Weighting and estimation

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  • 1. Bayesian predictive inference of a finite population mean without specifying the relation between the study variable and the covariates
    Articles and reports: 12-001-X202400200004
    Description: While we avoid specifying the parametric relationship between the study variable and covariates, we illustrate the advantage of including a spatial component to better account for the covariates in our models to make Bayesian predictive inference. We treat each unique covariate combination as an individual stratum, then we use small area estimation techniques to make inference about the finite population mean of the continuous response variable. The two spatial models used are the conditional autoregressive and simple conditional autoregressive models. We include the spatial effects by creating the adjacency matrix via the Mahalanobis distance between covariates. We also show how to incorporate survey weights into the spatial models when dealing with probability survey data. We compare the results of two non-spatial models including the Scott-Smith model and the Battese, Harter, and Fuller model to the spatial models. We illustrate the comparison between the aforementioned models with an application using BMI data from eight counties in California. Our goal is to have neighboring strata yield similar predictions, and to increase the difference between strata that are not neighbors. Ultimately, using the spatial models shows less global pooling compared to the non-spatial models, which was the desired outcome.
    Release date: 2024-12-20
  • 2. Robust adaptive survey design for time changes in mixed-mode response propensities
    Articles and reports: 12-001-X202400200005
    Description: Adaptive survey designs (ASDs) tailor recruitment protocols to population subgroups that are relevant to a survey. In recent years, effective ASD optimization has been the topic of research and several applications. However, the performance of an optimized ASD over time is sensitive to time changes in response propensities. How adaptation strategies can adjust to such variation over time is not yet fully understood. In this paper, we propose a robust optimization approach in the context of sequential mixed-mode surveys employing Bayesian analysis. The approach is formulated as a mathematical programming problem that explicitly accounts for uncertainty due to time change. ASD decisions can then be made by considering time-dependent variation in conditional mode response propensities and between-mode correlations in response propensities. The approach is demonstrated using a case study: the 2014-2017 Dutch Health Survey. We evaluate the sensitivity of ASD performance to 1) the budget level and 2) the length of applicable historic time-series data. We find there is only a moderate dependence on the budget level and the dependence on historic data is moderated by the amount of seasonality during the year.
    Release date: 2024-12-20
  • 3. A small area estimation approach for reconciling differences in two surveys of recreational fishing effort
    Articles and reports: 12-001-X202400200009
    Description: Many studies face the problem of comparing estimates obtained with different survey methodology, including differences in frames, measurement instruments, and modes of delivery. The problem arises in multimode surveys and in surveys that are redesigned. Major redesign of survey processes could affect survey estimates systematically, and it is important to quantify and adjust for such discontinuities between the designs to ensure comparability of estimates over time. We propose a small area estimation approach to reconcile two sets of survey estimates, and apply it to two surveys in the Marine Recreational Information Program (MRIP), which monitors recreational fishing along the Atlantic and Gulf coasts of the United States. We develop a log-normal model for the estimates from the two surveys, accounting for temporal dynamics through regression on population size and state-by-wave seasonal factors, and accounting in part for changing coverage properties through regression on wireless telephone penetration. Using the estimated design variances, we develop a regression model that is analytically consistent with the log-normal mean model. We use the modeled design variances in a Fay-Herriot small area estimation procedure to obtain empirical best linear unbiased predictors of the reconciled estimates of fishing effort (requiring predictions at new sets of covariates), and provide an asymptotically valid mean square error approximation.
    Release date: 2024-12-20
  • 4. A hierarchical gamma prior for modeling random effects in small area estimation
    Articles and reports: 12-001-X202400200011
    Description: Small area estimation (SAE) is becoming increasingly popular among survey statisticians. Since the direct estimates of small areas usually have large standard errors, model-based approaches are often adopted to borrow strength across areas. SAE models often use covariates to link different areas and random effects to account for the additional variation. Recent studies showed that random effects are not necessary for all areas, so global-local (GL) shrinkage priors have been introduced to effectively model the sparsity in random effects. The GL priors vary in tail behavior, and their performance differs under different sparsity levels of random effects. As a result, one needs to fit the model with different choices of priors and then select the most appropriate one based on the deviance information criterion or other evaluation metrics. In this paper, we propose a flexible prior for modeling random effects in SAE. The hyperparameters of the prior determine the tail behavior and can be estimated in a fully Bayesian framework. Therefore, the resulting model is adaptive to the sparsity level of random effects without repetitive fitting. We demonstrate the performance of the proposed prior via simulations and real applications.
    Release date: 2024-12-20
  • 5. Relaxed calibration of survey weights
    Articles and reports: 12-001-X202400200012
    Description: Population surveys are nowadays rarely analysed in isolation from any auxiliary information, often in the form of population counts, totals and other summaries. Calibration, or benchmarking, by which the weighted sample totals of auxiliary variables are matched to their (known) population totals, is widely applied. Methods for adjusting the weights to satisfy these constraints involve iterative procedures with unknown finite-sample properties. We develop an alternative method in which the weights are calibrated by minimising a quadratic function, requiring no iterations and yielding a unique solution. The relative priority of each constraint is represented by a tuning parameter. The properties of the weights and of the calibration estimator, as functions of these parameters, are explored analytically and by simulations. A connection of the proposed method with ridge calibration is established.
    Release date: 2024-12-20
  • 6. Inference from sampling with response probabilities estimated via calibration
    Articles and reports: 12-001-X202400200013
    Description: A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we highlight problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We present the results of a simulation study in order to illustrate these elements.
    Release date: 2024-12-20
  • 7. Design consistent random forest models for data collected from a complex sample
    Articles and reports: 12-001-X202400200015
    Description: Random forest models, which are the result of averaging the estimated values from a large number of tree models, represent a useful and flexible tool for modeling the data nonparametrically to provide accurately predicted values. There are many potential applications for these types of models when dealing with survey data. However, survey data is usually collected using an informative sample design, so it is necessary to have an algorithm for creating random forest models that account for this design during model estimation. The tree models used in the forest are typically obtained by estimating tree models on bootstrapped samples of the original data. Since the models depend on the observed data and the values observed in the sample depend on the informative sample design, the usual method for estimation is likely to lead to a biased random forest model when applied to survey data. In this article, we provide an algorithm and a set of conditions that produce consistent random forest models under an informative sample design and compare this method to the usual random forest modeling method. We show that ignoring the design can lead to biased model estimates.
    Release date: 2024-12-20
  • 8. Small Area Estimation Methodology Using Labour Force Survey Data
    Articles and reports: 75-005-M2024003
    Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.
    Release date: 2024-09-17
  • 9. Authors’ response to comments on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”: Some new developments on likelihood approaches to estimation of participation probabilities for non-probability samples
    Articles and reports: 12-001-X202400100001
    Description: Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.
    Release date: 2024-06-25
  • 10. Comments by Changbao Wu on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
    Articles and reports: 12-001-X202400100002
    Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.
    Release date: 2024-06-25
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Analysis (569)

Analysis (569) (0 to 10 of 569 results)

  • 1. Bayesian predictive inference of a finite population mean without specifying the relation between the study variable and the covariates
    Articles and reports: 12-001-X202400200004
    Description: While we avoid specifying the parametric relationship between the study variable and covariates, we illustrate the advantage of including a spatial component to better account for the covariates in our models to make Bayesian predictive inference. We treat each unique covariate combination as an individual stratum, then we use small area estimation techniques to make inference about the finite population mean of the continuous response variable. The two spatial models used are the conditional autoregressive and simple conditional autoregressive models. We include the spatial effects by creating the adjacency matrix via the Mahalanobis distance between covariates. We also show how to incorporate survey weights into the spatial models when dealing with probability survey data. We compare the results of two non-spatial models including the Scott-Smith model and the Battese, Harter, and Fuller model to the spatial models. We illustrate the comparison between the aforementioned models with an application using BMI data from eight counties in California. Our goal is to have neighboring strata yield similar predictions, and to increase the difference between strata that are not neighbors. Ultimately, using the spatial models shows less global pooling compared to the non-spatial models, which was the desired outcome.
    Release date: 2024-12-20
  • 2. Robust adaptive survey design for time changes in mixed-mode response propensities
    Articles and reports: 12-001-X202400200005
    Description: Adaptive survey designs (ASDs) tailor recruitment protocols to population subgroups that are relevant to a survey. In recent years, effective ASD optimization has been the topic of research and several applications. However, the performance of an optimized ASD over time is sensitive to time changes in response propensities. How adaptation strategies can adjust to such variation over time is not yet fully understood. In this paper, we propose a robust optimization approach in the context of sequential mixed-mode surveys employing Bayesian analysis. The approach is formulated as a mathematical programming problem that explicitly accounts for uncertainty due to time change. ASD decisions can then be made by considering time-dependent variation in conditional mode response propensities and between-mode correlations in response propensities. The approach is demonstrated using a case study: the 2014-2017 Dutch Health Survey. We evaluate the sensitivity of ASD performance to 1) the budget level and 2) the length of applicable historic time-series data. We find there is only a moderate dependence on the budget level and the dependence on historic data is moderated by the amount of seasonality during the year.
    Release date: 2024-12-20
  • 3. A small area estimation approach for reconciling differences in two surveys of recreational fishing effort
    Articles and reports: 12-001-X202400200009
    Description: Many studies face the problem of comparing estimates obtained with different survey methodology, including differences in frames, measurement instruments, and modes of delivery. The problem arises in multimode surveys and in surveys that are redesigned. Major redesign of survey processes could affect survey estimates systematically, and it is important to quantify and adjust for such discontinuities between the designs to ensure comparability of estimates over time. We propose a small area estimation approach to reconcile two sets of survey estimates, and apply it to two surveys in the Marine Recreational Information Program (MRIP), which monitors recreational fishing along the Atlantic and Gulf coasts of the United States. We develop a log-normal model for the estimates from the two surveys, accounting for temporal dynamics through regression on population size and state-by-wave seasonal factors, and accounting in part for changing coverage properties through regression on wireless telephone penetration. Using the estimated design variances, we develop a regression model that is analytically consistent with the log-normal mean model. We use the modeled design variances in a Fay-Herriot small area estimation procedure to obtain empirical best linear unbiased predictors of the reconciled estimates of fishing effort (requiring predictions at new sets of covariates), and provide an asymptotically valid mean square error approximation.
    Release date: 2024-12-20
  • 4. A hierarchical gamma prior for modeling random effects in small area estimation
    Articles and reports: 12-001-X202400200011
    Description: Small area estimation (SAE) is becoming increasingly popular among survey statisticians. Since the direct estimates of small areas usually have large standard errors, model-based approaches are often adopted to borrow strength across areas. SAE models often use covariates to link different areas and random effects to account for the additional variation. Recent studies showed that random effects are not necessary for all areas, so global-local (GL) shrinkage priors have been introduced to effectively model the sparsity in random effects. The GL priors vary in tail behavior, and their performance differs under different sparsity levels of random effects. As a result, one needs to fit the model with different choices of priors and then select the most appropriate one based on the deviance information criterion or other evaluation metrics. In this paper, we propose a flexible prior for modeling random effects in SAE. The hyperparameters of the prior determine the tail behavior and can be estimated in a fully Bayesian framework. Therefore, the resulting model is adaptive to the sparsity level of random effects without repetitive fitting. We demonstrate the performance of the proposed prior via simulations and real applications.
    Release date: 2024-12-20
  • 5. Relaxed calibration of survey weights
    Articles and reports: 12-001-X202400200012
    Description: Population surveys are nowadays rarely analysed in isolation from any auxiliary information, often in the form of population counts, totals and other summaries. Calibration, or benchmarking, by which the weighted sample totals of auxiliary variables are matched to their (known) population totals, is widely applied. Methods for adjusting the weights to satisfy these constraints involve iterative procedures with unknown finite-sample properties. We develop an alternative method in which the weights are calibrated by minimising a quadratic function, requiring no iterations and yielding a unique solution. The relative priority of each constraint is represented by a tuning parameter. The properties of the weights and of the calibration estimator, as functions of these parameters, are explored analytically and by simulations. A connection of the proposed method with ridge calibration is established.
    Release date: 2024-12-20
  • 6. Inference from sampling with response probabilities estimated via calibration
    Articles and reports: 12-001-X202400200013
    Description: A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we highlight problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We present the results of a simulation study in order to illustrate these elements.
    Release date: 2024-12-20
  • 7. Design consistent random forest models for data collected from a complex sample
    Articles and reports: 12-001-X202400200015
    Description: Random forest models, which are the result of averaging the estimated values from a large number of tree models, represent a useful and flexible tool for modeling the data nonparametrically to provide accurately predicted values. There are many potential applications for these types of models when dealing with survey data. However, survey data is usually collected using an informative sample design, so it is necessary to have an algorithm for creating random forest models that account for this design during model estimation. The tree models used in the forest are typically obtained by estimating tree models on bootstrapped samples of the original data. Since the models depend on the observed data and the values observed in the sample depend on the informative sample design, the usual method for estimation is likely to lead to a biased random forest model when applied to survey data. In this article, we provide an algorithm and a set of conditions that produce consistent random forest models under an informative sample design and compare this method to the usual random forest modeling method. We show that ignoring the design can lead to biased model estimates.
    Release date: 2024-12-20
  • 8. Small Area Estimation Methodology Using Labour Force Survey Data
    Articles and reports: 75-005-M2024003
    Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.
    Release date: 2024-09-17
  • 9. Authors’ response to comments on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”: Some new developments on likelihood approaches to estimation of participation probabilities for non-probability samples
    Articles and reports: 12-001-X202400100001
    Description: Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.
    Release date: 2024-06-25
  • 10. Comments by Changbao Wu on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
    Articles and reports: 12-001-X202400100002
    Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.
    Release date: 2024-06-25
Reference (27)

Reference (27) (0 to 10 of 27 results)

  • 1. Sampling and Weighting Technical Report, Census of Population
    Surveys and statistical programs – Documentation: 98-306-X
    Description:

    This report describes sampling, weighting and estimation procedures used in the Census of Population. It provides operational and theoretical justifications for them, and presents the results of the evaluations of these procedures.

    Release date: 2023-10-04
  • 2. Effective Income Tax and Transfer Rates: Technical Reference Note
    Notices and consultations: 75F0002M2019006
    Description:

    In 2018, Statistics Canada released two new data tables with estimates of effective tax and transfer rates for individual tax filers and census families. These estimates are derived from the Longitudinal Administrative Databank. This publication provides a detailed description of the methods used to derive the estimates of effective tax and transfer rates.

    Release date: 2019-04-16
  • 3. Revisions to 2006 to 2011 income data Archived
    Surveys and statistical programs – Documentation: 75F0002M2015003
    Description:

    This note discusses revised income estimates from the Survey of Labour and Income Dynamics (SLID). These revisions to the SLID estimates make it possible to compare results from the Canadian Income Survey (CIS) to earlier years. The revisions address the issue of methodology differences between SLID and CIS.

    Release date: 2015-12-17
  • 4. Population and Family Estimation Methods at Statistics Canada
    Surveys and statistical programs – Documentation: 91-528-X
    Description:

    This manual provides detailed descriptions of the data sources and methods used by Statistics Canada to estimate population. They comprise Postcensal and intercensal population estimates; base population; births and deaths; immigration; emigration; non-permanent residents; interprovincial migration; subprovincial estimates of population; population estimates by age, sex and marital status; and census family estimates. A glossary of principal terms is contained at the end of the manual, followed by the standard notation used.

    Until now, literature on the methodological changes for estimates calculations has always been spread throughout various Statistics Canada publications and background papers. This manual provides users of demographic statistics with a comprehensive compilation of the current procedures used by Statistics Canada to prepare population and family estimates.

    Release date: 2015-11-17
  • 5. Methodology for measuring the underground economy by province and territory Archived
    Surveys and statistical programs – Documentation: 13-605-X201500414166
    Description:

    Estimates of the underground economy by province and territory for the period 2007 to 2012 are now available for the first time. The objective of this technical note is to explain how the methodology employed to derive upper-bound estimates of the underground economy for the provinces and territories differs from that used to derive national estimates.

    Release date: 2015-04-29
  • 6. Sampling and Weighting Technical Report, National Household Survey, 2011 Archived
    Surveys and statistical programs – Documentation: 99-002-X2011001
    Description:

    This report describes sampling and weighting procedures used in the 2011 National Household Survey. It provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.

    Release date: 2015-01-28
  • 7. Sampling and Weighting Technical Report, National Household Survey
    Surveys and statistical programs – Documentation: 99-002-X
    Description: This report describes sampling and weighting procedures used in the 2011 National Household Survey. It provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.
    Release date: 2015-01-28
  • 8. 2006 Census Technical Report: Sampling and Weighting
    Surveys and statistical programs – Documentation: 92-568-X
    Description:

    This report describes sampling and weighting procedures used in the 2006 Census. It reviews the history of these procedures in Canadian censuses, provides operational and theoretical justifications for them, and presents the results of the evaluation studies of these procedures.

    Release date: 2009-08-11
  • 9. Improvements in 2006 to the Labour Force Survey (LFS) Archived
    Surveys and statistical programs – Documentation: 71F0031X2006003
    Description:

    This paper introduces and explains modifications made to the Labour Force Survey estimates in January 2006. Some of these modifications include changes to the population estimates, improvements to the public and private sector estimates and historical updates to several small Census Agglomerations (CA).

    Release date: 2006-01-25
  • 10. The Effects of the Revised Estimation Methodology on Estimates from Household Expenditure Surveys Archived
    Surveys and statistical programs – Documentation: 62F0026M2005002
    Description:

    This document will provide an overview of the differences between the old and the new weighting methodologies and the effect of the new weighting system on estimations.

    Release date: 2005-06-30
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