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- Articles and reports: 12-001-X202300200009Description: In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.Release date: 2024-01-03
- Articles and reports: 12-001-X202200200006Description:
Non-probability samples are deprived of the powerful design probability for randomization-based inference. This deprivation, however, encourages us to take advantage of a natural divine probability that comes with any finite population. A key metric from this perspective is the data defect correlation (ddc), which is the model-free finite-population correlation between the individual’s sample inclusion indicator and the individual’s attribute being sampled. A data generating mechanism is equivalent to a probability sampling, in terms of design effect, if and only if its corresponding ddc is of N-1/2 (stochastic) order, where N is the population size (Meng, 2018). Consequently, existing valid linear estimation methods for non-probability samples can be recast as various strategies to miniaturize the ddc down to the N-1/2 order. The quasi design-based methods accomplish this task by diminishing the variability among the N inclusion propensities via weighting. The super-population model-based approach achieves the same goal through reducing the variability of the N individual attributes by replacing them with their residuals from a regression model. The doubly robust estimators enjoy their celebrated property because a correlation is zero whenever one of the variables being correlated is constant, regardless of which one. Understanding the commonality of these methods through ddc also helps us see clearly the possibility of “double-plus robustness”: a valid estimation without relying on the full validity of either the regression model or the estimated inclusion propensity, neither of which is guaranteed because both rely on device probability. The insight generated by ddc also suggests counterbalancing sub-sampling, a strategy aimed at creating a miniature of the population out of a non-probability sample, and with favorable quality-quantity trade-off because mean-squared errors are much more sensitive to ddc than to the sample size, especially for large populations.
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: 11-522-X201700014738Description:
In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.
Release date: 2016-03-24 - 5. The Potential Use of Remote Sensing to Produce Field Crop Statistics at Statistics Canada ArchivedSurveys and statistical programs – Documentation: 11-522-X201300014259Description:
In an effort to reduce response burden on farm operators, Statistics Canada is studying alternative approaches to telephone surveys for producing field crop estimates. One option is to publish harvested area and yield estimates in September as is currently done, but to calculate them using models based on satellite and weather data, and data from the July telephone survey. However before adopting such an approach, a method must be found which produces estimates with a sufficient level of accuracy. Research is taking place to investigate different possibilities. Initial research results and issues to consider are discussed in this paper.
Release date: 2014-10-31 - 6. How Postal Codes Map to Geographic Areas ArchivedArticles and reports: 92F0138M2007001Description:
Statistics Canada creates files that provide the link between postal codes and the geographic areas by which it disseminates statistical data. By linking postal codes to the Statistics Canada geographic areas, Statistics Canada facilitates the extraction and subsequent aggregation of data for selected geographic areas from files available to users. Users can then take data from Statistics Canada for their areas and tabulate this with other data for these same areas to create a combined statistical profile for these areas.
An issue has been the methodology used by Statistics Canada to establish the linkage of postal codes to geographic areas. In order to address this issue, Statistics Canada decided to create a conceptual framework on which to base the rules for linking postal codes and Statistics Canada's geographic areas. This working paper presents the conceptual framework and the geocoding rules. The methodology described in this paper will be the basis for linking postal codes to the 2006 Census geographic areas. This paper is presented for feedback from users of Statistics Canada's postal codes related products.
Release date: 2007-02-12 - 7. The growing importance of the service industries: The need for sub-annual indicators (IV-B) ArchivedArticles and reports: 11F0024M20050008805Description:
This paper reports on the potential development of sub-annual indicators for selected service industries using Goods and Services Tax (GST) data. The services sector is now of central importance to advanced economies; however, our knowledge of this sector remains incomplete, partly due to a lack of data. The Voorburg Group on Service Statistics has been meeting for almost twenty years to develop and incorporate better measures for the services sector. Despite this effort, many sub-annual economic measures continue to rely on output data for the goods-producing sector and, with the exception of distributive trades, on employment data for service industries.
The development of sub-annual indicators for service industries raises two questions regarding the national statistical program. First, is there a need for service output indicators to supplement existing sub-annual measures? And second, what service industries are the most promising for development? The paper begins by reviewing the importance of service industries and how they behave during economic downturns. Next, it examines considerations in determining which service industries to select as GST-based, sub-annual indicators. A case study of the accommodation services industry serves to illustrate improving timeliness and accuracy. We conclude by discussing the opportunities for, and limitations of, these indicators.
Release date: 2005-10-20 - Articles and reports: 11-522-X20020016719Description:
This study takes a look at the modelling methods used for public health data. Public health has a renewed interest in the impact of the environment on health. Ecological or contextual studies ideally investigate these relationships using public health data augmented with environmental characteristics in multilevel or hierarchical models. In these models, individual respondents in health data are the first level and community data are the second level. Most public health data use complex sample survey designs, which require analyses accounting for the clustering, nonresponse, and poststratification to obtain representative estimates of prevalence of health risk behaviours.
This study uses the Behavioral Risk Factor Surveillance System (BRFSS), a state-specific US health risk factor surveillance system conducted by the Center for Disease Control and Prevention, which assesses health risk factors in over 200,000 adults annually. BRFSS data are now available at the metropolitan statistical area (MSA) level and provide quality health information for studies of environmental effects. MSA-level analyses combining health and environmental data are further complicated by joint requirements of the survey sample design and the multilevel analyses.
We compare three modelling methods in a study of physical activity and selected environmental factors using BRFSS 2000 data. Each of the methods described here is a valid way to analyse complex sample survey data augmented with environmental information, although each accounts for the survey design and multilevel data structure in a different manner and is thus appropriate for slightly different research questions.
Release date: 2004-09-13 - 9. Alternative Work Practices and Quit Rates: Methodological Issues and Empirical Evidence for Canada ArchivedArticles and reports: 11F0019M2003199Geography: CanadaDescription:
Using a nationally representative sample of establishments, we have examined whether selected alternative work practices (AWPs) tend to reduce quit rates. Overall, our analysis provides strong evidence of a negative association between these AWPs and quit rates among establishments of more than 10 employees operating in high-skill services. We also found some evidence of a negative association in low-skill services. However, the magnitude of this negative association was reduced substantially when we added an indicator of whether the workplace has a formal policy of information sharing. There was very little evidence of a negative association in manufacturing. While establishments with self-directed workgroups have lower quit rates than others, none of the bundles of work practices considered yielded a negative and statistically significant effect. We surmise that key AWPs might be more successful in reducing labour turnover in technologically complex environments than in low-skill ones.
Release date: 2003-03-17 - 10. The effect of record linkage errors on statistical inference in cohort mortality studies ArchivedArticles and reports: 11-522-X20010016277Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The advent of computerized record-linkage methodology has facilitated the conduct of cohort mortality studies in which exposure data in one database are electronically linked with mortality data from another database. In this article, the impact of linkage errors on estimates of epidemiological indicators of risk, such as standardized mortality ratios and relative risk regression model parameters, is explored. It is shown that these indicators can be subject to bias and additional variability in the presence of linkage errors, with false links and non-links leading to positive and negative bias, respectively, in estimates of the standardized mortality ratio. Although linkage errors always increase the uncertainty in the estimates, bias can be effectively eliminated in the special case in which the false positive rate equals the false negative rate within homogeneous states defined by cross-classification of the covariates of interest.
Release date: 2002-09-12
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- Articles and reports: 12-001-X202300200009Description: In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.Release date: 2024-01-03
- Articles and reports: 12-001-X202200200006Description:
Non-probability samples are deprived of the powerful design probability for randomization-based inference. This deprivation, however, encourages us to take advantage of a natural divine probability that comes with any finite population. A key metric from this perspective is the data defect correlation (ddc), which is the model-free finite-population correlation between the individual’s sample inclusion indicator and the individual’s attribute being sampled. A data generating mechanism is equivalent to a probability sampling, in terms of design effect, if and only if its corresponding ddc is of N-1/2 (stochastic) order, where N is the population size (Meng, 2018). Consequently, existing valid linear estimation methods for non-probability samples can be recast as various strategies to miniaturize the ddc down to the N-1/2 order. The quasi design-based methods accomplish this task by diminishing the variability among the N inclusion propensities via weighting. The super-population model-based approach achieves the same goal through reducing the variability of the N individual attributes by replacing them with their residuals from a regression model. The doubly robust estimators enjoy their celebrated property because a correlation is zero whenever one of the variables being correlated is constant, regardless of which one. Understanding the commonality of these methods through ddc also helps us see clearly the possibility of “double-plus robustness”: a valid estimation without relying on the full validity of either the regression model or the estimated inclusion propensity, neither of which is guaranteed because both rely on device probability. The insight generated by ddc also suggests counterbalancing sub-sampling, a strategy aimed at creating a miniature of the population out of a non-probability sample, and with favorable quality-quantity trade-off because mean-squared errors are much more sensitive to ddc than to the sample size, especially for large populations.
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: 11-522-X201700014738Description:
In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.
Release date: 2016-03-24 - 5. How Postal Codes Map to Geographic Areas ArchivedArticles and reports: 92F0138M2007001Description:
Statistics Canada creates files that provide the link between postal codes and the geographic areas by which it disseminates statistical data. By linking postal codes to the Statistics Canada geographic areas, Statistics Canada facilitates the extraction and subsequent aggregation of data for selected geographic areas from files available to users. Users can then take data from Statistics Canada for their areas and tabulate this with other data for these same areas to create a combined statistical profile for these areas.
An issue has been the methodology used by Statistics Canada to establish the linkage of postal codes to geographic areas. In order to address this issue, Statistics Canada decided to create a conceptual framework on which to base the rules for linking postal codes and Statistics Canada's geographic areas. This working paper presents the conceptual framework and the geocoding rules. The methodology described in this paper will be the basis for linking postal codes to the 2006 Census geographic areas. This paper is presented for feedback from users of Statistics Canada's postal codes related products.
Release date: 2007-02-12 - 6. The growing importance of the service industries: The need for sub-annual indicators (IV-B) ArchivedArticles and reports: 11F0024M20050008805Description:
This paper reports on the potential development of sub-annual indicators for selected service industries using Goods and Services Tax (GST) data. The services sector is now of central importance to advanced economies; however, our knowledge of this sector remains incomplete, partly due to a lack of data. The Voorburg Group on Service Statistics has been meeting for almost twenty years to develop and incorporate better measures for the services sector. Despite this effort, many sub-annual economic measures continue to rely on output data for the goods-producing sector and, with the exception of distributive trades, on employment data for service industries.
The development of sub-annual indicators for service industries raises two questions regarding the national statistical program. First, is there a need for service output indicators to supplement existing sub-annual measures? And second, what service industries are the most promising for development? The paper begins by reviewing the importance of service industries and how they behave during economic downturns. Next, it examines considerations in determining which service industries to select as GST-based, sub-annual indicators. A case study of the accommodation services industry serves to illustrate improving timeliness and accuracy. We conclude by discussing the opportunities for, and limitations of, these indicators.
Release date: 2005-10-20 - Articles and reports: 11-522-X20020016719Description:
This study takes a look at the modelling methods used for public health data. Public health has a renewed interest in the impact of the environment on health. Ecological or contextual studies ideally investigate these relationships using public health data augmented with environmental characteristics in multilevel or hierarchical models. In these models, individual respondents in health data are the first level and community data are the second level. Most public health data use complex sample survey designs, which require analyses accounting for the clustering, nonresponse, and poststratification to obtain representative estimates of prevalence of health risk behaviours.
This study uses the Behavioral Risk Factor Surveillance System (BRFSS), a state-specific US health risk factor surveillance system conducted by the Center for Disease Control and Prevention, which assesses health risk factors in over 200,000 adults annually. BRFSS data are now available at the metropolitan statistical area (MSA) level and provide quality health information for studies of environmental effects. MSA-level analyses combining health and environmental data are further complicated by joint requirements of the survey sample design and the multilevel analyses.
We compare three modelling methods in a study of physical activity and selected environmental factors using BRFSS 2000 data. Each of the methods described here is a valid way to analyse complex sample survey data augmented with environmental information, although each accounts for the survey design and multilevel data structure in a different manner and is thus appropriate for slightly different research questions.
Release date: 2004-09-13 - 8. Alternative Work Practices and Quit Rates: Methodological Issues and Empirical Evidence for Canada ArchivedArticles and reports: 11F0019M2003199Geography: CanadaDescription:
Using a nationally representative sample of establishments, we have examined whether selected alternative work practices (AWPs) tend to reduce quit rates. Overall, our analysis provides strong evidence of a negative association between these AWPs and quit rates among establishments of more than 10 employees operating in high-skill services. We also found some evidence of a negative association in low-skill services. However, the magnitude of this negative association was reduced substantially when we added an indicator of whether the workplace has a formal policy of information sharing. There was very little evidence of a negative association in manufacturing. While establishments with self-directed workgroups have lower quit rates than others, none of the bundles of work practices considered yielded a negative and statistically significant effect. We surmise that key AWPs might be more successful in reducing labour turnover in technologically complex environments than in low-skill ones.
Release date: 2003-03-17 - 9. The effect of record linkage errors on statistical inference in cohort mortality studies ArchivedArticles and reports: 11-522-X20010016277Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The advent of computerized record-linkage methodology has facilitated the conduct of cohort mortality studies in which exposure data in one database are electronically linked with mortality data from another database. In this article, the impact of linkage errors on estimates of epidemiological indicators of risk, such as standardized mortality ratios and relative risk regression model parameters, is explored. It is shown that these indicators can be subject to bias and additional variability in the presence of linkage errors, with false links and non-links leading to positive and negative bias, respectively, in estimates of the standardized mortality ratio. Although linkage errors always increase the uncertainty in the estimates, bias can be effectively eliminated in the special case in which the false positive rate equals the false negative rate within homogeneous states defined by cross-classification of the covariates of interest.
Release date: 2002-09-12 - 10. Delineation of Canada's North: An Examination of the North-South Relationship in Canada ArchivedArticles and reports: 92F0138M2000003Description:
Statistics Canada's interest in a common delineation of the north for statistical analysis purposes evolved from research to devise a classification to further differentiate the largely rural and remote areas that make up 96% of Canada's land area. That research led to the establishment of the census metropolitan area and census agglomeration influenced zone (MIZ) concept. When applied to census subdivisions, the MIZ categories did not work as well in northern areas as in the south. Therefore, the Geography Division set out to determine a north-south divide that would differentiate the north from the south independent of any standard geographic area boundaries.
This working paper describes the methodology used to define a continuous line across Canada to separate the north from the south, as well as lines marking transition zones on both sides of the north-south line. It also describes the indicators selected to derive the north-south line and makes comparisons to alternative definitions of the north. The resulting classification of the north complements the MIZ classification. Together, census metropolitan areas, census agglomerations, MIZ and the North form a new Statistical Area Classification (SAC) for Canada.
Two related Geography working papers (catalogue no. 92F0138MPE) provide further details about the MIZ classification. Working paper no. 2000-1 (92F0138MPE00001) briefly describes MIZ and includes tables of selected socio-economic characteristics from the 1991 Census tabulated by the MIZ categories, and working paper no. 2000-2 (92F0138MPE00002) describes the methodology used to define the MIZ classification.
Release date: 2000-02-03
Reference (3)
Reference (3) ((3 results))
- 1. The Potential Use of Remote Sensing to Produce Field Crop Statistics at Statistics Canada ArchivedSurveys and statistical programs – Documentation: 11-522-X201300014259Description:
In an effort to reduce response burden on farm operators, Statistics Canada is studying alternative approaches to telephone surveys for producing field crop estimates. One option is to publish harvested area and yield estimates in September as is currently done, but to calculate them using models based on satellite and weather data, and data from the July telephone survey. However before adopting such an approach, a method must be found which produces estimates with a sufficient level of accuracy. Research is taking place to investigate different possibilities. Initial research results and issues to consider are discussed in this paper.
Release date: 2014-10-31 - 2. Survey of Financial Security - Methodology for Estimating the Value of Employer Pension Plan Benefits ArchivedSurveys and statistical programs – Documentation: 13F0026M2001003Description:
Initial results from the Survey of Financial Security (SFS), which provides information on the net worth of Canadians, were released on March 15 2001, in The daily. The survey collected information on the value of the financial and non-financial assets owned by each family unit and on the amount of their debt.
Statistics Canada is currently refining this initial estimate of net worth by adding to it an estimate of the value of benefits accrued in employer pension plans. This is an important addition to any asset and debt survey as, for many family units, it is likely to be one of the largest assets. With the aging of the population, information on pension accumulations is greatly needed to better understand the financial situation of those nearing retirement. These updated estimates of the Survey of Financial Security will be released in late fall 2001.
The process for estimating the value of employer pension plan benefits is a complex one. This document describes the methodology for estimating that value, for the following groups: a) persons who belonged to an RPP at the time of the survey (referred to as current plan members); b) persons who had previously belonged to an RPP and either left the money in the plan or transferred it to a new plan; c) persons who are receiving RPP benefits.
This methodology was proposed by Hubert Frenken and Michael Cohen. The former has many years of experience with Statistics Canada working with data on employer pension plans; the latter is a principal with the actuarial consulting firm William M. Mercer. Earlier this year, Statistics Canada carried out a public consultation on the proposed methodology. This report includes updates made as a result of feedback received from data users.
Release date: 2001-09-05 - 3. Survey of Financial Security - Estimating the Value of Employer Pension Plan Benefits - A Discussion Paper ArchivedSurveys and statistical programs – Documentation: 13F0026M2001002Description:
The Survey of Financial Security (SFS) will provide information on the net worth of Canadians. In order to do this, information was collected - in May and June 1999 - on the value of the assets and debts of each of the families or unattached individuals in the sample. The value of one particular asset is not easy to determine, or to estimate. That is the present value of the amount people have accrued in their employer pension plan. These plans are often called registered pension plans (RPP), as they must be registered with Canada Customs and Revenue Agency. Although some RPP members receive estimates of the value of their accrued benefit, in most cases plan members would not know this amount. However, it is likely to be one of the largest assets for many family units. And, as the baby boomers approach retirement, information on their pension accumulations is much needed to better understand their financial readiness for this transition.
The intent of this paper is to: present, for discussion, a methodology for estimating the present value of employer pension plan benefits for the Survey of Financial Security; and to seek feedback on the proposed methodology. This document proposes a methodology for estimating the value of employer pension plan benefits for the following groups:a) persons who belonged to an RPP at the time of the survey (referred to as current plan members); b) persons who had previously belonged to an RPP and either left the money in the plan or transferred it to a new plan; c) persons who are receiving RPP benefits.
Release date: 2001-02-07
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