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- Articles and reports: 12-001-X202300200005Description: Population undercoverage is one of the main hurdles faced by statistical analysis with non-probability survey samples. We discuss two typical scenarios of undercoverage, namely, stochastic undercoverage and deterministic undercoverage. We argue that existing estimation methods under the positivity assumption on the propensity scores (i.e., the participation probabilities) can be directly applied to handle the scenario of stochastic undercoverage. We explore strategies for mitigating biases in estimating the mean of the target population under deterministic undercoverage. In particular, we examine a split population approach based on a convex hull formulation, and construct estimators with reduced biases. A doubly robust estimator can be constructed if a followup subsample of the reference probability survey with measurements on the study variable becomes feasible. Performances of six competing estimators are investigated through a simulation study and issues which require further investigation are briefly discussed.Release date: 2024-01-03
- Articles and reports: 12-001-X202300200016Description: In this discussion, I will present some additional aspects of three major areas of survey theory developed or studied by Jean-Claude Deville: calibration, balanced sampling and the generalized weight-share method.Release date: 2024-01-03
- Articles and reports: 12-001-X202300200017Description: Jean-Claude Deville, who passed away in October 2021, was one of the most influential researchers in the field of survey statistics over the past 40 years. This article traces some of his contributions that have had a profound impact on both survey theory and practice. This article will cover the topics of balanced sampling using the cube method, calibration, the weight-sharing method, the development of variance expressions of complex estimators using influence function and quota sampling.Release date: 2024-01-03
- Articles and reports: 12-001-X202200200002Description:
We provide a critical review and some extended discussions on theoretical and practical issues with analysis of non-probability survey samples. We attempt to present rigorous inferential frameworks and valid statistical procedures under commonly used assumptions, and address issues on the justification and verification of assumptions in practical applications. Some current methodological developments are showcased, and problems which require further investigation are mentioned. While the focus of the paper is on non-probability samples, the essential role of probability survey samples with rich and relevant information on auxiliary variables is highlighted.
Release date: 2022-12-15 - Articles and reports: 12-001-X202200200011Description:
Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.
Release date: 2022-12-15 - Articles and reports: 89-648-X2022001Description:
This report explores the size and nature of the attrition challenges faced by the Longitudinal and International Study of Adults (LISA) survey, as well as the use of a non-response weight adjustment and calibration strategy to mitigate the effects of attrition on the LISA estimates. The study focuses on data from waves 1 (2012) to 4 (2018) and uses practical examples based on selected demographic variables, to illustrate how attrition be assessed and treated.
Release date: 2022-11-14 - Articles and reports: 12-001-X202100200005Description:
Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.
Release date: 2022-01-06 - Articles and reports: 11-522-X202100100014Description: Recent developments in questionnaire administration modes and data extraction have favored the use of nonprobability samples, which are often affected by selection bias that arises from the lack of a sample design or self-selection of the participants. This bias can be addressed by several adjustments, whose applicability depends on the type of auxiliary information available. Calibration weighting can be used when only population totals of auxiliary variables are available. If a reference survey that followed a probability sampling design is available, several methods can be applied, such as Propensity Score Adjustment, Statistical Matching or Mass Imputation, and doubly robust estimators. In the case where a complete census of the target population is available for some auxiliary covariates, estimators based in superpopulation models (often used in probability sampling) can be adapted to the nonprobability sampling case. We studied the combination of some of these methods in order to produce less biased and more efficient estimates, as well as the use of modern prediction techniques (such as Machine Learning classification and regression algorithms) in the modelling steps of the adjustments described. We also studied the use of variable selection techniques prior to the modelling step in Propensity Score Adjustment. Results show that adjustments based on the combination of several methods might improve the efficiency of the estimates, and the use of Machine Learning and variable selection techniques can contribute to reduce the bias and the variance of the estimators to a greater extent in several situations.
Key Words: nonprobability sampling; calibration; Propensity Score Adjustment; Matching.
Release date: 2021-10-15 - Articles and reports: 12-001-X201800254960Description:
Based on auxiliary information, calibration is often used to improve the precision of estimates. However, calibration weighting may not be appropriate for all variables of interest of the survey, particularly those not related to the auxiliary variables used in calibration. In this paper, we propose a criterion to assess, for any variable of interest, the impact of calibration weighting on the precision of the estimated total. This criterion can be used to decide on the weights associated with each survey variable of interest and determine the variables for which calibration weighting is appropriate.
Release date: 2018-12-20 - Articles and reports: 12-001-X201800154963Description:
The probability-sampling-based framework has dominated survey research because it provides precise mathematical tools to assess sampling variability. However increasing costs and declining response rates are expanding the use of non-probability samples, particularly in general population settings, where samples of individuals pulled from web surveys are becoming increasingly cheap and easy to access. But non-probability samples are at risk for selection bias due to differential access, degrees of interest, and other factors. Calibration to known statistical totals in the population provide a means of potentially diminishing the effect of selection bias in non-probability samples. Here we show that model calibration using adaptive LASSO can yield a consistent estimator of a population total as long as a subset of the true predictors is included in the prediction model, thus allowing large numbers of possible covariates to be included without risk of overfitting. We show that the model calibration using adaptive LASSO provides improved estimation with respect to mean square error relative to standard competitors such as generalized regression (GREG) estimators when a large number of covariates are required to determine the true model, with effectively no loss in efficiency over GREG when smaller models will suffice. We also derive closed form variance estimators of population totals, and compare their behavior with bootstrap estimators. We conclude with a real world example using data from the National Health Interview Survey.
Release date: 2018-06-21
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Analysis (63)
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- Articles and reports: 12-001-X202300200005Description: Population undercoverage is one of the main hurdles faced by statistical analysis with non-probability survey samples. We discuss two typical scenarios of undercoverage, namely, stochastic undercoverage and deterministic undercoverage. We argue that existing estimation methods under the positivity assumption on the propensity scores (i.e., the participation probabilities) can be directly applied to handle the scenario of stochastic undercoverage. We explore strategies for mitigating biases in estimating the mean of the target population under deterministic undercoverage. In particular, we examine a split population approach based on a convex hull formulation, and construct estimators with reduced biases. A doubly robust estimator can be constructed if a followup subsample of the reference probability survey with measurements on the study variable becomes feasible. Performances of six competing estimators are investigated through a simulation study and issues which require further investigation are briefly discussed.Release date: 2024-01-03
- Articles and reports: 12-001-X202300200016Description: In this discussion, I will present some additional aspects of three major areas of survey theory developed or studied by Jean-Claude Deville: calibration, balanced sampling and the generalized weight-share method.Release date: 2024-01-03
- Articles and reports: 12-001-X202300200017Description: Jean-Claude Deville, who passed away in October 2021, was one of the most influential researchers in the field of survey statistics over the past 40 years. This article traces some of his contributions that have had a profound impact on both survey theory and practice. This article will cover the topics of balanced sampling using the cube method, calibration, the weight-sharing method, the development of variance expressions of complex estimators using influence function and quota sampling.Release date: 2024-01-03
- Articles and reports: 12-001-X202200200002Description:
We provide a critical review and some extended discussions on theoretical and practical issues with analysis of non-probability survey samples. We attempt to present rigorous inferential frameworks and valid statistical procedures under commonly used assumptions, and address issues on the justification and verification of assumptions in practical applications. Some current methodological developments are showcased, and problems which require further investigation are mentioned. While the focus of the paper is on non-probability samples, the essential role of probability survey samples with rich and relevant information on auxiliary variables is highlighted.
Release date: 2022-12-15 - Articles and reports: 12-001-X202200200011Description:
Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.
Release date: 2022-12-15 - Articles and reports: 89-648-X2022001Description:
This report explores the size and nature of the attrition challenges faced by the Longitudinal and International Study of Adults (LISA) survey, as well as the use of a non-response weight adjustment and calibration strategy to mitigate the effects of attrition on the LISA estimates. The study focuses on data from waves 1 (2012) to 4 (2018) and uses practical examples based on selected demographic variables, to illustrate how attrition be assessed and treated.
Release date: 2022-11-14 - Articles and reports: 12-001-X202100200005Description:
Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.
Release date: 2022-01-06 - Articles and reports: 11-522-X202100100014Description: Recent developments in questionnaire administration modes and data extraction have favored the use of nonprobability samples, which are often affected by selection bias that arises from the lack of a sample design or self-selection of the participants. This bias can be addressed by several adjustments, whose applicability depends on the type of auxiliary information available. Calibration weighting can be used when only population totals of auxiliary variables are available. If a reference survey that followed a probability sampling design is available, several methods can be applied, such as Propensity Score Adjustment, Statistical Matching or Mass Imputation, and doubly robust estimators. In the case where a complete census of the target population is available for some auxiliary covariates, estimators based in superpopulation models (often used in probability sampling) can be adapted to the nonprobability sampling case. We studied the combination of some of these methods in order to produce less biased and more efficient estimates, as well as the use of modern prediction techniques (such as Machine Learning classification and regression algorithms) in the modelling steps of the adjustments described. We also studied the use of variable selection techniques prior to the modelling step in Propensity Score Adjustment. Results show that adjustments based on the combination of several methods might improve the efficiency of the estimates, and the use of Machine Learning and variable selection techniques can contribute to reduce the bias and the variance of the estimators to a greater extent in several situations.
Key Words: nonprobability sampling; calibration; Propensity Score Adjustment; Matching.
Release date: 2021-10-15 - Articles and reports: 12-001-X201800254960Description:
Based on auxiliary information, calibration is often used to improve the precision of estimates. However, calibration weighting may not be appropriate for all variables of interest of the survey, particularly those not related to the auxiliary variables used in calibration. In this paper, we propose a criterion to assess, for any variable of interest, the impact of calibration weighting on the precision of the estimated total. This criterion can be used to decide on the weights associated with each survey variable of interest and determine the variables for which calibration weighting is appropriate.
Release date: 2018-12-20 - Articles and reports: 12-001-X201800154963Description:
The probability-sampling-based framework has dominated survey research because it provides precise mathematical tools to assess sampling variability. However increasing costs and declining response rates are expanding the use of non-probability samples, particularly in general population settings, where samples of individuals pulled from web surveys are becoming increasingly cheap and easy to access. But non-probability samples are at risk for selection bias due to differential access, degrees of interest, and other factors. Calibration to known statistical totals in the population provide a means of potentially diminishing the effect of selection bias in non-probability samples. Here we show that model calibration using adaptive LASSO can yield a consistent estimator of a population total as long as a subset of the true predictors is included in the prediction model, thus allowing large numbers of possible covariates to be included without risk of overfitting. We show that the model calibration using adaptive LASSO provides improved estimation with respect to mean square error relative to standard competitors such as generalized regression (GREG) estimators when a large number of covariates are required to determine the true model, with effectively no loss in efficiency over GREG when smaller models will suffice. We also derive closed form variance estimators of population totals, and compare their behavior with bootstrap estimators. We conclude with a real world example using data from the National Health Interview Survey.
Release date: 2018-06-21
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Reference (2)
Reference (2) ((2 results))
- Surveys and statistical programs – Documentation: 75F0002M2005009Description:
The release of the 2003 data from the Survey of Labour and Income Dynamics (SLID) was accompanied by a historical revision which accomplished three things. First, the survey weights were updated to take into account new population projections based on the 2001 Census of Population, instead of the 1996 Census. Second, a new procedure in the weight adjustments was introduced to take into account an external source of information on the overall distribution of income in the population, namely the T4 file of employer remittances to Canada Revenue Agency. Third, the low income estimates were revised due to new low income cut-offs (LICOs). This paper describes the second of these improvements' the new weighting procedure to reflect the distribution of income in the population with greater accuracy. Part 1 explains in non-technical terms how this new procedure came about and how it works. Part 2 provides some examples of the impacts on the results for previous years.
Release date: 2005-07-22 - 2. Simultaneous calibration of several surveys ArchivedSurveys and statistical programs – Documentation: 11-522-X19990015684Description:
Often, the same information is gathered almost simultaneously for several different surveys. In France, this practice is institutionalized for household surveys that have a common set of demographic variables, i.e., employment, residence and income. These variables are important co-factors for the variables of interest in each survey, and if used carefully, can reinforce the estimates derived from each survey. Techniques for calibrating uncertain data can apply naturally in this context. This involves finding the best unbiased estimator in common variables and calibrating each survey based on that estimator. The estimator thus obtained in each survey is always a linear estimator, the weightings of which can be easily explained and the variance can be obtained with no new problems, as can the variance estimate. To supplement the list of regression estimators, this technique can also be seen as a ridge-regression estimator, or as a Bayesian-regression estimator.
Release date: 2000-03-02
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