中混杂因子的控制和排序

研究可交换条件下多维结构回归模型中总体平均处理效应的混杂因子的控制和排序问题,利用矩阵的迹定义混杂因子的控制效率,通过控制效率来控制混杂因子,并给出混杂因子的排序,同时给出一个应用实例。     

多反应变量重复测量的混合效应模型及其应用

本文给出了多反应变量重复测量的协方差矩阵结构,探讨了用迭代广义最小二乘法来求解其带协变量和不带协变量的混合效应模型中固定效应和随机效应系数,并对１９９１年四川省高血压调查资料进行实例分析,得到其结论符合实际情况．     

关于广义Potthoff—Roy估计

本文考察了生长曲线模型的定义形式,并因此建立了相应的广义Potthoff-Roy估计,在最小范数准则下,给出了估计的最佳选择并且讨论了协变量以及改进估计的方法,尤其当设计阵病态时,给出了两类新的岭型Potthoff-Roy估计。     

含不可忽略缺失数据非线性再生散度模型参数的Bayes估计

给出协变量带有不可忽略缺失数据的非线性再生散度模型的Bayes方法,缺失数据机制由Logistic回归模型来确定.Gibbs抽样技术和Metropolis-Hastings算法(简称MH算法)用来得到模型参数、缺失数据机制中回归系数的联合Bayes估计,并用实例加以说明.     

因果推断中的混杂控制

因果分析中混杂的控制是一个难题，本文探讨总体平均效应估计中混杂的控制问题，给出充分控制子集的识别方法。     

一个推广增长曲线模型协差阵的最小二乘估计及其优良性

在准正态情形与独立同分布情形下,分别给出了一个推广增长曲线模型中协差阵的最小二乘估计,并得到了最小二乘估计成为一致最小方差不变二次无偏估计的充要条件．     

基于协同克里格的橡胶园土壤速效钾空间变异性

选取有效变量的协同克里格方法能够提高县域尺度橡胶园土壤速效钾的空间预测精度,对橡胶树精准施肥管理具有重要意义。本研究以海南省白沙县橡胶园0～20 cm耕层土壤为对象,采用地统计学分析土壤速效钾的空间变异特征,运用相关分析筛选显著的特征变量,并比较不同变量的协同克里格(COK)空间插值精度。结果表明: 研究区土壤速效钾平均含量为44.65 g·kg^-1,总体处于缺乏状态;变异系数为52.6%,属中等变异强度;块金效应为12.5%,存在较强的空间自相关。有机质、高程与土壤速效钾含量关系密切,均呈极显著相关;有机质(COK₁)、高程(COK₂)、有机质+高程(COK₃)3种协变量的COK空间插值预测精度均高于普通克里格法(OK),交叉验证模型拟合精度为COK₁>COK₃> COK₂>OK;拟合精度与协变量选取的数量不呈正比,选取相关性更高的协变量更有利于反映区域土壤属性的空间异质性。研究区土壤速效钾含量具有西北部较高、中偏东部地区较低的分布特点。研究结果为今后开展橡胶园土壤钾素管理提供了理论依据。     

Estimation in capture-recapture models when covariates are subject to measurement errors

We consider estimation problems in capture-recapture models when the covariates or the auxiliary variables are measured with errors. The naive approach, which ignores measurement errors, is found to be unacceptable in the estimation of both regression parameters and population size: it yields estimators with biases increasing with the magnitude of errors, and flawed confidence intervals. To account for measurement errors, we derive a regression parameter estimator using a regression calibration method. We develop modified estimators of the population size accordingly. A simulation study shows that the resulting estimators are more satisfactory than those from either the naive approach or the simulation extrapolation (SIMEX) method. Data from a bird species Prinia flaviventris in Hong Kong are analyzed with and without the assumption of measurement errors, to demonstrate the effects of errors on estimations.     

Differential measurement errors in zero-truncated regression models for count data

Measurement errors in covariates may result in biased estimates in regression analysis. Most methods to correct this bias assume nondifferential measurement errors-i.e., that measurement errors are independent of the response variable. However, in regression models for zero-truncated count data, the number of error-prone covariate measurements for a given observational unit can equal its response count, implying a situation of differential measurement errors. To address this challenge, we develop a modified conditional score approach to achieve consistent estimation. The proposed method represents a novel technique, with efficiency gains achieved by augmenting random errors, and performs well in a simulation study. The method is demonstrated in an ecology application.     

Laplace approximation in measurement error models

Likelihood analysis for regression models with measurement errors in explanatory variables typically involves integrals that do not have a closed-form solution. In this case, numerical methods such as Gaussian quadrature are generally employed. However, when the dimension of the integral is large, these methods become computationally demanding or even unfeasible. This paper proposes the use of the Laplace approximation to deal with measurement error problems when the likelihood function involves high-dimensional integrals. The cases considered are generalized linear models with multiple covariates measured with error and generalized linear mixed models with measurement error in the covariates. The asymptotic order of the approximation and the asymptotic properties of the Laplace-based estimator for these models are derived. The method is illustrated using simulations and real-data analysis.     

Bayesian semiparametric nonlinear mixed-effects joint models for data with skewness, missing responses, and measurement errors in covariates

Summary It is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed-effects (SNLME) models with a normal distribution. Normality assumption of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models, but some covariates may often be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. Inferential procedures can be complicated dramatically when data with skewness, missing values, and measurement error are observed. In the literature, there has been considerable interest in accommodating either skewness, incompleteness or covariate measurement error in such models, but there has been relatively little study concerning all three features simultaneously. In this article, our objective is to address the simultaneous impact of skewness, missingness, and covariate measurement error by jointly modeling the response and covariate processes based on a flexible Bayesian SNLME model. The method is illustrated using a real AIDS data set to compare potential models with various scenarios and different distribution specifications.     

Simultaneous inference for semiparametric nonlinear mixed-effects models with covariate measurement errors and missing responses

Semiparametric nonlinear mixed-effects (NLME) models are flexible for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain interindividual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. We propose two approximate likelihood methods for semiparametric NLME models with covariate measurement errors and nonignorable missing responses. The methods are illustrated in a real data example. Simulation results show that both methods perform well and are much better than the commonly used naive method.     

Logistic regression for clustered data from environmental monitoring programs

Large-scale surveys, such as national forest inventories and vegetation monitoring programs, usually have complex sampling designs that include geographical stratification and units organized in clusters. When models are developed using data from such programs, a key question is whether or not to utilize design information when analyzing the relationship between a response variable and a set of covariates. Standard statistical regression methods often fail to account for complex sampling designs, which may lead to severely biased estimators of model coefficients. Furthermore, ignoring that data are spatially correlated within clusters may underestimate the standard errors of regression coefficient estimates, with a risk for drawing wrong conclusions. We first review general approaches that account for complex sampling designs, e.g. methods using probability weighting, and stress the need to explore the effects of the sampling design when applying logistic regression models. We then use Monte Carlo simulation to compare the performance of the standard logistic regression model with two approaches to model correlated binary responses, i.e. cluster-specific and population-averaged logistic regression models. As an example, we analyze the occurrence of epiphytic hair lichens in the genus Bryoria; an indicator of forest ecosystem integrity. Based on data from the National Forest Inventory (NFI) for the period 1993–2014 we generated a data set on hair lichen occurrence on  >100,000 Picea abies trees distributed throughout Sweden. The NFI data included ten covariates representing forest structure and climate variables potentially affecting lichen occurrence. Our analyses show the importance of taking complex sampling designs and correlated binary responses into account in logistic regression modeling to avoid the risk of obtaining notably biased parameter estimators and standard errors, and erroneous interpretations about factors affecting e.g. hair lichen occurrence. We recommend comparisons of unweighted and weighted logistic regression analyses as an essential step in development of models based on data from large-scale surveys.     

A Bayesian Approach to Joint Mixed‐Effects Models with a Skew‐Normal Distribution and Measurement Errors in Covariates

Summary In recent years, nonlinear mixed‐effects (NLME) models have been proposed for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain intersubject variations. However, one often assumes that both model random error and random effects are normally distributed, which may not always give reliable results if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. In this article, we address these issues simultaneously by jointly modeling the response and covariate processes using a Bayesian approach to NLME models with covariate measurement errors and a skew‐normal distribution. A real data example is offered to illustrate the methodologies by comparing various potential models with different distribution specifications. It is showed that the models with skew‐normality assumption may provide more reasonable results if the data exhibit skewness and the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.