Survey Methodology
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June 2015
The journal Survey Methodology Volume 41, Number 1 (June 2015) contains the following 13 papers:
Regular Papers
Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random area effects
Isabel Molina, J.N.K. Rao and Gauri Sankar Datta
Abstract
A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.
Small area estimation combining information from several sources
Jae-kwang Kim, Seunghwan Park and Seo-young Kim
Abstract
An area-level model approach to combining information from several sources is considered in the context of small area estimation. At each small area, several estimates are computed and linked through a system of structural error models. The best linear unbiased predictor of the small area parameter can be computed by the general least squares method. Parameters in the structural error models are estimated using the theory of measurement error models. Estimation of mean squared errors is also discussed. The proposed method is applied to the real problem of labor force surveys in Korea.
Observed best prediction via nested-error regression with potentially misspecified mean and variance
Jiming Jiang, Thuan Nguyen and J. Sunil Rao
Abstract
We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.
A method of determining the winsorization threshold, with an application to domain estimation
Cyril Favre Martinoz, David Haziza and Jean-François Beaumont
Abstract
In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.
Modified regression estimator for repeated business surveys with changing survey frames
John Preston
Abstract
Composite estimation is a technique applicable to repeated surveys with controlled overlap between successive surveys. This paper examines the modified regression estimators that incorporate information from previous time periods into estimates for the current time period. The range of modified regression estimators are extended to the situation of business surveys with survey frames that change over time, due to the addition of "births� and the deletion of "deaths�. Since the modified regression estimators can deviate from the generalized regression estimator over time, it is proposed to use a compromise modified regression estimator, a weighted average of the modified regression estimator and the generalised regression estimator. A Monte Carlo simulation study shows that the proposed compromise modified regression estimator leads to significant efficiency gains in both the point-in-time and movement estimates.
Exploring recursion for optimal estimators under cascade rotation
Jan Kowalski and Jacek Wesołowski
Abstract
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial defined in terms of the rotation pattern ( happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix defined in terms of the rotation pattern and the roots of the polynomial . In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Optimal adjustments for inconsistency in imputed data
Jeroen Pannekoek and Li-Chun Zhang
Abstract
Imputed micro data often contain conflicting information. The situation may e.g., arise from partial imputation, where one part of the imputed record consists of the observed values of the original record and the other the imputed values. Edit-rules that involve variables from both parts of the record will often be violated. Or, inconsistency may be caused by adjustment for errors in the observed data, also referred to as imputation in Editing. Under the assumption that the remaining inconsistency is not due to systematic errors, we propose to make adjustments to the micro data such that all constraints are simultaneously satisfied and the adjustments are minimal according to a chosen distance metric. Different approaches to the distance metric are considered, as well as several extensions of the basic situation, including the treatment of categorical data, unit imputation and macro-level benchmarking. The properties and interpretations of the proposed methods are illustrated using business-economic data.
Dealing with non-ignorable nonresponse in survey sampling: A latent modeling approach
Alina Matei and M. Giovanna Ranalli
Abstract
Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse. By noting that for a particular survey variable, we just have observed and unobserved values, in this work we exploit the connection between unit and item nonresponse. In particular, we assume that the factors that drive unit response are the same as those that drive item response on selected variables of interest. Response probabilities are then estimated using a latent covariate that measures the will to respond to the survey and that can explain a part of the unknown behavior of a unit to participate in the survey. This latent covariate is estimated using latent trait models. This approach is particularly relevant for sensitive items and, therefore, can handle non-ignorable nonresponse. Auxiliary information known for both respondents and nonrespondents can be included either in the latent variable model or in the response probability estimation process. The approach can also be used when auxiliary information is not available, and we focus here on this case. We propose an estimator using a reweighting system based on the previous latent covariate when no other observed auxiliary information is available. Results on its performance are encouraging from simulation studies on both real and simulated data.
One step or two? Calibration weighting from a complete list frame with nonresponse
Phillip S. Kott and Dan Liao
Abstract
When a random sample drawn from a complete list frame suffers from unit nonresponse, calibration weighting to population totals can be used to remove nonresponse bias under either an assumed response (selection) or an assumed prediction (outcome) model. Calibration weighting in this way can not only provide double protection against nonresponse bias, it can also decrease variance. By employing a simple trick one can estimate the variance under the assumed prediction model and the mean squared error under the combination of an assumed response model and the probability-sampling mechanism simultaneously. Unfortunately, there is a practical limitation on what response model can be assumed when design weights are calibrated to population totals in a single step. In particular, the choice for the response function cannot always be logistic. That limitation does not hinder calibration weighting when performed in two steps: from the respondent sample to the full sample to remove the response bias and then from the full sample to the population to decrease variance. There are potential efficiency advantages from using the two-step approach as well even when the calibration variables employed in each step is a subset of the calibration variables in the single step. Simultaneous mean-squared-error estimation using linearization is possible, but more complicated than when calibrating in a single step.
The relevance of follow ups in data collection for the Quality Assurance system of the Portuguese Population and Housing Census
Paula Vicente, Elizabeth Reis and �lvaro Rosa
Abstract
The operationalization of the Population and Housing Census in Portugal is managed by a hierarchical structure in which Statistics Portugal is at the top and local government institutions at the bottom. When the Census takes place every ten years, local governments are asked to collaborate with Statistics Portugal in the execution and monitoring of the fieldwork operations at the local level. During the Pilot Test stage of the 2011 Census, local governments were asked for additional collaboration: to answer the Perception of Risk survey, whose aim was to gather information to design a quality assurance instrument that could be used to monitor the Census operations. The response rate of the survey was desired to be 100%, however, by the deadline of data collection nearly a quarter of local governments had not responded to the survey and thus a decision was made to make a follow up mailing. In this paper, we examine whether the same conclusions could have been reached from survey without follow ups as with them and evaluate the influence of follow ups on the conception of the quality assurance instrument. Comparison of responses on a set of perception variables revealed that local governments answering previous or after the follow up did not differ. However the configuration of the quality assurance instrument changed when including follow up responses.
Measuring temporary employment. Do survey or register data tell the truth?
Dimitris Pavlopoulos and Jeroen K. Vermunt
Abstract
One of the main variables in the Dutch Labour Force Survey is the variable measuring whether a respondent has a permanent or a temporary job. The aim of our study is to determine the measurement error in this variable by matching the information obtained by the longitudinal part of this survey with unique register data from the Dutch Institute for Employee Insurance. Contrary to previous approaches confronting such datasets, we take into account that also register data are not error-free and that measurement error in these data is likely to be correlated over time. More specifically, we propose the estimation of the measurement error in these two sources using an extended hidden Markov model with two observed indicators for the type of contract. Our results indicate that none of the two sources should be considered as error-free. For both indicators, we find that workers in temporary contracts are often misclassified as having a permanent contract. Particularly for the register data, we find that measurement errors are strongly autocorrelated, as, if made, they tend to repeat themselves. In contrast, when the register is correct, the probability of an error at the next time period is almost zero. Finally, we find that temporary contracts are more widespread than the Labour Force Survey suggests, while transition rates between temporary to permanent contracts are much less common than both datasets suggest.
Generalized framework for defining the optimal inclusion probabilities of one-stage sampling designs for multivariate and multi-domain surveys
Piero Demetrio Falorsi and Paolo Righi
Abstract
This paper introduces a general framework for deriving the optimal inclusion probabilities for a variety of survey contexts in which disseminating survey estimates of pre-established accuracy for a multiplicity of both variables and domains of interest is required. The framework can define either standard stratified or incomplete stratified sampling designs. The optimal inclusion probabilities are obtained by minimizing costs through an algorithm that guarantees the bounding of sampling errors at the domains level, assuming that the domain membership variables are available in the sampling frame. The target variables are unknown, but can be predicted with suitable super-population models. The algorithm takes properly into account this model uncertainty. Some experiments based on real data show the empirical properties of the algorithm.
An efficient estimation method for matrix survey sampling
Takis Merkouris
Abstract
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
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