Variance estimation for a low income proportion

Summary. Proportions below a given fraction of a quantile of an income distribution are often estimated from survey data in comparisons of poverty. We consider the estimation of the variance of such a proportion, estimated from Family Expenditure Survey data. We show how a linearization method of variance estimation may be applied to this proportion, allowing for the effects of both a complex sampling design and weighting by a raking method to population controls. We show that, for data for 1998–1999, the estimated variances are always increased when allowance is made for the design and raking weights, the principal effect arising from the design. We also study the properties of a simplified variance estimator and discuss extensions to a wider class of poverty measures.     

A Monte Carlo comparison of some variance estimators of the Horvitz–Thompson estimator

At the design and estimation stage of a survey, large survey organization often uses auxiliary information. This article discusses various procedures for improving variance estimation of the Horvitz–Thompson estimator of a finite population total with the aid of auxiliary information. To study the design-based properties of the proposed variance estimators relative to the standard one, a small scale Monte Carlo study is performed.     

VARIANCE ESTIMATION WITH HIGHLY STRATIFIED SAMPLING DESIGNS WITH UNEQUAL PROBABILITIES

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.     

Developments in sample survey theory: An appraisal

Recent developments in sample survey theory include the following topics: foundational aspects of inference, resampling methods for variance and confidence interval estimation, imputation for nonresponse and analysis of complex survey data. An overview and appraisal of some of these developments are presented.     

Estimation bias of different design and analytical strategies in dual-frame telephone surveys: an empirical evaluation

Dual-frame survey designs have become increasingly popular in large-scale telephone surveys. This is due to the lack of coverage of the traditional landline survey design and the escalating use of cell phones in recent years. Several estimation strategies have been proposed and their properties have been discussed under ideal scenarios, including pseudo-maximum-likelihood estimation, single-frame estimation, and simple composite estimation [C.J. Skinner and J.N.K. Rao, Estimation in dual frame surveys with complex designs, J. Am. Statist. Assoc. 91 (1996), pp. 349–356; S.L. Lohr and J.N.K. Rao, Inference from dual frame surveys, J. Am. Statist. Assoc. 95 (2000), pp. 271–280]. In practice, estimation in dual-frame telephone surveys is vulnerable to biases and errors (e.g. inaccessibility, topic/mode salience, and measurement error). The investigation of the performance of popular dual-frame estimation methods is scarce in real and less ideal scenarios. Through an innovatively designed simulation study, we compare the estimation bias under different sampling designs with various estimation strategies. To reduce bias, different raking strategies are compared. Simulated scenarios incorporating sampling costs are examined for practical considerations. Overall, the cell phone-only design yields results with the least bias and variance. When accurate covariate information is available for post-stratification, raking estimates from the cell phone-any design also perform very well. We also provide SAS macros for this simulation evaluation upon request. Survey practitioners can fine-tune the parameters based on their prior knowledge of the target population and run the simulation under different scenarios to gain more insights into how to optimally design and analyse telephone surveys.     

Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.     

The relative impact of interviewer effects and sample design effects on survey precision

One of the principal sources of error in data collected from structured face-to-face interviews is the interviewer. The other major component of imprecision in survey estimates is sampling variance. It is rare, however, to find studies in which the complex sampling variance and the complex interviewer variance are both computed. This paper compares the relative impact of interviewer effects and sample design effects on survey precision by making use of an interpenetrated primary sampling unit–interviewer experiment which was designed by the authors for implementation in the second wave of the British Household Panel Study as part of its scientific programme. It also illustrates the use of a multilevel (hierarchical) approach in which the interviewer and sample design effects are estimated simultaneously while being incorporated in a substantive model of interest.     

重权数在复杂调查的方差估计中的应用

 方差估计是抽样调查的重要组成部分,重抽样方法是常用的方差估计方法。重权数方法与重抽样方法类似,也是利用计算机的优势通过重复获得大量不同的子样本的重权数估计目标参数的估计量和方差估计量,是一种稳健、通用、有效的方差估计方法。本文主要介绍重权数在复杂抽样调查的方差计算中的理论和应用。     

Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data

Under complex survey sampling, in particular when selection probabilities depend on the response variable (informative sampling), the sample and population distributions are different, possibly resulting in selection bias. This article is concerned with this problem by fitting two statistical models, namely: the variance components model (a two-stage model) and the fixed effects model (a single-stage model) for one-way analysis of variance, under complex survey design, for example, two-stage sampling, stratification, and unequal probability of selection, etc. Classical theory underlying the use of the two-stage model involves simple random sampling for each of the two stages. In such cases the model in the sample, after sample selection, is the same as model for the population; before sample selection. When the selection probabilities are related to the values of the response variable, standard estimates of the population model parameters may be severely biased, leading possibly to false inference. The idea behind the approach is to extract the model holding for the sample data as a function of the model in the population and of the first order inclusion probabilities. And then fit the sample model, using analysis of variance, maximum likelihood, and pseudo maximum likelihood methods of estimation. The main feature of the proposed techniques is related to their behavior in terms of the informativeness parameter. We also show that the use of the population model that ignores the informative sampling design, yields biased model fitting.     

中国广义回归抽样估计系统的构建及应用

在抽样理论和应用研究方面,中国一直比较重视抽样方案设计,而忽视抽样估计方法研究。本文在系统总结加拿大等西方国家成功经验的基础上,引入并改进了一套广义回归估计系统,应用在复杂的连续多阶抽样调查中。本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体模型进行扩展,建立各种类型的回归模型进行模型辅助的广义回归估计,最终形成一套广义回归估计系统,为中国抽样估计的应用研究奠定理论基础。最后,本文以中国农产量的连续多阶抽样调查为例,给出了具体的回归估计程序,从而验证这套系统的实践性和应用价值。     

抽样调查中的校准估计法

本文梳理总结了校准估计法自首次提出以来的研究成果。理论方法的发展集中在最短距离法、工具向量法和模型校准法三种校准方法的研究上;方法应用的发展体现在对简单参数和复杂参数的校准估计上。对小域估计、无回答、二重抽样等特定抽样问题和总体分位数、总体方差估计中校准估计法的具体应用作了重点梳理介绍。对校准估计法的理论和应用研究前景作了展望。     

Graphical technique for comparing designs for random models

Methods for comparing designs for a random (or mixed) linear model have focused primarily on criteria based on single-valued functions. In general, these functions are difficult to use, because of their complex forms, in addition to their dependence on the model's unknown variance components. In this paper, a graphical approach is presented for comparing designs for random models. The one-way model is used for illustration. The proposed approach is based on using quantiles of an estimator of a function of the variance components. The dependence of these quantiles on the true values of the variance components is depicted by plotting the so-called quantile dispersion graphs (QDGs), which provide a comprehensive picture of the quality of estimation obtained with a given design. The QDGs can therefore be used to compare several candidate designs. Two methods of estimation of variance components are considered, namely analysis of variance and maximum-likelihood estimation.     

Asymptotic design-cum-model based estimation of variances of estimated linear regression coefficients in survey sampling with unequal probabilities

Postulating a super-population linear regression model for a variable of interest on an auxiliary variable we consider design-based estimation of regression coefficients on drawing a sample with unequal probabilities from a survey population. Asymptotic design-cum-model based variance estimation procedures are proposed.     

Sampling within households in household surveys

Summary.  The number of people to select within selected households has significant consequences for the conduct and output of household surveys. The operational and data quality implications of this choice are carefully considered in many surveys, but the effect on statistical efficiency is not well understood. The usual approach is to select all people in each selected household, where operational and data quality concerns make this feasible. If not, one person is usually selected from each selected household. We find that this strategy is not always justified, and we develop intermediate designs between these two extremes. Current practices were developed when household survey field procedures needed to be simple and robust; however, more complex designs are now feasible owing to the increasing use of computer-assisted interviewing. We develop more flexible designs by optimizing survey cost, based on a simple cost model, subject to a required variance for an estimator of population total. The innovation lies in the fact that household sample sizes are small integers, which creates challenges in both design and estimation. The new methods are evaluated empirically by using census and health survey data, showing considerable improvement over existing methods in some cases.     

Variance estimation in complex survey sampling for generalized linear models

Summary.  Complex survey sampling is often used to sample a fraction of a large finite population. In general, the survey is conducted so that each unit (e.g. subject) in the sample has a different probability of being selected into the sample. For generalizability of the sample to the population, both the design and the probability of being selected into the sample must be incorporated in the analysis. In this paper we focus on non-standard regression models for complex survey data. In our motivating example, which is based on data from the Medical Expenditure Panel Survey, the outcome variable is the subject's 'total health care expenditures in the year 2002'. Previous analyses of medical cost data suggest that the variance is approximately equal to the mean raised to the power of 1.5, which is a non-standard variance function. Currently, the regression parameters for this model cannot be easily estimated in standard statistical software packages. We propose a simple two-step method to obtain consistent regression parameter and variance estimates; the method proposed can be implemented within any standard sample survey package. The approach is applicable to complex sample surveys with any number of stages.     

Investigating impacts of complex sampling on latent growth curve modelling

We investigate the impacts of complex sampling on point and standard error estimates in latent growth curve modelling of survey data. Methodological issues are illustrated with empirical evidence from the analysis of longitudinal data on life satisfaction trajectories using data from the British Household Panel Survey, a national representative survey in Great Britain. A multi-process second-order latent growth curve model with conditional linear growth is used to study variation in the two perceived life satisfaction latent factors considered. The benefits of accounting for the complex survey design are considered, including obtaining unbiased both point and standard error estimates, and therefore correctly specified confidence intervals and statistical tests. We conclude that, even for the rather elaborated longitudinal data models that were considered, estimation procedures are affected by variance-inflating impacts of complex sampling.     

Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.     

Generalised Variance Function Estimation for Binary Variables in Large‐Scale Sample Surveys

Generalised variance function (GVF) models are data analysis techniques often used in large‐scale sample surveys to approximate the design variance of point estimators for population means and proportions. Some potential advantages of the GVF approach include operational simplicity, more stable sampling errors estimates and providing a convenient method of summarising results when a high number of survey variables is considered. In this paper, several parametric and nonparametric methods for GVF estimation with binary variables are proposed and compared. The behavior of these estimators is analysed under heteroscedasticity and in the presence of outliers and influential observations. An empirical study based on the annual survey of living conditions in Galicia (a region in the northwest of Spain) illustrates the behaviour of the proposed estimators.     

Properties of design-based functional principal components analysis

This work aims at performing functional principal components analysis (FPCA) with Horvitz–Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model-assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville [1999. Variance estimation for complex statistics and estimators: linearization and residual techniques. Survey Methodology 25, 193–203], we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA’ estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.     

The new strategy for the concise presentation of sampling errors in the Italian Structural Business Statistics Survey

Reporting sampling errors of survey estimates is a problem that is commonly addressed when compiling a survey report. Because of the vast number of study variables or population characteristics and of interest domains in a survey, it is almost impossible to calculate and to publish the standard errors for each statistic. A way of overcoming such problem would be to estimate indirectly the sampling errors by using generalized variance functions, which define a statistical relationship between the sampling errors and the corresponding estimates. One of the problems with this approach is that the model specification has to be consistent with a roughly constant design effect. If the design effects vary greatly across estimates, as in the case of the Business Surveys, the prediction model is not correctly specified and the least-square estimation is biased. In this paper, we show an extension of the generalized variance functions, which address the above problems, which could be used in contexts similar to those encountered in Business Surveys. The proposed method has been applied to the Italian Structural Business Statistics Survey case.