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  • 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) (20 to 30 of 69 results)

  • 21. Estimation of the monthly unemployment rate through structural time series modelling in a rotating panel design Archived
    Articles and reports: 12-001-X200900211040
    Description:

    In this paper a multivariate structural time series model is described that accounts for the panel design of the Dutch Labour Force Survey and is applied to estimate monthly unemployment rates. Compared to the generalized regression estimator, this approach results in a substantial increase of the accuracy due to a reduction of the standard error and the explicit modelling of the bias between the subsequent waves.

    Release date: 2009-12-23
  • 22. Estimates for small area compositions subjected to informative missing data Archived
    Articles and reports: 12-001-X200900211041
    Description:

    Estimation of small area (or domain) compositions may suffer from informative missing data, if the probability of missing varies across the categories of interest as well as the small areas. We develop a double mixed modeling approach that combines a random effects mixed model for the underlying complete data with a random effects mixed model of the differential missing-data mechanism. The effect of sampling design can be incorporated through a quasi-likelihood sampling model. The associated conditional mean squared error of prediction is approximated in terms of a three-part decomposition, corresponding to a naive prediction variance, a positive correction that accounts for the hypothetical parameter estimation uncertainty based on the latent complete data, and another positive correction for the extra variation due to the missing data. We illustrate our approach with an application to the estimation of Municipality household compositions based on the Norwegian register household data, which suffer from informative under-registration of the dwelling identity number.

    Release date: 2009-12-23
  • 23. Small area population prediction via hierarchical models Archived
    Articles and reports: 12-001-X200900211042
    Description:

    This paper proposes an approach for small area prediction based on data obtained from periodic surveys and censuses. We apply our approach to obtain population predictions for the municipalities not sampled in the Brazilian annual Household Survey (PNAD), as well as to increase the precision of the design-based estimates obtained for the sampled municipalities. In addition to the data provided by the PNAD, we use census demographic data from 1991 and 2000, as well as a complete population count conducted in 1996. Hierarchically non-structured and spatially structured growth models that gain strength from all the sampled municipalities are proposed and compared.

    Release date: 2009-12-23
  • 24. Variations by health region in treatment and survival after heart attack Archived
    Articles and reports: 82-003-X200900210872
    Geography: Canada
    Description:

    This article examines geographical variations in 30-day revascularization rates and 30-day in-hospital mortality rates for Canadian heart attack (acute myocardial infarction) patients. The data are from the Health Person-Oriented Information Database and pertain to health regions with at least 100,000 population in seven provinces for the years 1995/1996 and 2003/2004.

    Release date: 2009-06-17
  • 25. A balanced sampling approach for multi-way stratification designs for small area estimation Archived
    Articles and reports: 12-001-X200800210763
    Description:

    The present work illustrates a sampling strategy useful for obtaining planned sample size for domains belonging to different partitions of the population and in order to guarantee the sampling errors of domain estimates be lower than given thresholds. The sampling strategy that covers the multivariate multi-domain case is useful when the overall sample size is bounded and consequently the standard solution of using a stratified sample with the strata given by cross-classification of variables defining the different partitions is not feasible since the number of strata is larger than the overall sample size. The proposed sampling strategy is based on the use of balanced sampling selection technique and on a GREG-type estimation. The main advantages of the solution is the computational feasibility which allows one to easily implement an overall small area strategy considering jointly the sampling design and the estimator and improving the efficiency of the direct domain estimators. An empirical simulation on real population data and different domain estimators shows the empirical properties of the examined sample strategy.

    Release date: 2008-12-23
  • 26. Small area estimation under a two-part random effects model with application to estimation of literacy in developing countries Archived
    Articles and reports: 12-001-X200800210764
    Description:

    This paper considers situations where the target response value is either zero or an observation from a continuous distribution. A typical example analyzed in the paper is the assessment of literacy proficiency with the possible outcome being either zero, indicating illiteracy, or a positive score measuring the level of literacy. Our interest is in how to obtain valid estimates of the average response, or the proportion of positive responses in small areas, for which only small samples or no samples are available. As in other small area estimation problems, the small sample sizes in at least some of the sampled areas and/or the existence of nonsampled areas requires the use of model based methods. Available methods, however, are not suitable for this kind of data because of the mixed distribution of the responses, having a large peak at zero, juxtaposed to a continuous distribution for the rest of the responses. We develop, therefore, a suitable two-part random effects model and show how to fit the model and assess its goodness of fit, and how to compute the small area estimators of interest and measure their precision. The proposed method is illustrated using simulated data and data obtained from a literacy survey conducted in Cambodia.

    Release date: 2008-12-23
  • 27. In this issue (Vol. 34, no. 2) Archived
    Articles and reports: 12-001-X200800210768
    Description:

    In this Issue is a column where the Editor biefly presents each paper of the current issue of Survey Methodology. As well, it sometimes contain informations on structure or management changes in the journal.

    Release date: 2008-12-23
  • 28. Small area estimation under a two-level model Archived
    Articles and reports: 12-001-X200800110612
    Description:

    Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.

    Release date: 2008-06-26
  • 29. An integrated modeling approach to unemployment rate estimation for sub-provincial areas of Canada Archived
    Articles and reports: 12-001-X200800110614
    Geography: Canada
    Description:

    The Canadian Labour Force Survey (LFS) produces monthly estimates of the unemployment rate at national and provincial levels. The LFS also releases unemployment estimates for sub-provincial areas such as Census Metropolitan Areas (CMAs) and Urban Centers (UCs). However, for some sub-provincial areas, the direct estimates are not reliable since the sample size in some areas is quite small. The small area estimation in LFS concerns estimation of unemployment rates for local sub-provincial areas such as CMA/UCs using small area models. In this paper, we will discuss various models including the Fay-Herriot model and cross-sectional and time series models. In particular, an integrated non-linear mixed effects model will be proposed under the hierarchical Bayes (HB) framework for the LFS unemployment rate estimation. Monthly Employment Insurance (EI) beneficiary data at the CMA/UC level are used as auxiliary covariates in the model. A HB approach with the Gibbs sampling method is used to obtain the estimates of posterior means and posterior variances of the CMA/UC level unemployment rates. The proposed HB model leads to reliable model-based estimates in terms of CV reduction. Model fit analysis and comparison of the model-based estimates with the direct estimates are presented in the paper.

    Release date: 2008-06-26
  • 30. Small area estimation under a restriction Archived
    Articles and reports: 12-001-X200800110619
    Description:

    Small area prediction based on random effects, called EBLUP, is a procedure for constructing estimates for small geographical areas or small subpopulations using existing survey data. The total of the small area predictors is often forced to equal the direct survey estimate and such predictors are said to be calibrated. Several calibrated predictors are reviewed and a criterion that unifies the derivation of these calibrated predictors is presented. The predictor that is the unique best linear unbiased predictor under the criterion is derived and the mean square error of the calibrated predictors is discussed. Implicit in the imposition of the restriction is the possibility that the small area model is misspecified and the predictors are biased. Augmented models with one additional explanatory variable for which the usual small area predictors achieve the self-calibrated property are considered. Simulations demonstrate that calibrated predictors have slightly smaller bias compared to those of the usual EBLUP predictor. However, if the bias is a concern, a better approach is to use an augmented model with an added auxiliary variable that is a function of area size. In the simulation, the predictors based on the augmented model had smaller MSE than EBLUP when the incorrect model was used for prediction. Furthermore, there was a very small increase in MSE relative to EBLUP if the auxiliary variable was added to the correct model.

    Release date: 2008-06-26
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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