Weighting and estimation

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All (638) (30 to 40 of 638 results)

31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. 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
38. 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
39. 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
40. Comments by Julie Gershunskaya and Vladislav Beresovsky on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
Articles and reports: 12-001-X202400100003
Description: Beaumont, Bosa, Brennan, Charlebois and Chu (2024) propose innovative model selection approaches for estimation of participation probabilities for non-probability sample units. We focus our discussion on the choice of a likelihood and parameterization of the model, which are key for the effectiveness of the techniques developed in the paper. We consider alternative likelihood and pseudo-likelihood based methods for estimation of participation probabilities and present simulations implementing and comparing the AIC based variable selection. We demonstrate that, under important practical scenarios, the approach based on a likelihood formulated over the observed pooled non-probability and probability samples performed better than the pseudo-likelihood based alternatives. The contrast in sensitivity of the AIC criteria is especially large for small probability sample sizes and low overlap in covariates domains.
Release date: 2024-06-25

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Analysis (610)

Analysis (610) (60 to 70 of 610 results)

61. The missing information principle ‒ A paradigm for analysis of messy sample survey data
Articles and reports: 12-001-X202300200018
Description: Sample surveys, as a tool for policy development and evaluation and for scientific, social and economic research, have been employed for over a century. In that time, they have primarily served as tools for collecting data for enumerative purposes. Estimation of these characteristics has been typically based on weighting and repeated sampling, or design-based, inference. However, sample data have also been used for modelling the unobservable processes that gave rise to the finite population data. This type of use has been termed analytic, and often involves integrating the sample data with data from secondary sources.
Alternative approaches to inference in these situations, drawing inspiration from mainstream statistical modelling, have been strongly promoted. The principal focus of these alternatives has been on allowing for informative sampling. Modern survey sampling, though, is more focussed on situations where the sample data are in fact part of a more complex set of data sources all carrying relevant information about the process of interest. When an efficient modelling method such as maximum likelihood is preferred, the issue becomes one of how it should be modified to account for both complex sampling designs and multiple data sources. Here application of the Missing Information Principle provides a clear way forward.
In this paper I review how this principle has been applied to resolve so-called “messy” data analysis issues in sampling. I also discuss a scenario that is a consequence of the rapid growth in auxiliary data sources for survey data analysis. This is where sampled records from one accessible source or register are linked to records from another less accessible source, with values of the response variable of interest drawn from this second source, and where a key output is small area estimates for the response variable for domains defined on the first source.
Release date: 2024-01-03
62. Mapping Production Activity in Yukon: Experimental Indexes of Grid Square-based Gross Domestic Product
Articles and reports: 11-633-X2023003
Description: This paper spans the academic work and estimation strategies used in national statistics offices. It addresses the issue of producing fine, grid-level geography estimates for Canada by exploring the measurement of subprovincial and subterritorial gross domestic product using Yukon as a test case.
Release date: 2023-12-15
63. Combining data from surveys and related sources
Articles and reports: 12-001-X202300100003
Description: To improve the precision of inferences and reduce costs there is considerable interest in combining data from several sources such as sample surveys and administrative data. Appropriate methodology is required to ensure satisfactory inferences since the target populations and methods for acquiring data may be quite different. To provide improved inferences we use methodology that has a more general structure than the ones in current practice. We start with the case where the analyst has only summary statistics from each of the sources. In our primary method, uncertain pooling, it is assumed that the analyst can regard one source, survey r, as the single best choice for inference. This method starts with the data from survey r and adds data from those other sources that are shown to form clusters that include survey r. We also consider Dirichlet process mixtures, one of the most popular nonparametric Bayesian methods. We use analytical expressions and the results from numerical studies to show properties of the methodology.
Release date: 2023-06-30
64. Official Statistics based on the Dutch Health Survey during the Covid-19 Pandemic
Articles and reports: 12-001-X202300100004
Description: The Dutch Health Survey (DHS), conducted by Statistics Netherlands, is designed to produce reliable direct estimates at an annual frequency. Data collection is based on a combination of web interviewing and face-to-face interviewing. Due to lockdown measures during the Covid-19 pandemic there was no or less face-to-face interviewing possible, which resulted in a sudden change in measurement and selection effects in the survey outcomes. Furthermore, the production of annual data about the effect of Covid-19 on health-related themes with a delay of about one year compromises the relevance of the survey. The sample size of the DHS does not allow the production of figures for shorter reference periods. Both issues are solved by developing a bivariate structural time series model (STM) to estimate quarterly figures for eight key health indicators. This model combines two series of direct estimates, a series based on complete response and a series based on web response only and provides model-based predictions for the indicators that are corrected for the loss of face-to-face interviews during the lockdown periods. The model is also used as a form of small area estimation and borrows sample information observed in previous reference periods. In this way timely and relevant statistics describing the effects of the corona crisis on the development of Dutch health are published. In this paper the method based on the bivariate STM is compared with two alternative methods. The first one uses a univariate STM where no correction for the lack of face-to-face observation is applied to the estimates. The second one uses a univariate STM that also contains an intervention variable that models the effect of the loss of face-to-face response during the lockdown.
Release date: 2023-06-30
65. Comments by Jae Kwang Kim and HaiYing Wang on “Statistical disclosure control and developments in formal privacy: In memoriam to Chris Skinner”: A note on weight smoothing in survey sampling
Articles and reports: 12-001-X202300100005
Description: Weight smoothing is a useful technique in improving the efficiency of design-based estimators at the risk of bias due to model misspecification. As an extension of the work of Kim and Skinner (2013), we propose using weight smoothing to construct the conditional likelihood for efficient analytic inference under informative sampling. The Beta prime distribution can be used to build a parameter model for weights in the sample. A score test is developed to test for model misspecification in the weight model. A pretest estimator using the score test can be developed naturally. The pretest estimator is nearly unbiased and can be more efficient than the design-based estimator when the weight model is correctly specified, or the original weights are highly variable. A limited simulation study is presented to investigate the performance of the proposed methods.
Release date: 2023-06-30
66. An extension of the weight share method when using a continuous sampling frame
Articles and reports: 12-001-X202300100011
Description: The definition of statistical units is a recurring issue in the domain of sample surveys. Indeed, not all the populations surveyed have a readily available sampling frame. For some populations, the sampled units are distinct from the observation units and producing estimates on the population of interest raises complex questions, which can be addressed by using the weight share method (Deville and Lavallée, 2006). However, the two populations considered in this approach are discrete. In some fields of study, the sampled population is continuous: this is for example the case of forest inventories for which, frequently, the trees surveyed are those located on plots of which the centers are points randomly drawn in a given area. The production of statistical estimates from the sample of trees surveyed poses methodological difficulties, as do the associated variance calculations. The purpose of this paper is to generalize the weight share method to the continuous (sampled population) ? discrete (surveyed population) case, from the extension proposed by Cordy (1993) of the Horvitz-Thompson estimator for drawing points carried out in a continuous universe.
Release date: 2023-06-30
67. Multilevel time series modelling of antenatal care coverage in Bangladesh at disaggregated administrative levels
Articles and reports: 12-001-X202200200010
Description:
Multilevel time series (MTS) models are applied to estimate trends in time series of antenatal care coverage at several administrative levels in Bangladesh, based on repeated editions of the Bangladesh Demographic and Health Survey (BDHS) within the period 1994-2014. MTS models are expressed in an hierarchical Bayesian framework and fitted using Markov Chain Monte Carlo simulations. The models account for varying time lags of three or four years between the editions of the BDHS and provide predictions for the intervening years as well. It is proposed to apply cross-sectional Fay-Herriot models to the survey years separately at district level, which is the most detailed regional level. Time series of these small domain predictions at the district level and their variance-covariance matrices are used as input series for the MTS models. Spatial correlations among districts, random intercept and slope at the district level, and different trend models at district level and higher regional levels are examined in the MTS models to borrow strength over time and space. Trend estimates at district level are obtained directly from the model outputs, while trend estimates at higher regional and national levels are obtained by aggregation of the district level predictions, resulting in a numerically consistent set of trend estimates.

Release date: 2022-12-15
68. Optimal linear estimation in two-phase sampling
Articles and reports: 12-001-X202200200011
Description:
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
69. Bayesian spatial models for estimating means of sampled and non-sampled small areas
Articles and reports: 12-001-X202200200012
Description:
In many applications, the population means of geographically adjacent small areas exhibit a spatial variation. If available auxiliary variables do not adequately account for the spatial pattern, the residual variation will be included in the random effects. As a result, the independent and identical distribution assumption on random effects of the Fay-Herriot model will fail. Furthermore, limited resources often prevent numerous sub-populations from being included in the sample, resulting in non-sampled small areas. The problem can be exacerbated for predicting means of non-sampled small areas using the above Fay-Herriot model as the predictions will be made based solely on the auxiliary variables. To address such inadequacy, we consider Bayesian spatial random-effect models that can accommodate multiple non-sampled areas. Under mild conditions, we establish the propriety of the posterior distributions for various spatial models for a useful class of improper prior densities on model parameters. The effectiveness of these spatial models is assessed based on simulated and real data. Specifically, we examine predictions of statewide four-person family median incomes based on the 1990 Current Population Survey and the 1980 Census for the United States of America.

Release date: 2022-12-15
70. Market Basket Measure Technical Paper: The other necessities component
Articles and reports: 75F0002M2022006
Description:
This technical paper describes how the cost for "other necessities" is estimated in the 2018-base MBM. It provides a brief overview of the theory and application of techniques for estimating costs of "other necessities" in poverty lines and deconstructs the 2018-base MBM other necessities component to provide insights on how it is constructed. The aim of this paper is to provide a more detailed understanding of how the other necessities component of the MBM is estimated.

Release date: 2022-12-08

Reference (28)

Reference (28) (0 to 10 of 28 results)

1. A Framework for Projecting Housing Use Associated with Immigrants and Non-Permanent Residents
Surveys and statistical programs – Documentation: 11-633-X2026002
Description: Recent changes in Canada’s immigration levels have heightened interest in understanding how immigration affects housing demand. This article develops a methodological framework for projecting housing use associated with permanent residents (PRs) and non-permanent residents (NPRs) under alternative immigration scenarios. The framework applies observed per capita housing use rates from the Census of Population to estimate incremental housing use by tenure over time.
Release date: 2026-04-24
2. Technical Guide on Demographic Estimates at Statistics Canada
Surveys and statistical programs – Documentation: 91-528-X
Description: The Technical Guide on Demographic Estimates at Statistics Canada provides detailed descriptions of the most current data sources and methods used by the Centre for demography at Statistics Canada to produce demographic estimates as part of the Demographic estimates program. They comprise postcensal and intercensal population estimates; base population; births and deaths; immigrants; emigrants; returning emigrants; non-permanent residents; interprovincial migration; subprovincial estimates of population and intraprovincial migration; population estimates by age and gender; and census family estimates. A glossary of commonly used terms is available at the end of the guide.
Release date: 2025-12-17
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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

Date modified:: 2026-09-12