总体平均处理效应的拟极大似然估计

本文给出可交换条件下多维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。     

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。     

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。     

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。     

多QTL定位的压缩估计方法

本文综述了多标记分析和多QTL定位的压缩估计方法。对于前者,Xu（Genetics,2003,163：789—801）首先提出了Bayesian压缩估计方法。其关键在于让每个效应有一个特定的方差参数,而该方差又服从一定的先验分布,以致能从资料中估计之。由此,能够同时估计大量分子标记基因座的遗传效应,即使大多数标记的效应是可忽略的。然而,对于上位性遗传模型,其运算时间还是过长。为此,笔者将上述思想嵌入极大似然法,提出了惩罚最大似然方法。模拟研究显示：该方法能处理变量个数大于样本容量10倍左右的线性遗传模型。对于后者,本文详细介绍了基于固定区间和可变区间的Bayesian压缩估计方法。固定区间方法可处理中等密度的分子标记资料;可变区间方法则可分析高密度分子标记资料,甚至是上位性遗传模型。对于上位性检测,已介绍的惩罚最大似然方法和可变区间Bayesian压缩估计方法可供利用。应当指出,压缩估计方法在今后的eQTL和QTN定位以及基因互作网络分析等研究中也是有应用价值的。     

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．     

亲体量和环境对东海小黄鱼补充成功率的影响

补充成功率通常可用多个假说机制进行解释,模型选择方法通过选择最优模型而支持某种特定假说.然而,由于忽略模型不确定性,将单一模型结果应用到衰退种类的资源管理或许并不是行之有效的方案.本研究利用1992—2012年东海区海洋渔业统计、渔业资源监测和渔业资源同步调查获得的小黄鱼亲体量丰度、补充量丰度资料,以及同年东海北部5—8月海表温度(SST)、经向风应力(MWS)、纬向风应力(ZWS)、海平面气压(SSP)和长江径流量(RCR)等水文环境数据,采用AIC、最大校正R2和变量显著性3种独立的模型选择方法对竞争模型进行优化,根据模型选择结果探寻影响小黄鱼补充成功率的显著因素.同时,采用贝叶斯模型平均(BMA)方法,在模型不确定性假设背景下对多种变量进行了概率集成.选取平均绝对误差、均方预测误差和连续排序概率评分3种概率检验方法评估贝叶斯模型平均方法和标准模型选择方法的预报系统的整体性能.结果表明:3种模型选择方法获得的模型形式并不一致,AIC选择的预测变量有亲体量和经向风应力,变量显著性方法为亲体量,最大校正R2为亲体量、经向风应力和长江径流量.亲体量与补充成功率为显著负线性关系(P<0.01),表明种群可能通过自相蚕食、饵料竞争等过度补偿效应控制补充成功率;经向风应力强度和长江径流分别对补充成功率有近似显著的正效应(P=0.06)和负效应影响(P=0.07).在平均绝对误差和连续排序概率评分分析指标中,贝叶斯模型平均方法均最小,变量显著性方法最大,最大校正R2模型在均方预测误差中估计精度最高.基于贝叶斯模型平均的亲体-补充量集成预报不仅可以提供精度较高的预报均值,而且可以通过概率分布定量评价模型预报的不确定性.     

H广义线性模型中的参数估计的比较

本文研究H广义线性模型中未知参数的两种估计方法,一种是边际似然函数法,另一种是Lee和Nelder提出来的L-N法．对于一类具有两个随机效应的典型的Poisson-Gamma类模型,在一些正则性条件之下,我们已经证明了其中固定效应卢的L-N估计的强相合性及渐近正态性,并得到了其收敛于真值的速度．针对这类模型,本文进一步给出了其边际似然函数的解析表达式,并且通过Monte Carlo模拟,对模型中固定效应β的边际似然估计和L—N估计进行了比较,模拟表明L—N估计比边际似然估计在拟Poisson-Gamma模型中有着更加优良的表现,具有更高的精度。     

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.     

Models for longitudinal data: a generalized estimating equation approach

This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mother's smoking and children's respiratory disease.     

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.     

Process and measurement errors of population size: their mutual effects on precision and bias of estimates for demographic parameters

Knowing the parameters of population growth and regulation is fundamental for answering many ecological questions and the successful implementation of conservation strategies. Moreover, detecting a population trend is often a legal obligation. Yet, inherent process and measurement errors aggravate the ability to estimate these parameters from population time-series. We use numerical simulations to explore how the lengths of the time-series, process and measurement error influence estimates of demographic parameters. We first generate time-series of population sizes with given demographic parameters for density-dependent stochastic population growth, but assume that these population sizes are estimated with measurement errors. We then fit parameters for population growth, habitat capacity, total error and long-term trends to the ‘measured’ time-series data using non-linear regression. The length of the time-series and measurement error introduce a substantial bias in the estimates for population growth rate and to a lesser degree on estimates for habitat capacity, while process error has little effect on parameter bias. The total error term of the statistical model is dominated by process error as long as the latter is larger than the measurement error. A decline in population size is difficult to document as soon as either error becomes moderate, trends are not very pronounced, and time-series are short (<10–15 seasons). Detecting an annual decline of 1% within 6-year reporting periods, as required for the European Union for the species of Community Interest, appears unachievable.     

Modeling observation error and its effects in a random walk/extinction model

This paper examines the consequences of observation errors for the "random walk with drift", a model that incorporates density independence and is frequently used in population viability analysis. Exact expressions are given for biases in estimates of the mean, variance and growth parameters under very general models for the observation errors. For other quantities, such as the finite rate of increase, and probabilities about population size in the future we provide and evaluate approximate expressions. These expressions explain the biases induced by observation error without relying exclusively on simulations, and also suggest ways to correct for observation error. A secondary contribution is a careful discussion of observation error models, presented in terms of either log-abundance or abundance. This discussion recognizes that the bias and variance in observation errors may change over time, the result of changing sampling effort or dependence on the underlying population being sampled.     

Analysis of Misclassified Correlated Binary Data Using a Multivariate Probit Model when Covariates are Subject to Measurement Error

A multivariate probit model for correlated binary responses given the predictors of interest has been considered. Some of the responses are subject to classification errors and hence are not directly observable. Also measurements on some of the predictors are not available; instead the measurements on its surrogate are available. However, the conditional distribution of the unobservable predictors given the surrogate is completely specified. Models are proposed taking into account either or both of these sources of errors. Likelihood‐based methodologies are proposed to fit these models. To ascertain the effect of ignoring classification errors and /or measurement error on the estimates of the regression and correlation parameters, a sensitivity study is carried out through simulation. Finally, the proposed methodology is illustrated through an example.     

Measurement error in a random walk model with applications to population dynamics

Population abundances are rarely, if ever, known. Instead, they are estimated with some amount of uncertainty. The resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time. This article addresses some outstanding questions on the consequences of measurement error in one such dynamic model, the random walk with drift model, and proposes some new ways to correct for measurement error. We present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors, and we provide analytical results about the biases of estimators that ignore the measurement error. Our new estimators include both method of moments estimators and "pseudo"-estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model. We derive the asymptotic properties of our methods and existing methods, and we compare their finite-sample performance with a simulation experiment. We also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets.