Analysis

Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.

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.

Description: Non-probability samples are being increasingly explored in National Statistical Offices as an alternative to probability samples. However, it is well known that the use of a non-probability sample alone may produce estimates with significant bias due to the unknown nature of the underlying selection mechanism. Bias reduction can be achieved by integrating data from the non-probability sample with data from a probability sample provided that both samples contain auxiliary variables in common. We focus on inverse probability weighting methods, which involve modelling the probability of participation in the non-probability sample. First, we consider the logistic model along with pseudo maximum likelihood estimation. We propose a variable selection procedure based on a modified Akaike Information Criterion (AIC) that properly accounts for the data structure and the probability sampling design. We also propose a simple rank-based method of forming homogeneous post-strata. Then, we extend the Classification and Regression Trees (CART) algorithm to this data integration scenario, while again properly accounting for the probability sampling design. A bootstrap variance estimator is proposed that reflects two sources of variability: the probability sampling design and the participation model. Our methods are illustrated using Statistics Canada’s crowdsourcing and survey data.

Description: In this rejoinder, I address the comments from the discussants, Dr. Takumi Saegusa, Dr. Jae-Kwang Kim and Ms. Yonghyun Kwon. Dr. Saegusa’s comments about the differences between the conditional exchangeability (CE) assumption for causal inferences versus the CE assumption for finite population inferences using nonprobability samples, and the distinction between design-based versus model-based approaches for finite population inference using nonprobability samples, are elaborated and clarified in the context of my paper. Subsequently, I respond to Dr. Kim and Ms. Kwon’s comprehensive framework for categorizing existing approaches for estimating propensity scores (PS) into conditional and unconditional approaches. I expand their simulation studies to vary the sampling weights, allow for misspecified PS models, and include an additional estimator, i.e., scaled adjusted logistic propensity estimator (Wang, Valliant and Li (2021), denoted by sWBS). In my simulations, it is observed that the sWBS estimator consistently outperforms or is comparable to the other estimators under the misspecified PS model. The sWBS, as well as WBS or ABS described in my paper, do not assume that the overlapped units in both the nonprobability and probability reference samples are negligible, nor do they require the identification of overlap units as needed by the estimators proposed by Dr. Kim and Ms. Kwon.

Description: In some of non-probability sample literature, the conditional exchangeability assumption is considered to be necessary for valid statistical inference. This assumption is rooted in causal inference though its potential outcome framework differs greatly from that of non-probability samples. We describe similarities and differences of two frameworks and discuss issues to consider when adopting the conditional exchangeability assumption in non-probability sample setups. We also discuss the role of finite population inference in different approaches of propensity scores and outcome regression modeling to non-probability samples.

Description: Pseudo weight construction for data integration can be understood in the two-phase sampling framework. Using the two-phase sampling framework, we discuss two approaches to the estimation of propensity scores and develop a new way to construct the propensity score function for data integration using the conditional maximum likelihood method. Results from a limited simulation study are also presented.

Description: Nonprobability samples emerge rapidly to address time-sensitive priority topics in different areas. These data are timely but subject to selection bias. To reduce selection bias, there has been wide literature in survey research investigating the use of propensity-score (PS) adjustment methods to improve the population representativeness of nonprobability samples, using probability-based survey samples as external references. Conditional exchangeability (CE) assumption is one of the key assumptions required by PS-based adjustment methods. In this paper, I first explore the validity of the CE assumption conditional on various balancing score estimates that are used in existing PS-based adjustment methods. An adaptive balancing score is proposed for unbiased estimation of population means. The population mean estimators under the three CE assumptions are evaluated via Monte Carlo simulation studies and illustrated using the NIH SARS-CoV-2 seroprevalence study to estimate the proportion of U.S. adults with COVID-19 antibodies from April 01-August 04, 2020.

Description: Our comments respond to discussion from Sen, Brick, and Elliott. We weigh the potential upside and downside of Sen’s suggestion of using machine learning to identify bogus respondents through interactions and improbable combinations of variables. We join Brick in reflecting on bogus respondents’ impact on the state of commercial nonprobability surveys. Finally, we consider Elliott’s discussion of solutions to the challenge raised in our study.

Description: This discussion summarizes the interesting new findings around measurement errors in opt-in surveys by Kennedy, Mercer and Lau (KML). While KML enlighten readers about “bogus responding” and possible patterns in them, this discussion suggests combining these new-found results with other avenues of research in nonprobability sampling, such as improvement of representativeness.

Description: Kennedy, Mercer, and Lau explore misreporting by respondents in non-probability samples and discover a new feature, namely that of deliberate misreporting of demographic characteristics. This finding suggests that the “arms race” between researchers and those determined to disrupt the practice of social science is not over and researchers need to account for such respondents if using high-quality probability surveys to help reduce error in non-probability samples.

Description: This video is part of a series that is designed to give you a basic understanding of the Census of Population web pages. This video will provide an overview of the major links and products on the main page that are available to all users.

Description: This video is part of a series that is designed to give you a basic understanding of the Census of Population web pages. The purpose of this video is to explain where to find the most popular standard data product of the Census of Population, the 2021 Census Profile, and how to filter the data.

Description: This video is part of a series that is designed to give you a basic understanding of the Census of Population web pages. The purpose of this video is to explain how to add geographies in the 2021 Census Profile and to present the various downloading options to see the data.

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: This paper deals with the desirability of designing surveys in such a way that results can be compared to previous existing data. The writer explains why there are practical difficulties in assessing the significance of data collected in a one-time survey where these data stand alone and are not readily comparable to other existing data, i.e., where control group data or other benchmarks do not exist.

Description: The government survey sponsor should plan carefully what he expects to get from the supplier, specifying who is to do what, when, including details of what the sponsor will do. If there are many eligible suppliers, only a small number should be invited to submit proposals, increasing as the value of the contract increases. Procedures for screening suppliers and selecting the successful one should be organized before proposals are received. These should include visits to review suppliers, facilities and organization, as a good relationship between a sponsor and a supplier depends largely on good faith and willing cooperation. Sponsor-supplier relationships are more formal, and more time-consuming in the selection process, than in the private sector.

Description: Various research methods are discussed in terms of evaluating government programs and meeting the needs of users in the private sector. A brief evaluation of social trend studies is given, as well as a description of problems associated with consumer research.

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The paper illustrates several practical problems in the adaptation of statistical theory to survey design in the context of the revision of an employment survey programme.

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The Reverse Record Check is the main vehicle used to assess the level of undercoverage in the Canadian Census of Population. A sample of persons is selected from sources independent of the current census and extensive tracing operations are undertaken to determine the usual address of each selected person as of Census day. Census records are then checked to determine whether or not each selected person was enumerated. The tracing is by far the most complex, costly and time-consuming operation associated with this study. It involves extensive use of administrative records as well as tracing in the field. This paper describes the various tracing methods used as well as the success obtained from each of them.

Description: In this paper three types of ratio estimators, namely combined, post-stratified and a generalized ratio estimator developed earlier by Singh (1969) and Naga Reddy (1974), are considered. Based on an empirical evaluation, their efficiencies are compared for two large scale household surveys, namely the Canadian Labour Force Survey and the Survey of Consumer Finances.

Description: Statistics on sales of establishments classified as restaurants, caterers and taverns have been collected since 1951. The sample has not been updated for births since 1968 and as a result, it is not representative of the current universe. This paper reports on several methodological aspects of the redesign. The sampling unit, sample design, sample size and allocation, data collection methods, edits and imputations, accumulations and calculations, frame and sample maintenance are described. The new survey will reduce manual procedures wherever possible. Collection, editing, imputation, tabulation and updating procedures will be completely computerized. Data collection will be decentralized and will take place via telephone.

Description: The Farm Expenditure Survey was developed to provide annual expenditure estimates for the Western Grain Stabilization Act which is an income stabilization program for grain farmers in the prairies and Peace River district of British Columbia. This paper describes the design of the 1979 survey which incorporated a stratified two-stage design in the area sample and a single take-all stratum in the list sample.

Description: An alternative to the direct selection of sample is suggested, which while retaining the efficiency at the same level simplifies the selection and variance estimation processes in a wide variety of situations. If n* is the largest feasible pPS sample size that can be drawn from a given population of size N, then the proposed method entails selection of m (=N - n*) units using a pPS scheme and rejecting these units from the population such that the remainder is a pPS sample of n* units; the final sample of n units is then selected as a subsample from the remainder set. This method for selecting the pPS sample can be seen as an analogue of SRS where it is well known that the “unsampled” part of the population as well as any subsample from this part are also SRS from the entire population when SRS is the procedure used. The method is very practical for situations where m is less than the actual sample size n. Moreover, the method has the additional advantage in the context of continuing surveys, e.g. Canadian Labour Force Survey (LFS), where the number of primary sampling units (PSU’s) may have to be increased (or decreased) subsequent to the initial selection of the sample. The method also has advantages in the case of sample rotation. Main features of the proposed scheme and its limitations are given. Efficiency of the method is also evaluated empirically.

Description: The problem considered in this paper is the estimation of various agricultural variables using a multiple frame approach. The list frame is completely contained within the area frame. The stratification for the list and area frames are based on different criteria. Overall, the multiple frame shows some gains in terms of variance over the area frame. However, a more careful analysis reveals problem areas associated with the list frame such as the method of stratification and the degeneration of list strata over time.

Description: The fact sheets in this series provide an "at-a-glance" overview of particular aspects of education in Canada and summarize key data trends in selected tables published as part of the Pan-Canadian Education Indicators Program (PCEIP).

The PCEIP mission is to publish a set of statistical measures on education systems in Canada for policy makers, practitioners and the general public to monitor the performance of education systems across jurisdictions and over time. PCEIP is a joint venture of Statistics Canada and the Council of Ministers of Education, Canada (CMEC).

Description: Statistics Canada's Quality of Employment in Canada publication is intended to provide Canadians and Canadian organizations with a better understanding of quality of employment using an internationally-supported statistical framework. Quality of employment is approached as a multidimensional concept, characterized by different elements, which relate to human needs in various ways. To cover all relevant aspects, the framework identified seven dimensions and twelve sub-dimensions of quality of employment.

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The articles published in EnviroStats use statistics to illustrate topical environmental issues. The publication is intended for a general readership rather than an expert audience.

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The documents in this collection are based on data from the Longitudinal and International Study of Adults, a survey that examines a variety of topics on the well-being of Canadians and measures the effect of changes in certain areas on people's lives. The survey covers several topics, such as jobs, health, adult education and training, income and earnings, as well as the family dynamic. Reports on the survey content, concepts, methodology and data quality are also available.

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This report helps users understand how we balance protecting confidentiality and meeting needs for data. It provides information at a high level for major variables such as those related to gender, Indigenous peoples, visible minority, ethnocultural diversity, instruction in the official minority language and religious groups.

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Human Activity and the Environment (16-201-X) focuses on current environmental issues. The latest information and statistics are gathered from many sources to produce an in-depth analytical article.

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Health fact sheets will include short, focused, single-theme analysis documents. Over the course of the series, analysis will include topics on: Health conditions, lifestyle, well-being, disability, prevention and detection of disease, deaths, pregnancy and birth, health care services and environmental factors.

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The Report on the Demographic Situation in Canada analyses recent demographic patterns at the national, provincial and subprovincial levels. Trends in population growth and the evolution of the various components of Canada's population growth - fertility, mortality and migration (interprovincial and international) - as well as marital status, are examined. The Report on the Demographic Situation in Canada has been published annually or biennially since 1985. Beginning in 2011, the Report is available as a dynamic, internet-only publication in order to provide the most recent data and analyses on Canadian demographics as soon as they are available.

Description: Articles in the Economic Insights series highlight issues related to the growth and development of Canada's economy. In some cases, these articles highlight new insights or synthesize the results of previous research carried out by Statistics Canada; in others, they provide contextual information that accompanies the release of new data or updates from previous papers. The Economic Insights series features concise examinations of economic events, research results, trends, and important structural changes in the economy.

Description:

Over 80 indicators measure the health of the Canadian population and the effectiveness of the health care system. Designed to provide comparable information at the health region and provincial/territorial levels, these data are produced from a wide range of the most recently available sources.

This Internet publication is produced by Statistics Canada and the Canadian Institute for Health Information.