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All (75) (0 to 10 of 75 results)

  • 1. Longitudinal Administrative Data Dictionary
    Surveys and statistical programs – Documentation: 12-585-X
    Description: This product is the dictionary for the Longitudinal Administrative Databank (LAD). The dictionary contains a complete description for each of the income and demographic variables in the LAD, including name, acronym, definition, source, historical availability and historical continuity.

    The following is a partial list of LAD variables: age, sex, marital status, family type, number and age of children, total income, wages and salaries, self-employment, Employment Insurance, Old Age Security, Canada and Quebec Pension Plans, social assistance, investment income, rental income, alimony, registered retirement savings plan (RRSP) income and contributions, low-income status, full-time education deduction, provincial refundable tax credits, goods and service tax (GST) credits, Canada Child Tax Benefits, selected immigration variables, Tax Free Savings (TFSA) information and Canadian Controlled Private Corporations (CCPC) information.

    Release date: 2023-11-10
  • 2. Municipal Financial and Socioeconomic Data Dashboard
    Data Visualization: 71-607-X2022004
    Description:

    This interactive dashboard presents key financial, economic and socio-economic data for individual municipalities and other local public administrations.

    Release date: 2022-07-26
  • 3. Small area estimation using Fay-Herriot area level model with sampling variance smoothing and modeling
    Articles and reports: 12-001-X202100200007
    Description:

    In this paper, we consider the Fay-Herriot model for small area estimation. In particular, we are interested in the impact of sampling variance smoothing and modeling on the model-based estimates. We present methods of smoothing and modeling for the sampling variances and apply the proposed models to a real data analysis. Our results indicate that sampling variance smoothing can improve the efficiency and accuracy of the model-based estimator. For sampling variance modeling, the HB models of You (2016) and Sugasawa, Tamae and Kubokawa (2017) perform equally well to improve the direct survey estimates.

    Release date: 2022-01-06
  • 4. Measuring uncertainty associated with model-based small area estimators Archived
    Articles and reports: 12-001-X201800254958
    Description:

    Domains (or subpopulations) with small sample sizes are called small areas. Traditional direct estimators for small areas do not provide adequate precision because the area-specific sample sizes are small. On the other hand, demand for reliable small area statistics has greatly increased. Model-based indirect estimators of small area means or totals are currently used to address difficulties with direct estimation. These estimators are based on linking models that borrow information across areas to increase the efficiency. In particular, empirical best (EB) estimators under area level and unit level linear regression models with random small area effects have received a lot of attention in the literature. Model mean squared error (MSE) of EB estimators is often used to measure the variability of the estimators. Linearization-based estimators of model MSE as well as jackknife and bootstrap estimators are widely used. On the other hand, National Statistical Agencies are often interested in estimating the design MSE of EB estimators in line with traditional design MSE estimators associated with direct estimators for large areas with adequate sample sizes. Estimators of design MSE of EB estimators can be obtained for area level models but they tend to be unstable when the area sample size is small. Composite MSE estimators are proposed in this paper and they are obtained by taking a weighted sum of the design MSE estimator and the model MSE estimator. Properties of the MSE estimators under the area level model are studied in terms of design bias, relative root mean squared error and coverage rate of confidence intervals. The case of a unit level model is also examined under simple random sampling within each area. Results of a simulation study show that the proposed composite MSE estimators provide a good compromise in estimating the design MSE.

    Release date: 2018-12-20
  • 5. Methodology of the Canadian Labour Force Survey
    Surveys and statistical programs – Documentation: 71-526-X
    Description:

    The Canadian Labour Force Survey (LFS) is the official source of monthly estimates of total employment and unemployment. Following the 2011 census, the LFS underwent a sample redesign to account for the evolution of the population and labour market characteristics, to adjust to changes in the information needs and to update the geographical information used to carry out the survey. The redesign program following the 2011 census culminated with the introduction of a new sample at the beginning of 2015. This report is a reference on the methodological aspects of the LFS, covering stratification, sampling, collection, processing, weighting, estimation, variance estimation and data quality.

    Release date: 2017-12-21
  • 6. Special Orders for Small Area Data
    61C9956
    Description:

    The Income Statistics Division offers custom tabulations designed to meet specific data requirements. From the income tax forms submitted each year by Canadians, a wealth of economic and demographic information is available, subject to confidentiality restrictions. The statistics are derived primarily from the annual tax file provided by the Canada Revenue Agency.

    Data are available starting in 1982 for some postal areas, some census regions, and for user-defined areas according to a postal code conversion file. Most current data are for the 2019 tax year.

    Release date: 2017-07-12
  • 7. Comparison of unit level and area level small area estimators Archived
    Articles and reports: 12-001-X201600114540
    Description:

    In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.

    Release date: 2016-06-22
  • 8. Model-assisted optimal allocation for planned domains using composite estimation Archived
    Articles and reports: 12-001-X201500214230
    Description:

    This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.

    Release date: 2015-12-17
  • 9. Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design Archived
    Articles and reports: 12-001-X201500214231
    Description:

    Rotating panels are widely applied by national statistical institutes, for example, to produce official statistics about the labour force. Estimation procedures are generally based on traditional design-based procedures known from classical sampling theory. A major drawback of this class of estimators is that small sample sizes result in large standard errors and that they are not robust for measurement bias. Two examples showing the effects of measurement bias are rotation group bias in rotating panels, and systematic differences in the outcome of a survey due to a major redesign of the underlying process. In this paper we apply a multivariate structural time series model to the Dutch Labour Force Survey to produce model-based figures about the monthly labour force. The model reduces the standard errors of the estimates by taking advantage of sample information collected in previous periods, accounts for rotation group bias and autocorrelation induced by the rotating panel, and models discontinuities due to a survey redesign. Additionally, we discuss the use of correlated auxiliary series in the model to further improve the accuracy of the model estimates. The method is applied by Statistics Netherlands to produce accurate official monthly statistics about the labour force that are consistent over time, despite a redesign of the survey process.

    Release date: 2015-12-17
  • 10. Model-based small area estimation under informative sampling Archived
    Articles and reports: 12-001-X201500214248
    Description:

    Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.

    Release date: 2015-12-17
Data (1)

Data (1) ((1 result))

  • 1. Municipal Financial and Socioeconomic Data Dashboard
    Data Visualization: 71-607-X2022004
    Description:

    This interactive dashboard presents key financial, economic and socio-economic data for individual municipalities and other local public administrations.

    Release date: 2022-07-26
Analysis (69)

Analysis (69) (0 to 10 of 69 results)

  • 1. Small area estimation using Fay-Herriot area level model with sampling variance smoothing and modeling
    Articles and reports: 12-001-X202100200007
    Description:

    In this paper, we consider the Fay-Herriot model for small area estimation. In particular, we are interested in the impact of sampling variance smoothing and modeling on the model-based estimates. We present methods of smoothing and modeling for the sampling variances and apply the proposed models to a real data analysis. Our results indicate that sampling variance smoothing can improve the efficiency and accuracy of the model-based estimator. For sampling variance modeling, the HB models of You (2016) and Sugasawa, Tamae and Kubokawa (2017) perform equally well to improve the direct survey estimates.

    Release date: 2022-01-06
  • 2. Measuring uncertainty associated with model-based small area estimators Archived
    Articles and reports: 12-001-X201800254958
    Description:

    Domains (or subpopulations) with small sample sizes are called small areas. Traditional direct estimators for small areas do not provide adequate precision because the area-specific sample sizes are small. On the other hand, demand for reliable small area statistics has greatly increased. Model-based indirect estimators of small area means or totals are currently used to address difficulties with direct estimation. These estimators are based on linking models that borrow information across areas to increase the efficiency. In particular, empirical best (EB) estimators under area level and unit level linear regression models with random small area effects have received a lot of attention in the literature. Model mean squared error (MSE) of EB estimators is often used to measure the variability of the estimators. Linearization-based estimators of model MSE as well as jackknife and bootstrap estimators are widely used. On the other hand, National Statistical Agencies are often interested in estimating the design MSE of EB estimators in line with traditional design MSE estimators associated with direct estimators for large areas with adequate sample sizes. Estimators of design MSE of EB estimators can be obtained for area level models but they tend to be unstable when the area sample size is small. Composite MSE estimators are proposed in this paper and they are obtained by taking a weighted sum of the design MSE estimator and the model MSE estimator. Properties of the MSE estimators under the area level model are studied in terms of design bias, relative root mean squared error and coverage rate of confidence intervals. The case of a unit level model is also examined under simple random sampling within each area. Results of a simulation study show that the proposed composite MSE estimators provide a good compromise in estimating the design MSE.

    Release date: 2018-12-20
  • 3. Comparison of unit level and area level small area estimators Archived
    Articles and reports: 12-001-X201600114540
    Description:

    In this paper, we compare the EBLUP and pseudo-EBLUP estimators for small area estimation under the nested error regression model and three area level model-based estimators using the Fay-Herriot model. We conduct a design-based simulation study to compare the model-based estimators for unit level and area level models under informative and non-informative sampling. In particular, we are interested in the confidence interval coverage rate of the unit level and area level estimators. We also compare the estimators if the model has been misspecified. Our simulation results show that estimators based on the unit level model perform better than those based on the area level. The pseudo-EBLUP estimator is the best among unit level and area level estimators.

    Release date: 2016-06-22
  • 4. Model-assisted optimal allocation for planned domains using composite estimation Archived
    Articles and reports: 12-001-X201500214230
    Description:

    This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.

    Release date: 2015-12-17
  • 5. Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design Archived
    Articles and reports: 12-001-X201500214231
    Description:

    Rotating panels are widely applied by national statistical institutes, for example, to produce official statistics about the labour force. Estimation procedures are generally based on traditional design-based procedures known from classical sampling theory. A major drawback of this class of estimators is that small sample sizes result in large standard errors and that they are not robust for measurement bias. Two examples showing the effects of measurement bias are rotation group bias in rotating panels, and systematic differences in the outcome of a survey due to a major redesign of the underlying process. In this paper we apply a multivariate structural time series model to the Dutch Labour Force Survey to produce model-based figures about the monthly labour force. The model reduces the standard errors of the estimates by taking advantage of sample information collected in previous periods, accounts for rotation group bias and autocorrelation induced by the rotating panel, and models discontinuities due to a survey redesign. Additionally, we discuss the use of correlated auxiliary series in the model to further improve the accuracy of the model estimates. The method is applied by Statistics Netherlands to produce accurate official monthly statistics about the labour force that are consistent over time, despite a redesign of the survey process.

    Release date: 2015-12-17
  • 6. Model-based small area estimation under informative sampling Archived
    Articles and reports: 12-001-X201500214248
    Description:

    Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.

    Release date: 2015-12-17
  • 7. Small area estimation combining information from several sources Archived
    Articles and reports: 12-001-X201500114150
    Description:

    An area-level model approach to combining information from several sources is considered in the context of small area estimation. At each small area, several estimates are computed and linked through a system of structural error models. The best linear unbiased predictor of the small area parameter can be computed by the general least squares method. Parameters in the structural error models are estimated using the theory of measurement error models. Estimation of mean squared errors is also discussed. The proposed method is applied to the real problem of labor force surveys in Korea.

    Release date: 2015-06-29
  • 8. Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random area effects Archived
    Articles and reports: 12-001-X201500114161
    Description:

    A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.

    Release date: 2015-06-29
  • 9. Observed best prediction via nested-error regression with potentially misspecified mean and variance Archived
    Articles and reports: 12-001-X201500114200
    Description:

    We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.

    Release date: 2015-06-29
  • 10. Hierarchical Bayes Modeling of Survey-Weighted Small Area Proportions Archived
    Articles and reports: 12-001-X201400114030
    Description:

    The paper reports the results of a Monte Carlo simulation study that was conducted to compare the effectiveness of four different hierarchical Bayes small area models for producing state estimates of proportions based on data from stratified simple random samples from a fixed finite population. Two of the models adopted the commonly made assumptions that the survey weighted proportion for each sampled small area has a normal distribution and that the sampling variance of this proportion is known. One of these models used a linear linking model and the other used a logistic linking model. The other two models both employed logistic linking models and assumed that the sampling variance was unknown. One of these models assumed a normal distribution for the sampling model while the other assumed a beta distribution. The study found that for all four models the credible interval design-based coverage of the finite population state proportions deviated markedly from the 95 percent nominal level used in constructing the intervals.

    Release date: 2014-06-27
Reference (4)

Reference (4) ((4 results))

  • 1. Longitudinal Administrative Data Dictionary
    Surveys and statistical programs – Documentation: 12-585-X
    Description: This product is the dictionary for the Longitudinal Administrative Databank (LAD). The dictionary contains a complete description for each of the income and demographic variables in the LAD, including name, acronym, definition, source, historical availability and historical continuity.

    The following is a partial list of LAD variables: age, sex, marital status, family type, number and age of children, total income, wages and salaries, self-employment, Employment Insurance, Old Age Security, Canada and Quebec Pension Plans, social assistance, investment income, rental income, alimony, registered retirement savings plan (RRSP) income and contributions, low-income status, full-time education deduction, provincial refundable tax credits, goods and service tax (GST) credits, Canada Child Tax Benefits, selected immigration variables, Tax Free Savings (TFSA) information and Canadian Controlled Private Corporations (CCPC) information.

    Release date: 2023-11-10
  • 2. Methodology of the Canadian Labour Force Survey
    Surveys and statistical programs – Documentation: 71-526-X
    Description:

    The Canadian Labour Force Survey (LFS) is the official source of monthly estimates of total employment and unemployment. Following the 2011 census, the LFS underwent a sample redesign to account for the evolution of the population and labour market characteristics, to adjust to changes in the information needs and to update the geographical information used to carry out the survey. The redesign program following the 2011 census culminated with the introduction of a new sample at the beginning of 2015. This report is a reference on the methodological aspects of the LFS, covering stratification, sampling, collection, processing, weighting, estimation, variance estimation and data quality.

    Release date: 2017-12-21
  • 3. Neighbourhood Insights - Your Guide to the Statistical Information Packages Available From Small Area and Administrative Data Division, Statistics Canada Archived
    Surveys and statistical programs – Documentation: 17-507-X
    Description:

    "Neighbourhood insights" is your guide to the statistical information packages available from the Small Area and Administrative Data Division. The guide provides descriptions of the various databanks, the geographic availability and the pricing structure. The guide also contains sample statistical tables showing data for Canada.

    Release date: 2006-05-04
  • 4. Useful Information for Construction Archived
    Surveys and statistical programs – Documentation: 64F0004X
    Description:

    This practical and informative guide for the construction industry will assist in navigating through numerous Statistics Canada products and services.

    Release date: 2002-12-13
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