含非随机缺失数据的面板数据参数估计方法

抽样调查领域常采用对多个受访者进行跟踪调查得到面板数据,进而对总体特性进行统计推断,在面板数据中常含缺失数据,大多数处理面板缺失数据的软件都是直接删去含缺失值的受访者以得到完全数据集,当数据缺失机制为非随机缺失时会导致总体参数估计结果有偏。本文针对数据缺失机制为非随机缺失情形下,如何对面板数据进行统计分析进行了阐述,主要采用的是基于模型的似然推断法,对目标变量、缺失指示变量和随机效应向量的联合分布建模,在已有选择模型和模式混合模型的基础上,引入随机效应,研究目标变量期望的计算方法,并研究随机效应杂合模型下参数的估计方法,在变量分布相对简单的情形下给出了用极大似然法推断总体参数的估计步骤,最后通过模拟分析比较方法的优劣。     

左删失数据的双惩罚贝叶斯Tobit分位回归方法

在含潜变量的纵向数据混合效应模型应用中,通常包含大量截尾数据,若直接采用一般贝叶斯Tobit分位回归模型,参数估计的马尔科夫链蒙特卡罗抽样算法将会极其复杂,造成计算效率低下且估计结果偏差较大。同时,在高维情形下,由于受大量未知随机效应的干扰,固定效应中关键变量的选择与系数估计变得更为困难。为了解决上述问题,文章提出了一种新的双Adaptive Lasso惩罚贝叶斯Tobit分位回归方法,主要研究响应变量左删失情形下高维纵向数据的变量选择与参数估计问题。通过将Adaptive Lasso惩罚同时引入固定效应与随机效应的先验分布中,构造了参数估计的Gibbs抽样算法。蒙特卡罗模拟结果表明,新方法较无惩罚法和Lasso惩罚法在重要变量选择及系数估计上均更占优势。     

缺失偏态数据下线性回归模型的统计推断

研究缺失偏态数据下线性回归模型的参数估计问题,针对缺失偏态数据,为克服样本分布扭曲缺点和提高模型的回归系数、尺度参数和偏度参数的估计效果,提出了一种适合偏态数据下线性回归模型中缺失数据的修正回归插补方法.通过随机模拟和实例研究,并与均值插补、回归插补、随机回归插补方法比较,结果表明所提出的修正回归插补方法是有效可行的.     

基于随机森林模型的分类数据缺失值插补

缺失数据是影响调查问卷数据质量的重要因素,对调查问卷中的缺失值进行插补可以显著提高调查数据的质量。调查问卷的数据类型多以分类型数据为主,数据挖掘技术中的分类算法是处理属性分类问题的常用方法,随机森林模型是众多分类算法中精度较高的方法之一。将随机森林模型引入调查问卷缺失数据的插补研究中,提出了基于随机森林模型的分类数据缺失值插补方法,并根据不同的缺失模式探讨了相应的插补步骤。通过与其它方法的实证模拟比较,表明随机森林插补法得到的插补值准确度更优、可信度更高。     

缺失数据的多重插补方法

插补法是对缺失数据的调整方法,多重插补弥补了单一插补的缺陷,采用一系列可能的数据集来填充每一个缺失数据值,反映了缺失数据的不确定性。本文介绍了多重插补程序的三种数据插补方法:回归预测法、倾向得分法和蒙特卡罗的马氏链方法,并且对多重插补的插补效果进行推断,指出多重插补存在的问题。     

处理缺失数据的分数插补法研究

随着研究中对数据质量要求的提高,缺失数据相关问题也越来越受到重视.文章主要论述了处理缺失数据的方法之一——分数插补法的理论基础,并在此基础上研究了分数热卡插补法及其方差估计,同时使用模拟数据,对分数热卡插补法的实现过程做了模拟研究.通过对比实验,可以得到分数热卡插补法能够在保证原有数据分布的基础上,减少因插补造成的偏差,提供更加准确的插补结果.     

缺失数据下非线性均值方差模型的参数估计

文章在响应变量随机缺失下研究非线性均值方差模型的参数估计问题.基于回归插补和随机回归插补两种缺失插补方法以及结合Gauss-Newton迭代计算算法给出该模型中未知参数的极大似然估计.并通过对两个随机模拟例子实际例子的研究分析,结果都表明了所提出的模型与统计方法具有可行性和实用性.     

分层随机抽样条件下缺失数据的多重插补方法

介绍分层随机抽样条件下多重插补法处理缺失数据的基本思想,分析可忽略无回答的分层随机抽样建立多重插补的常用方法,并通过实例加以说明.     

含缺失数据的半参数模型的稳健估计

文章在响应变量随机缺失下,基于分位数回归研究了半参数模型的稳健估计问题。首先基于B样条基函数近似技术,将模型非参数函数的估计问题转化为样条系数向量估计问题;其次,在响应变量随机缺失下,提出了一种新的插补方法,对缺失的响应变量进行多重插补;再次,基于插补后的数据集,构造出新的分位数目标函数,得到模型非参数函数以及参数向量的稳健估计;最后给出了有效算法计算多重插补估计量。通过模拟研究验证了所提方法的有效性和稳健性。     

缺失偏态数据下联合位置与尺度模型的统计推断

为了研究缺失偏态数据下的联合位置与尺度模型,基于分布自身的特点,提出了一种适合缺失偏态数据下联合建模的插补方法———修正随机回归插补方法,该方法对缺失数据下模型偏度参数的调整十分显著。通过随机模拟和实例研究,并与回归插补和随机回归插补方法进行比较,结果表明,所提出的修正随机回归插补方法是有用和有效的。     

Decomposition of Prediction Error in Multilevel Models

ABSTRACT

We present a decomposition of prediction error for the multilevel model in the context of predicting a future observable y _*j in the jth group of a hierarchical dataset. The multilevel prediction rule is used for prediction and the components of prediction error are estimated via a simulation study that spans the various combinations of level-1 (individual) and level-2 (group) sample sizes and different intraclass correlation values. Additionally, analytical results present the increase in predicted mean square error (PMSE) with respect to prediction error bias. The components of prediction error provide information with respect to the cost of parameter estimation versus data imputation for predicting future values in a hierarchical data set. Specifically, the cost of parameter estimation is very small compared to data imputation.     

Variance estimation when donor imputation is used to fill in missing values

Donor imputation is frequently used in surveys. However, very few variance estimation methods that take into account donor imputation have been developed in the literature. This is particularly true for surveys with high sampling fractions using nearest donor imputation, often called nearest‐neighbour imputation. In this paper, the authors develop a variance estimator for donor imputation based on the assumption that the imputed estimator of a domain total is approximately unbiased under an imputation model; that is, a model for the variable requiring imputation. Their variance estimator is valid, irrespective of the magnitude of the sampling fractions and the complexity of the donor imputation method, provided that the imputation model mean and variance are accurately estimated. They evaluate its performance in a simulation study and show that nonparametric estimation of the model mean and variance via smoothing splines brings robustness with respect to imputation model misspecifications. They also apply their variance estimator to real survey data when nearest‐neighbour imputation has been used to fill in the missing values. The Canadian Journal of Statistics 37: 400–416; 2009 © 2009 Statistical Society of Canada     

Imputation of Household Survey Data Using Linear Mixed Models

Mixed models are regularly used in the analysis of clustered data, but are only recently being used for imputation of missing data. In household surveys where multiple people are selected from each household, imputation of missing values should preserve the structure pertaining to people within households and should not artificially change the apparent intracluster correlation (ICC). This paper focuses on the use of multilevel models for imputation of missing data in household surveys. In particular, the performance of a best linear unbiased predictor for both stochastic and deterministic imputation using a linear mixed model is compared to imputation based on a single level linear model, both with and without information about household respondents. In this paper an evaluation is carried out in the context of imputing hourly wage rate in the Household, Income and Labour Dynamics of Australia Survey. Nonresponse is generated under various assumptions about the missingness mechanism for persons and households, and with low, moderate and high intra‐household correlation to assess the benefits of the multilevel imputation model under different conditions. The mixed model and single level model with information about the household respondent lead to clear improvements when the ICC is moderate or high, and when there is informative missingness.     

Confidence Intervals for Intraclass Correlation in Inter-Rater Reliability

Abstract Calculation of a confidence interval for intraclass correlation to assess inter‐rater reliability is problematic when the number of raters is small and the rater effect is not negligible. Intervals produced by existing methods are uninformative: the lower bound is often close to zero, even in cases where the reliability is good and the sample size is large. In this paper, we show that this problem is unavoidable without extra assumptions and we propose two new approaches. The first approach assumes that the raters are sufficiently trained and is related to a sensitivity analysis. The second approach is based on a model with fixed rater effect. Using either approach, we obtain conservative and informative confidence intervals even from samples with only two raters. We illustrate our point with data on the development of neuromotor functions in children and adolescents.     

Doubly robust point and variance estimation in the presence of imputed survey data

Imputation is often used in surveys to treat item nonresponse. It is well known that treating the imputed values as observed values may lead to substantial underestimation of the variance of the point estimators. To overcome the problem, a number of variance estimation methods have been proposed in the literature, including resampling methods such as the jackknife and the bootstrap. In this paper, we consider the problem of doubly robust inference in the presence of imputed survey data. In the doubly robust literature, point estimation has been the main focus. In this paper, using the reverse framework for variance estimation, we derive doubly robust linearization variance estimators in the case of deterministic and random regression imputation within imputation classes. Also, we study the properties of several jackknife variance estimators under both negligible and nonnegligible sampling fractions. A limited simulation study investigates the performance of various variance estimators in terms of relative bias and relative stability. Finally, the asymptotic normality of imputed estimators is established for stratified multistage designs under both deterministic and random regression imputation. The Canadian Journal of Statistics 40: 259–281; 2012 © 2012 Statistical Society of Canada     

Multilevel modelling of complex survey data

Summary.  Multilevel modelling is sometimes used for data from complex surveys involving multistage sampling, unequal sampling probabilities and stratification. We consider generalized linear mixed models and particularly the case of dichotomous responses. A pseudolikelihood approach for accommodating inverse probability weights in multilevel models with an arbitrary number of levels is implemented by using adaptive quadrature. A sandwich estimator is used to obtain standard errors that account for stratification and clustering. When level 1 weights are used that vary between elementary units in clusters, the scaling of the weights becomes important. We point out that not only variance components but also regression coefficients can be severely biased when the response is dichotomous. The pseudolikelihood methodology is applied to complex survey data on reading proficiency from the American sample of the 'Program for international student assessment' 2000 study, using the Stata program gllamm which can estimate a wide range of multilevel and latent variable models. Performance of pseudo-maximum-likelihood with different methods for handling level 1 weights is investigated in a Monte Carlo experiment. Pseudo-maximum-likelihood estimators of (conditional) regression coefficients perform well for large cluster sizes but are biased for small cluster sizes. In contrast, estimators of marginal effects perform well in both situations. We conclude that caution must be exercised in pseudo-maximum-likelihood estimation for small cluster sizes when level 1 weights are used.     

Prediction in Multilevel Logistic Regression

The purpose of this article is to present a new method to predict the response variable of an observation in a new cluster for a multilevel logistic regression. The central idea is based on the empirical best estimator for the random effect. Two estimation methods for multilevel model are compared: penalized quasi-likelihood and Gauss–Hermite quadrature. The performance measures for the prediction of the probability for a new cluster observation of the multilevel logistic model in comparison with the usual logistic model are examined through simulations and an application.     

The effects of income imputation on microanalyses: evidence from the European Community Household Panel

Summary.  Social surveys are usually affected by item and unit non-response. Since it is unlikely that a sample of respondents is a random sample, social scientists should take the missing data problem into account in their empirical analyses. Typically, survey methodologists try to simplify the work of data users by 'completing' the data, filling the missing variables through imputation. The aim of the paper is to give data users some guidelines on how to assess the effects of imputation on their microlevel analyses. We focus attention on the potential bias that is caused by imputation in the analysis of income variables, using the European Community Household Panel as an illustration.