Survey Methodology
Release date: June 30, 2020
The journal Survey Methodology Volume 46, Number 1 (June 2020) contains six papers.
Regular Papers
Are probability surveys bound to disappear for the production of official statistics?
For several decades, national statistical agencies around the world have been using probability surveys as their preferred tool to meet information needs about a population of interest. In the last few years, there has been a wind of change and other data sources are being increasingly explored. Five key factors are behind this trend: the decline in response rates in probability surveys, the high cost of data collection, the increased burden on respondents, the desire for access to “real-time” statistics, and the proliferation of non-probability data sources. Some people have even come to believe that probability surveys could gradually disappear. In this article, we review some approaches that can reduce, or even eliminate, the use of probability surveys, all the while preserving a valid statistical inference framework. All the approaches we consider use data from a non-probability source; data from a probability survey are also used in most cases. Some of these approaches rely on the validity of model assumptions, which contrasts with approaches based on the probability sampling design. These design-based approaches are generally not as efficient; yet, they are not subject to the risk of bias due to model misspecification.
Local polynomial estimation for a small area mean under informative sampling
by Marius Stefan and Michael A. Hidiroglou
Model-based methods are required to estimate small area parameters of interest, such as totals and means, when traditional direct estimation methods cannot provide adequate precision. Unit level and area level models are the most commonly used ones in practice. In the case of the unit level model, efficient model-based estimators can be obtained if the sample design is such that the sample and population models coincide: that is, the sampling design is non-informative for the model. If on the other hand, the sampling design is informative for the model, the selection probabilities will be related to the variable of interest, even after conditioning on the available auxiliary data. This will imply that the population model no longer holds for the sample. Pfeffermann and Sverchkov (2007) used the relationships between the population and sample distribution of the study variable to obtain approximately unbiased semi-parametric predictors of the area means under informative sampling schemes. Their procedure is valid for both sampled and non-sampled areas. Verret, Rao and Hidiroglou (2015) studied alternative procedures that incorporate a suitable function of the unit selection probabilities as an additional auxiliary variable. Their procedure resulted in approximately unbiased empirical best linear unbiased prediction (EBLUP) estimators for the small area means. In this paper, we extend the Verret et al. (2015) procedure by not assuming anything about the inclusion probabilities. Rather, we incorporate them into the unit level model via a smooth function of the inclusion probabilities. This function is estimated via a local approximation resulting in a local polynomial estimator. A conditional bootstrap method is proposed for the estimation of mean squared error (MSE) of the local polynomial and EBLUP estimators. The bias and efficiency properties of the local polynomial estimator are investigated via a simulation. Results for the bootstrap estimator of MSE are also presented.
Small area estimation methods under cut-off sampling
by María Guadarrama, Isabel Molina and Yves Tillé
Cut-off sampling is applied when there is a subset of units from the population from which getting the required information is too expensive or difficult and, therefore, those units are deliberately excluded from sample selection. If those excluded units are different from the sampled ones in the characteristics of interest, naïve estimators may be severely biased. Calibration estimators have been proposed to reduce the design-bias. However, when estimating in small domains, they can be inefficient even in the absence of cut-off sampling. Model-based small area estimation methods may prove useful for reducing the bias due to cut-off sampling if the assumed model holds for the whole population. At the same time, for small domains, these methods provide more efficient estimators than calibration methods. Since model-based properties are obtained assuming that the model holds but no model is exactly true, here we analyze the design properties of calibration and model-based procedures for estimation of small domain characteristics under cut-off sampling. Our results confirm that model-based estimators reduce the bias due to cut-off sampling and perform significantly better in terms of design mean squared error.
Model-assisted sample design is minimax for model-based prediction
Probability sampling designs are sometimes used in conjunction with model-based predictors of finite population quantities. These designs should minimize the anticipated variance (AV), which is the variance over both the superpopulation and sampling processes, of the predictor of interest. The AV-optimal design is well known for model-assisted estimators which attain the Godambe-Joshi lower bound for the AV of design-unbiased estimators. However, no optimal probability designs have been found for model-based prediction, except under conditions such that the model-based and model-assisted estimators coincide; these cases can be limiting. This paper shows that the Godambe-Joshi lower bound is an upper bound for the AV of the best linear unbiased estimator of a population total, where the upper bound is over the space of all covariate sets. Therefore model-assisted optimal designs are a sensible choice for model-based prediction when there is uncertainty about the form of the final model, as there often would be prior to conducting the survey. Simulations confirm the result over a range of scenarios, including when the relationship between the target and auxiliary variables is nonlinear and modeled using splines. The AV is lowest relative to the bound when an important design variable is not associated with the target variable.
Considering interviewer and design effects when planning sample sizes
by Stefan Zins and Jan Pablo Burgard
Selecting the right sample size is central to ensure the quality of a survey. The state of the art is to account for complex sampling designs by calculating effective sample sizes. These effective sample sizes are determined using the design effect of central variables of interest. However, in face-to-face surveys empirical estimates of design effects are often suspected to be conflated with the impact of the interviewers. This typically leads to an over-estimation of design effects and consequently risks misallocating resources towards a higher sample size instead of using more interviewers or improving measurement accuracy. Therefore, we propose a corrected design effect that separates the interviewer effect from the effects of the sampling design on the sampling variance. The ability to estimate the corrected design effect is tested using a simulation study. In this respect, we address disentangling cluster and interviewer variance. Corrected design effects are estimated for data from the European Social Survey (ESS) round 6 and compared with conventional design effect estimates. Furthermore, we show that for some countries in the ESS round 6 the estimates of conventional design effect are indeed strongly inflated by interviewer effects.
A new double hot-deck imputation method for missing values under boundary conditions
by Yousung Park and Tae Yeon Kwon
In surveys, logical boundaries among variables or among waves of surveys make imputation of missing values complicated. We propose a new regression-based multiple imputation method to deal with survey nonresponses with two-sided logical boundaries. This imputation method automatically satisfies the boundary conditions without an additional acceptance/rejection procedure and utilizes the boundary information to derive an imputed value and to determine the suitability of the imputed value. Simulation results show that our new imputation method outperforms the existing imputation methods for both mean and quantile estimations regardless of missing rates, error distributions, and missing-mechanisms. We apply our method to impute the self-reported variable “years of smoking” in successive health screenings of Koreans.
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