Statistics by subject – Statistical methods

Filter results by

Help for filters and search
Currently selected filters that can be removed

Keyword(s)

Year of publication

1 facets displayed. 1 facets selected.

Filter results by

Help for filters and search
Currently selected filters that can be removed

Keyword(s)

Year of publication

1 facets displayed. 1 facets selected.

Filter results by

Help for filters and search
Currently selected filters that can be removed

Keyword(s)

Year of publication

1 facets displayed. 1 facets selected.

Filter results by

Help for filters and search
Currently selected filters that can be removed

Keyword(s)

Year of publication

1 facets displayed. 1 facets selected.

Other available resources to support your research.

Help for sorting results
Browse our central repository of key standard concepts, definitions, data sources and methods.
Loading
Loading in progress, please wait...
All (49)

All (49) (25 of 49 results)

  • Articles and reports: 12-001-X20060029550
    Description:

    In this paper, the geometric, optimization-based, and Lavallée and Hidiroglou (LH) approaches to stratification are compared. The geometric stratification method is an approximation, whereas the other two approaches, which employ numerical methods to perform stratification, may be seen as optimal stratification methods. The algorithm of the geometric stratification is very simple compared to the two other approaches, but it does not take into account the construction of a take-all stratum, which is usually constructed when a positively skewed population is stratified. In the optimization-based stratification, one may consider any form of optimization function and its constraints. In a comparative numerical study based on five positively skewed artificial populations, the optimization approach was more efficient in each of the cases studied compared to the geometric stratification. In addition, the geometric and optimization approaches are compared with the LH algorithm. In this comparison, the geometric stratification approach was found to be less efficient than the LH algorithm, whereas efficiency of the optimization approach was similar to the efficiency of the LH algorithm. Nevertheless, strata boundaries evaluated via the geometric stratification may be seen as efficient starting points for the optimization approach.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029555
    Description:

    Researchers and policy makers often use data from nationally representative probability sample surveys. The number of topics covered by such surveys, and hence the amount of interviewing time involved, have typically increased over the years, resulting in increased costs and respondent burden. A potential solution to this problem is to carefully form subsets of the items in a survey and administer one such subset to each respondent. Designs of this type are called "split-questionnaire" designs or "matrix sampling" designs. The administration of only a subset of the survey items to each respondent in a matrix sampling design creates what can be considered missing data. Multiple imputation (Rubin 1987), a general-purpose approach developed for handling data with missing values, is appealing for the analysis of data from a matrix sample, because once the multiple imputations are created, data analysts can apply standard methods for analyzing complete data from a sample survey. This paper develops and evaluates a method for creating matrix sampling forms, each form containing a subset of items to be administered to randomly selected respondents. The method can be applied in complex settings, including situations in which skip patterns are present. Forms are created in such a way that each form includes items that are predictive of the excluded items, so that subsequent analyses based on multiple imputation can recover some of the information about the excluded items that would have been collected had there been no matrix sampling. The matrix sampling and multiple-imputation methods are evaluated using data from the National Health and Nutrition Examination Survey, one of many nationally representative probability sample surveys conducted by the National Center for Health Statistics, Centers for Disease Control and Prevention. The study demonstrates the feasibility of the approach applied to a major national health survey with complex structure, and it provides practical advice about appropriate items to include in matrix sampling designs in future surveys.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029553
    Description:

    Félix-Medina and Thompson (2004) proposed a variant of Link-tracing sampling in which it is assumed that a portion of the population, not necessarily the major portion, is covered by a frame of disjoint sites where members of the population can be found with high probabilities. A sample of sites is selected and the people in each of the selected sites are asked to nominate other members of the population. They proposed maximum likelihood estimators of the population sizes which perform acceptably provided that for each site the probability that a member is nominated by that site, called the nomination probability, is not small. In this research we consider Félix-Medina and Thompson's variant and propose three sets of estimators of the population sizes derived under the Bayesian approach. Two of the sets of estimators were obtained using improper prior distributions of the population sizes, and the other using Poisson prior distributions. However, we use the Bayesian approach only to assist us in the construction of estimators, while inferences about the population sizes are made under the frequentist approach. We propose two types of partly design-based variance estimators and confidence intervals. One of them is obtained using a bootstrap and the other using the delta method along with the assumption of asymptotic normality. The results of a simulation study indicate that (i) when the nomination probabilities are not small each of the proposed sets of estimators performs well and very similarly to maximum likelihood estimators; (ii) when the nomination probabilities are small the set of estimators derived using Poisson prior distributions still performs acceptably and does not have the problems of bias that maximum likelihood estimators have, and (iii) the previous results do not depend on the size of the fraction of the population covered by the frame.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029546
    Description:

    We discuss methods for the analysis of case-control studies in which the controls are drawn using a complex sample survey. The most straightforward method is the standard survey approach based on weighted versions of population estimating equations. We also look at more efficient methods and compare their robustness to model mis-specification in simple cases. Case-control family studies, where the within-cluster structure is of interest in its own right, are also discussed briefly.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029547
    Description:

    Calibration weighting can be used to adjust for unit nonresponse and/or coverage errors under appropriate quasi-randomization models. Alternative calibration adjustments that are asymptotically identical in a purely sampling context can diverge when used in this manner. Introducing instrumental variables into calibration weighting makes it possible for nonresponse (say) to be a function of a set of characteristics other than those in the calibration vector. When the calibration adjustment has a nonlinear form, a variant of the jackknife can remove the need for iteration in variance estimation.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029548
    Description:

    The theory of multiple imputation for missing data requires that imputations be made conditional on the sampling design. However, most standard software packages for performing model-based multiple imputation assume simple random samples, leading many practitioners not to account for complex sample design features, such as stratification and clustering, in their imputations. Theory predicts that analyses of such multiply-imputed data sets can yield biased estimates from the design-based perspective. In this article, we illustrate through simulation that (i) the bias can be severe when the design features are related to the survey variables of interest, and (ii) the bias can be reduced by controlling for the design features in the imputation models. The simulations also illustrate that conditioning on irrelevant design features in the imputation models can yield conservative inferences, provided that the models include other relevant predictors. These results suggest a prescription for imputers: the safest course of action is to include design variables in the specification of imputation models. Using real data, we demonstrate a simple approach for incorporating complex design features that can be used with some of the standard software packages for creating multiple imputations.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029554
    Description:

    Survey sampling to estimate a Consumer Price Index (CPI) is quite complicated, generally requiring a combination of data from at least two surveys: one giving prices, one giving expenditure weights. Fundamentally different approaches to the sampling process - probability sampling and purposive sampling - have each been strongly advocated and are used by different countries in the collection of price data. By constructing a small "world" of purchases and prices from scanner data on cereal and then simulating various sampling and estimation techniques, we compare the results of two design and estimation approaches: the probability approach of the United States and the purposive approach of the United Kingdom. For the same amount of information collected, but given the use of different estimators, the United Kingdom's methods appear to offer better overall accuracy in targeting a population superlative consumer price index.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029552
    Description:

    A survey of tourist visits originating intra and extra-region in Brittany was needed. For concrete material reasons, "border surveys" could no longer be used. The major problem is the lack of a sampling frame that allows for direct contact with tourists. This problem was addressed by applying the indirect sampling method, the weighting for which is obtained using the generalized weight share method developed recently by Lavallée (1995), Lavallée (2002), Deville (1999) and also presented recently in Lavallée and Caron (2001). This article shows how to adapt the method to the survey. A number of extensions are required. One of the extensions, designed to estimate the total of a population from which a Bernouilli sample has been taken, will be developed.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029549
    Description:

    In this article, we propose a Bernoulli-type bootstrap method that can easily handle multi-stage stratified designs where sampling fractions are large, provided simple random sampling without replacement is used at each stage. The method provides a set of replicate weights which yield consistent variance estimates for both smooth and non-smooth estimators. The method's strength is in its simplicity. It can easily be extended to any number of stages without much complication. The main idea is to either keep or replace a sampling unit at each stage with preassigned probabilities, to construct the bootstrap sample. A limited simulation study is presented to evaluate performance and, as an illustration, we apply the method to the 1997 Japanese National Survey of Prices.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029561
    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: 2006-12-21

  • Articles and reports: 12-001-X20060029551
    Description:

    To select a survey sample, it happens that one does not have a frame containing the desired collection units, but rather another frame of units linked in a certain way to the list of collection units. It can then be considered to select a sample from the available frame in order to produce an estimate for the desired target population by using the links existing between the two. This can be designated by Indirect Sampling.

    Estimation for the target population surveyed by Indirect Sampling can constitute a big challenge, in particular if the links between the units of the two are not one-to-one. The problem comes especially from the difficulty to associate a selection probability, or an estimation weight, to the surveyed units of the target population. In order to solve this type of estimation problem, the Generalized Weight Share Method (GWSM) has been developed by Lavallée (1995) and Lavallée (2002). The GWSM provides an estimation weight for every surveyed unit of the target population.

    This paper first describes Indirect Sampling, which constitutes the foundations of the GWSM. Second, an overview of the GWSM is given where we formulate the GWSM in a theoretical framework using matrix notation. Third, we present some properties of the GWSM such as unbiasedness and transitivity. Fourth, we consider the special case where the links between the two populations are expressed by indicator variables. Fifth, some special typical linkages are studied to assess their impact on the GWSM. Finally, we consider the problem of optimality. We obtain optimal weights in a weak sense (for specific values of the variable of interest), and conditions for which these weights are also optimal in a strong sense and independent of the variable of interest.

    Release date: 2006-12-21

  • Surveys and statistical programs – Documentation: 62F0026M2006001
    Description:

    This guide presents information of interest to users of data from the Survey of Household Spending, which gathers information on the spending habits, dwelling characteristics and household equipment of Canadian households. The survey covers private households in the 10 provinces. (The territories are surveyed every second year, starting in 1999.)

    This guide includes definitions of survey terms and variables, as well as descriptions of survey methodology and data quality. One section describes the various statistics that can be created using expenditure data (e.g., budget share, market share, aggregates and medians).

    Release date: 2006-12-12

  • Technical products: 68-514-X
    Description:

    Statistics Canada's approach to gathering and disseminating economic data has developed over several decades into a highly integrated system for collection and estimation that feeds the framework of the Canadian System of National Accounts.

    The key to this approach was creation of the Unified Enterprise Survey, the goal of which was to improve the consistency, coherence, breadth and depth of business survey data.

    The UES did so by bringing many of Statistics Canada's individual annual business surveys under a common framework. This framework included a single survey frame, a sample design framework, conceptual harmonization of survey content, means of using relevant administrative data, common data collection, processing and analysis tools, and a common data warehouse.

    Release date: 2006-11-20

  • Technical products: 75F0002M2006007
    Description:

    This paper summarizes the data available from SLID on housing characteristics and shelter costs, with a special focus on the imputation methods used for this data. From 1994 to 2001, the survey covered only a few housing characteristics, primarily ownership status and dwelling type. In 2002, with the start of sponsorship from Canada Mortgage and Housing Corporation (CMHC), several other characteristics and detailed shelter costs were added to the survey. Several imputation methods were also introduced at that time, in order to replace missing values due to survey non-response and to provide utility costs, which contribute to total shelter costs. These methods take advantage of SLID's longitudinal design and also use data from other sources such as the Labour Force Survey and the Census. In June 2006, further improvements in the imputation methods were introduced for 2004 and applied to past years in a historical revision. This report also documents that revision.

    Release date: 2006-07-26

  • Articles and reports: 12-001-X20060019256
    Description:

    In some situations the sample design of a survey is rather complex, consisting of fundamentally different designs in different domains. The design effect for estimates based upon the total sample is a weighted sum of the domain-specific design effects. We derive these weights under an appropriate model and illustrate their use with data from the European Social Survey (ESS).

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019259
    Description:

    We describe a general approach to setting the sampling design in surveys that are planned for making inferences about small areas (sub-domains). The approach requires a specification of the inferential priorities for the areas. Sample size allocation schemes are derived first for the direct estimator and then for composite and empirical Bayes estimators. The methods are illustrated on an example of planning a survey of the population of Switzerland and estimating the mean or proportion of a variable for each of its 26 cantons.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019263
    Description:

    In small area estimation, area level models such as the Fay - Herriot model (Fay and Herriot 1979) are widely used to obtain efficient model-based estimators for small areas. The sampling error variances are customarily assumed to be known in the model. In this paper we consider the situation where the sampling error variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling error variances estimators. The Gibbs sampling method is employed to obtain the small area HB estimators. The proposed HB approach automatically takes account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are small. We compare the proposed HB model with the Fay - Herriot model through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform quite well compared to the direct estimates. We also discussed the problem of priors on the variance components.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019264
    Description:

    Sampling for nonresponse follow-up (NRFU) was an innovation for U.S. Decennial Census methodology considered for the year 2000. Sampling for NRFU involves sending field enumerators to only a sample of the housing units that did not respond to the initial mailed questionnaire, thereby reducing costs but creating a major small-area estimation problem. We propose a model to impute the characteristics of the housing units that did not respond to the mailed questionnaire, to benefit from the large cost savings of NRFU sampling while still attaining acceptable levels of accuracy for small areas. Our strategy is to model household characteristics using low-dimensional covariates at detailed levels of geography and more detailed covariates at larger levels of geography. To do this, households are first classified into a small number of types. A hierarchical loglinear model then estimates the distribution of household types among the nonsample nonrespondent households in each block. This distribution depends on the characteristics of mailback respondents in the same block and sampled nonrespondents in nearby blocks. Nonsample nonrespondent households can then be imputed according to this estimated household type distribution. We evaluate the performance of our loglinear model through simulation. Results show that, when compared to estimates from alternative models, our loglinear model produces estimates with much smaller MSE in many cases and estimates with approximately the same size MSE in most other cases. Although sampling for NRFU was not used in the 2000 census, our estimation and imputation strategy can be used in any census or survey using sampling for NRFU where units are clustered such that the characteristics of nonrespondents are related to the characteristics of respondents in the same area and also related to the characteristics of sampled nonrespondents in nearby areas.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019257
    Description:

    In the presence of item nonreponse, two approaches have been traditionally used to make inference on parameters of interest. The first approach assumes uniform response within imputation cells whereas the second approach assumes ignorable response but make use of a model on the variable of interest as the basis for inference. In this paper, we propose a third appoach that assumes a specified ignorable response mechanism without having to specify a model on the variable of interest. In this case, we show how to obtain imputed values which lead to estimators of a total that are approximately unbiased under the proposed approach as well as the second approach. Variance estimators of the imputed estimators that are approximately unbiased are also obtained using an approach of Fay (1991) in which the order of sampling and response is reversed. Finally, simulation studies are conducted to investigate the finite sample performance of the methods in terms of bias and mean square error.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019258
    Description:

    This paper primarily aims at proposing a cost-effective strategy to estimate the intercensal unemployment rate at the provincial level in Iran. Taking advantage of the small area estimation (SAE) methods, this strategy is based on a single sampling at the national level. Three methods of synthetic, composite, and empirical Bayes estimators are used to find the indirect estimates of interest for the year 1996. Findings not only confirm the adequacy of the suggested strategy, but they also indicate that the composite and empirical Bayes estimators perform well and similarly.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019261
    Description:

    Sample allocation can be optimized with respect to various goals. When there is more than one goal, a compromise allocation must be chosen. In the past, the Reverse Record Check achieved that compromise by having a certain fraction of the sample optimally allocated for each goal (for example, two thirds of the sample is allocated to produce good-quality provincial estimates, and one third to produce a good-quality national estimate). This paper suggests a method that involves selecting the maximum of two or more optimal allocations. By analyzing the impact that the precision of population estimates has on the federal government's equalization payments to the provinces, we can set four goals for the Reverse Record Check's provincial sample allocation. The Reverse Record Check's subprovincial sample allocation requires the smoothing of stratum-level parameters. This paper shows how calibration can be used to achieve this smoothing. The calibration problem and its solution do not assume that the calibration constraints have a solution. This avoids convergence problems inherent in related methods such as the raking ratio.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019262
    Description:

    Hidden human populations, the Internet, and other networked structures conceptualized mathematically as graphs are inherently hard to sample by conventional means, and the most effective study designs usually involve procedures that select the sample by adaptively following links from one node to another. Sample data obtained in such studies are generally not representative at face value of the larger population of interest. However, a number of design and model based methods are now available for effective inference from such samples. The design based methods have the advantage that they do not depend on an assumed population model, but do depend for their validity on the design being implemented in a controlled and known way, which can be difficult or impossible in practice. The model based methods allow greater flexibly in the design, but depend on modeling of the population using stochastic graph models and also depend on the design being ignorable or of known form so that it can be included in the likelihood or Bayes equations. For both the design and the model based methods, the weak point often is the lack of control in how the initial sample is obtained, from which link-tracing commences. The designs described in this paper offer a third way, in which the sample selection probabilities become step by step less dependent on the initial sample selection. A Markov chain "random walk" model idealizes the natural design tendencies of a link-tracing selection sequence through a graph. This paper introduces uniform and targeted walk designs in which the random walk is nudged at each step to produce a design with the desired stationary probabilities. A sample is thus obtained that in important respects is representative at face value of the larger population of interest, or that requires only simple weighting factors to make it so.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019255
    Description:

    In this paper, we consider the estimation of quantiles using the calibration paradigm. The proposed methodology relies on an approach similar to the one leading to the original calibration estimators of Deville and Särndal (1992). An appealing property of the new methodology is that it is not necessary to know the values of the auxiliary variables for all units in the population. It suffices instead to know the corresponding quantiles for the auxiliary variables. When the quadratic metric is adopted, an analytic representation of the calibration weights is obtained. In this situation, the weights are similar to those leading to the generalized regression (GREG) estimator. Variance estimation and construction of confidence intervals are discussed. In a small simulation study, a calibration estimator is compared to other popular estimators for quantiles that also make use of auxiliary information.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019266
    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: 2006-07-20

  • Articles and reports: 12-001-X20060019260
    Description:

    This paper considers the use of imputation and weighting to correct for measurement error in the estimation of a distribution function. The paper is motivated by the problem of estimating the distribution of hourly pay in the United Kingdom, using data from the Labour Force Survey. Errors in measurement lead to bias and the aim is to use auxiliary data, measured accurately for a subsample, to correct for this bias. Alternative point estimators are considered, based upon a variety of imputation and weighting approaches, including fractional imputation, nearest neighbour imputation, predictive mean matching and propensity score weighting. Properties of these point estimators are then compared both theoretically and by simulation. A fractional predictive mean matching imputation approach is advocated. It performs similarly to propensity score weighting, but displays slight advantages of robustness and efficiency.

    Release date: 2006-07-20

Data (0)

Data (0) (0 results)

Your search for "" found no results in this section of the site.

You may try:

Analysis (36)

Analysis (36) (25 of 36 results)

  • Articles and reports: 12-001-X20060029550
    Description:

    In this paper, the geometric, optimization-based, and Lavallée and Hidiroglou (LH) approaches to stratification are compared. The geometric stratification method is an approximation, whereas the other two approaches, which employ numerical methods to perform stratification, may be seen as optimal stratification methods. The algorithm of the geometric stratification is very simple compared to the two other approaches, but it does not take into account the construction of a take-all stratum, which is usually constructed when a positively skewed population is stratified. In the optimization-based stratification, one may consider any form of optimization function and its constraints. In a comparative numerical study based on five positively skewed artificial populations, the optimization approach was more efficient in each of the cases studied compared to the geometric stratification. In addition, the geometric and optimization approaches are compared with the LH algorithm. In this comparison, the geometric stratification approach was found to be less efficient than the LH algorithm, whereas efficiency of the optimization approach was similar to the efficiency of the LH algorithm. Nevertheless, strata boundaries evaluated via the geometric stratification may be seen as efficient starting points for the optimization approach.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029555
    Description:

    Researchers and policy makers often use data from nationally representative probability sample surveys. The number of topics covered by such surveys, and hence the amount of interviewing time involved, have typically increased over the years, resulting in increased costs and respondent burden. A potential solution to this problem is to carefully form subsets of the items in a survey and administer one such subset to each respondent. Designs of this type are called "split-questionnaire" designs or "matrix sampling" designs. The administration of only a subset of the survey items to each respondent in a matrix sampling design creates what can be considered missing data. Multiple imputation (Rubin 1987), a general-purpose approach developed for handling data with missing values, is appealing for the analysis of data from a matrix sample, because once the multiple imputations are created, data analysts can apply standard methods for analyzing complete data from a sample survey. This paper develops and evaluates a method for creating matrix sampling forms, each form containing a subset of items to be administered to randomly selected respondents. The method can be applied in complex settings, including situations in which skip patterns are present. Forms are created in such a way that each form includes items that are predictive of the excluded items, so that subsequent analyses based on multiple imputation can recover some of the information about the excluded items that would have been collected had there been no matrix sampling. The matrix sampling and multiple-imputation methods are evaluated using data from the National Health and Nutrition Examination Survey, one of many nationally representative probability sample surveys conducted by the National Center for Health Statistics, Centers for Disease Control and Prevention. The study demonstrates the feasibility of the approach applied to a major national health survey with complex structure, and it provides practical advice about appropriate items to include in matrix sampling designs in future surveys.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029553
    Description:

    Félix-Medina and Thompson (2004) proposed a variant of Link-tracing sampling in which it is assumed that a portion of the population, not necessarily the major portion, is covered by a frame of disjoint sites where members of the population can be found with high probabilities. A sample of sites is selected and the people in each of the selected sites are asked to nominate other members of the population. They proposed maximum likelihood estimators of the population sizes which perform acceptably provided that for each site the probability that a member is nominated by that site, called the nomination probability, is not small. In this research we consider Félix-Medina and Thompson's variant and propose three sets of estimators of the population sizes derived under the Bayesian approach. Two of the sets of estimators were obtained using improper prior distributions of the population sizes, and the other using Poisson prior distributions. However, we use the Bayesian approach only to assist us in the construction of estimators, while inferences about the population sizes are made under the frequentist approach. We propose two types of partly design-based variance estimators and confidence intervals. One of them is obtained using a bootstrap and the other using the delta method along with the assumption of asymptotic normality. The results of a simulation study indicate that (i) when the nomination probabilities are not small each of the proposed sets of estimators performs well and very similarly to maximum likelihood estimators; (ii) when the nomination probabilities are small the set of estimators derived using Poisson prior distributions still performs acceptably and does not have the problems of bias that maximum likelihood estimators have, and (iii) the previous results do not depend on the size of the fraction of the population covered by the frame.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029546
    Description:

    We discuss methods for the analysis of case-control studies in which the controls are drawn using a complex sample survey. The most straightforward method is the standard survey approach based on weighted versions of population estimating equations. We also look at more efficient methods and compare their robustness to model mis-specification in simple cases. Case-control family studies, where the within-cluster structure is of interest in its own right, are also discussed briefly.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029547
    Description:

    Calibration weighting can be used to adjust for unit nonresponse and/or coverage errors under appropriate quasi-randomization models. Alternative calibration adjustments that are asymptotically identical in a purely sampling context can diverge when used in this manner. Introducing instrumental variables into calibration weighting makes it possible for nonresponse (say) to be a function of a set of characteristics other than those in the calibration vector. When the calibration adjustment has a nonlinear form, a variant of the jackknife can remove the need for iteration in variance estimation.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029548
    Description:

    The theory of multiple imputation for missing data requires that imputations be made conditional on the sampling design. However, most standard software packages for performing model-based multiple imputation assume simple random samples, leading many practitioners not to account for complex sample design features, such as stratification and clustering, in their imputations. Theory predicts that analyses of such multiply-imputed data sets can yield biased estimates from the design-based perspective. In this article, we illustrate through simulation that (i) the bias can be severe when the design features are related to the survey variables of interest, and (ii) the bias can be reduced by controlling for the design features in the imputation models. The simulations also illustrate that conditioning on irrelevant design features in the imputation models can yield conservative inferences, provided that the models include other relevant predictors. These results suggest a prescription for imputers: the safest course of action is to include design variables in the specification of imputation models. Using real data, we demonstrate a simple approach for incorporating complex design features that can be used with some of the standard software packages for creating multiple imputations.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029554
    Description:

    Survey sampling to estimate a Consumer Price Index (CPI) is quite complicated, generally requiring a combination of data from at least two surveys: one giving prices, one giving expenditure weights. Fundamentally different approaches to the sampling process - probability sampling and purposive sampling - have each been strongly advocated and are used by different countries in the collection of price data. By constructing a small "world" of purchases and prices from scanner data on cereal and then simulating various sampling and estimation techniques, we compare the results of two design and estimation approaches: the probability approach of the United States and the purposive approach of the United Kingdom. For the same amount of information collected, but given the use of different estimators, the United Kingdom's methods appear to offer better overall accuracy in targeting a population superlative consumer price index.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029552
    Description:

    A survey of tourist visits originating intra and extra-region in Brittany was needed. For concrete material reasons, "border surveys" could no longer be used. The major problem is the lack of a sampling frame that allows for direct contact with tourists. This problem was addressed by applying the indirect sampling method, the weighting for which is obtained using the generalized weight share method developed recently by Lavallée (1995), Lavallée (2002), Deville (1999) and also presented recently in Lavallée and Caron (2001). This article shows how to adapt the method to the survey. A number of extensions are required. One of the extensions, designed to estimate the total of a population from which a Bernouilli sample has been taken, will be developed.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029549
    Description:

    In this article, we propose a Bernoulli-type bootstrap method that can easily handle multi-stage stratified designs where sampling fractions are large, provided simple random sampling without replacement is used at each stage. The method provides a set of replicate weights which yield consistent variance estimates for both smooth and non-smooth estimators. The method's strength is in its simplicity. It can easily be extended to any number of stages without much complication. The main idea is to either keep or replace a sampling unit at each stage with preassigned probabilities, to construct the bootstrap sample. A limited simulation study is presented to evaluate performance and, as an illustration, we apply the method to the 1997 Japanese National Survey of Prices.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060029561
    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: 2006-12-21

  • Articles and reports: 12-001-X20060029551
    Description:

    To select a survey sample, it happens that one does not have a frame containing the desired collection units, but rather another frame of units linked in a certain way to the list of collection units. It can then be considered to select a sample from the available frame in order to produce an estimate for the desired target population by using the links existing between the two. This can be designated by Indirect Sampling.

    Estimation for the target population surveyed by Indirect Sampling can constitute a big challenge, in particular if the links between the units of the two are not one-to-one. The problem comes especially from the difficulty to associate a selection probability, or an estimation weight, to the surveyed units of the target population. In order to solve this type of estimation problem, the Generalized Weight Share Method (GWSM) has been developed by Lavallée (1995) and Lavallée (2002). The GWSM provides an estimation weight for every surveyed unit of the target population.

    This paper first describes Indirect Sampling, which constitutes the foundations of the GWSM. Second, an overview of the GWSM is given where we formulate the GWSM in a theoretical framework using matrix notation. Third, we present some properties of the GWSM such as unbiasedness and transitivity. Fourth, we consider the special case where the links between the two populations are expressed by indicator variables. Fifth, some special typical linkages are studied to assess their impact on the GWSM. Finally, we consider the problem of optimality. We obtain optimal weights in a weak sense (for specific values of the variable of interest), and conditions for which these weights are also optimal in a strong sense and independent of the variable of interest.

    Release date: 2006-12-21

  • Articles and reports: 12-001-X20060019256
    Description:

    In some situations the sample design of a survey is rather complex, consisting of fundamentally different designs in different domains. The design effect for estimates based upon the total sample is a weighted sum of the domain-specific design effects. We derive these weights under an appropriate model and illustrate their use with data from the European Social Survey (ESS).

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019259
    Description:

    We describe a general approach to setting the sampling design in surveys that are planned for making inferences about small areas (sub-domains). The approach requires a specification of the inferential priorities for the areas. Sample size allocation schemes are derived first for the direct estimator and then for composite and empirical Bayes estimators. The methods are illustrated on an example of planning a survey of the population of Switzerland and estimating the mean or proportion of a variable for each of its 26 cantons.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019263
    Description:

    In small area estimation, area level models such as the Fay - Herriot model (Fay and Herriot 1979) are widely used to obtain efficient model-based estimators for small areas. The sampling error variances are customarily assumed to be known in the model. In this paper we consider the situation where the sampling error variances are estimated individually by direct estimators. A full hierarchical Bayes (HB) model is constructed for the direct survey estimators and the sampling error variances estimators. The Gibbs sampling method is employed to obtain the small area HB estimators. The proposed HB approach automatically takes account of the extra uncertainty of estimating the sampling error variances, especially when the area-specific sample sizes are small. We compare the proposed HB model with the Fay - Herriot model through analysis of two survey data sets. Our results have shown that the proposed HB estimators perform quite well compared to the direct estimates. We also discussed the problem of priors on the variance components.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019264
    Description:

    Sampling for nonresponse follow-up (NRFU) was an innovation for U.S. Decennial Census methodology considered for the year 2000. Sampling for NRFU involves sending field enumerators to only a sample of the housing units that did not respond to the initial mailed questionnaire, thereby reducing costs but creating a major small-area estimation problem. We propose a model to impute the characteristics of the housing units that did not respond to the mailed questionnaire, to benefit from the large cost savings of NRFU sampling while still attaining acceptable levels of accuracy for small areas. Our strategy is to model household characteristics using low-dimensional covariates at detailed levels of geography and more detailed covariates at larger levels of geography. To do this, households are first classified into a small number of types. A hierarchical loglinear model then estimates the distribution of household types among the nonsample nonrespondent households in each block. This distribution depends on the characteristics of mailback respondents in the same block and sampled nonrespondents in nearby blocks. Nonsample nonrespondent households can then be imputed according to this estimated household type distribution. We evaluate the performance of our loglinear model through simulation. Results show that, when compared to estimates from alternative models, our loglinear model produces estimates with much smaller MSE in many cases and estimates with approximately the same size MSE in most other cases. Although sampling for NRFU was not used in the 2000 census, our estimation and imputation strategy can be used in any census or survey using sampling for NRFU where units are clustered such that the characteristics of nonrespondents are related to the characteristics of respondents in the same area and also related to the characteristics of sampled nonrespondents in nearby areas.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019257
    Description:

    In the presence of item nonreponse, two approaches have been traditionally used to make inference on parameters of interest. The first approach assumes uniform response within imputation cells whereas the second approach assumes ignorable response but make use of a model on the variable of interest as the basis for inference. In this paper, we propose a third appoach that assumes a specified ignorable response mechanism without having to specify a model on the variable of interest. In this case, we show how to obtain imputed values which lead to estimators of a total that are approximately unbiased under the proposed approach as well as the second approach. Variance estimators of the imputed estimators that are approximately unbiased are also obtained using an approach of Fay (1991) in which the order of sampling and response is reversed. Finally, simulation studies are conducted to investigate the finite sample performance of the methods in terms of bias and mean square error.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019258
    Description:

    This paper primarily aims at proposing a cost-effective strategy to estimate the intercensal unemployment rate at the provincial level in Iran. Taking advantage of the small area estimation (SAE) methods, this strategy is based on a single sampling at the national level. Three methods of synthetic, composite, and empirical Bayes estimators are used to find the indirect estimates of interest for the year 1996. Findings not only confirm the adequacy of the suggested strategy, but they also indicate that the composite and empirical Bayes estimators perform well and similarly.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019261
    Description:

    Sample allocation can be optimized with respect to various goals. When there is more than one goal, a compromise allocation must be chosen. In the past, the Reverse Record Check achieved that compromise by having a certain fraction of the sample optimally allocated for each goal (for example, two thirds of the sample is allocated to produce good-quality provincial estimates, and one third to produce a good-quality national estimate). This paper suggests a method that involves selecting the maximum of two or more optimal allocations. By analyzing the impact that the precision of population estimates has on the federal government's equalization payments to the provinces, we can set four goals for the Reverse Record Check's provincial sample allocation. The Reverse Record Check's subprovincial sample allocation requires the smoothing of stratum-level parameters. This paper shows how calibration can be used to achieve this smoothing. The calibration problem and its solution do not assume that the calibration constraints have a solution. This avoids convergence problems inherent in related methods such as the raking ratio.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019262
    Description:

    Hidden human populations, the Internet, and other networked structures conceptualized mathematically as graphs are inherently hard to sample by conventional means, and the most effective study designs usually involve procedures that select the sample by adaptively following links from one node to another. Sample data obtained in such studies are generally not representative at face value of the larger population of interest. However, a number of design and model based methods are now available for effective inference from such samples. The design based methods have the advantage that they do not depend on an assumed population model, but do depend for their validity on the design being implemented in a controlled and known way, which can be difficult or impossible in practice. The model based methods allow greater flexibly in the design, but depend on modeling of the population using stochastic graph models and also depend on the design being ignorable or of known form so that it can be included in the likelihood or Bayes equations. For both the design and the model based methods, the weak point often is the lack of control in how the initial sample is obtained, from which link-tracing commences. The designs described in this paper offer a third way, in which the sample selection probabilities become step by step less dependent on the initial sample selection. A Markov chain "random walk" model idealizes the natural design tendencies of a link-tracing selection sequence through a graph. This paper introduces uniform and targeted walk designs in which the random walk is nudged at each step to produce a design with the desired stationary probabilities. A sample is thus obtained that in important respects is representative at face value of the larger population of interest, or that requires only simple weighting factors to make it so.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019255
    Description:

    In this paper, we consider the estimation of quantiles using the calibration paradigm. The proposed methodology relies on an approach similar to the one leading to the original calibration estimators of Deville and Särndal (1992). An appealing property of the new methodology is that it is not necessary to know the values of the auxiliary variables for all units in the population. It suffices instead to know the corresponding quantiles for the auxiliary variables. When the quadratic metric is adopted, an analytic representation of the calibration weights is obtained. In this situation, the weights are similar to those leading to the generalized regression (GREG) estimator. Variance estimation and construction of confidence intervals are discussed. In a small simulation study, a calibration estimator is compared to other popular estimators for quantiles that also make use of auxiliary information.

    Release date: 2006-07-20

  • Articles and reports: 12-001-X20060019266
    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: 2006-07-20

  • Articles and reports: 12-001-X20060019260
    Description:

    This paper considers the use of imputation and weighting to correct for measurement error in the estimation of a distribution function. The paper is motivated by the problem of estimating the distribution of hourly pay in the United Kingdom, using data from the Labour Force Survey. Errors in measurement lead to bias and the aim is to use auxiliary data, measured accurately for a subsample, to correct for this bias. Alternative point estimators are considered, based upon a variety of imputation and weighting approaches, including fractional imputation, nearest neighbour imputation, predictive mean matching and propensity score weighting. Properties of these point estimators are then compared both theoretically and by simulation. A fractional predictive mean matching imputation approach is advocated. It performs similarly to propensity score weighting, but displays slight advantages of robustness and efficiency.

    Release date: 2006-07-20

  • Articles and reports: 89-552-M2006014
    Description:

    This paper examines the role of human capital accumulation in explaining the relative levels of income per capita across Canadian provinces. We use principally two different types of human capital indicators based respectively on university attainment and literacy test scores. A synthetic time series of the average literacy level of labour market entrants for each period between 1951 and 2001 is constructed from the demographic profile of literacy test scores taken from the 2003 Adult Literacy and Lifeskills Survey. The percentage of the working-age population holding a university degree is available since 1951 from the census figures. Our main results are the following. First, both human capital indicators are strong predictors of the relative levels of per capita income (minus government transfers) across provinces, along with the relative rates of urbanization and specific shocks in Alberta and Quebec. Second, the skills acquired by one extra year of schooling result in an increase in per capita income of around 7.3 percent. Third, we find that our literacy indicator does not outperform the university attainment indicator. This contrasts sharply with our recent result found at the cross-country level (Coulombe, Tremblay, and Marchand [2004]) and suggests substantial measurement error in cross-country schooling data. Fourth, by focusing on regional economies that have similar levels of social infrastructure and social development, our analysis provides potentially more reliable estimates of the contribution of human capital accumulation to relative living standards.

    Release date: 2006-04-05

  • Articles and reports: 12-001-X20050029052
    Description:

    Estimates of a sampling variance-covariance matrix are required in many statistical analyses, particularly for multilevel analysis. In univariate problems, functions relating the variance to the mean have been used to obtain variance estimates, pooling information across units or variables. We present variance and correlation functions for multivariate means of ordinal survey items, both for complete data and for data with structured non-response. Methods are also developed for assessing model fit, and for computing composite estimators that combine direct and model-based predictions. Survey data from the Consumer Assessments of Health Plans Study (CAHPS®) illustrate the application of the methodology.

    Release date: 2006-02-17

  • Articles and reports: 12-001-X20050029049
    Description:

    Nonresponse weight adjustment is commonly used to compensate for unit nonresponse in surveys. Often, a nonresponse model is postulated and design weights are adjusted by the inverse of estimated response probabilities. Typical nonresponse models are conditional on a vector of fixed auxiliary variables that are observed for every sample unit, such as variables used to construct the sampling design. In this note, we consider using data collection process variables as potential auxiliary variables. An example is the number of attempts to contact a sample unit. In our treatment, these auxiliary variables are taken to be random, even after conditioning on the selected sample, since they could change if the data collection process were repeated for a given sample. We show that this randomness introduces no bias and no additional variance component in the estimates of population totals when the nonresponse model is properly specified. Moreover, when nonresponse depends on the variables of interest, we argue that the use of data collection process variables is likely to reduce the nonresponse bias if they provide information about the variables of interest not already included in the nonresponse model and if they are associated with nonresponse. As a result, data collection process variables may well be beneficial to handle unit nonresponse. This is briefly illustrated using the Canadian Labour Force Survey.

    Release date: 2006-02-17

Reference (13)

Reference (13) (13 of 13 results)

  • Surveys and statistical programs – Documentation: 62F0026M2006001
    Description:

    This guide presents information of interest to users of data from the Survey of Household Spending, which gathers information on the spending habits, dwelling characteristics and household equipment of Canadian households. The survey covers private households in the 10 provinces. (The territories are surveyed every second year, starting in 1999.)

    This guide includes definitions of survey terms and variables, as well as descriptions of survey methodology and data quality. One section describes the various statistics that can be created using expenditure data (e.g., budget share, market share, aggregates and medians).

    Release date: 2006-12-12

  • Technical products: 68-514-X
    Description:

    Statistics Canada's approach to gathering and disseminating economic data has developed over several decades into a highly integrated system for collection and estimation that feeds the framework of the Canadian System of National Accounts.

    The key to this approach was creation of the Unified Enterprise Survey, the goal of which was to improve the consistency, coherence, breadth and depth of business survey data.

    The UES did so by bringing many of Statistics Canada's individual annual business surveys under a common framework. This framework included a single survey frame, a sample design framework, conceptual harmonization of survey content, means of using relevant administrative data, common data collection, processing and analysis tools, and a common data warehouse.

    Release date: 2006-11-20

  • Technical products: 75F0002M2006007
    Description:

    This paper summarizes the data available from SLID on housing characteristics and shelter costs, with a special focus on the imputation methods used for this data. From 1994 to 2001, the survey covered only a few housing characteristics, primarily ownership status and dwelling type. In 2002, with the start of sponsorship from Canada Mortgage and Housing Corporation (CMHC), several other characteristics and detailed shelter costs were added to the survey. Several imputation methods were also introduced at that time, in order to replace missing values due to survey non-response and to provide utility costs, which contribute to total shelter costs. These methods take advantage of SLID's longitudinal design and also use data from other sources such as the Labour Force Survey and the Census. In June 2006, further improvements in the imputation methods were introduced for 2004 and applied to past years in a historical revision. This report also documents that revision.

    Release date: 2006-07-26

  • Technical products: 12-002-X20060019253
    Description:

    Before any analytical results are released from the Research Data Centres (RDCs), RDC analysts must conduct disclosure risk analysis (or vetting). RDC analysts apply Statistics Canada's disclosure control guidelines, when reviewing all analytical output, as a means of ensuring the protection of survey respondents' confidentiality. For some data sets, such as the Aboriginal People's Survey (APS), Ethnic Diversity Survey (EDS), the Participation, Activity and Limitation Survey (PALS) and the Longitudinal Survey of Immigrants to Canada (LSIC), Statistics Canada has developed an additional set of guidelines that involve rounding analytical results, in order to ensure further confidentiality protection. This article will discuss the rationale for the additional rounding procedures used for these data sets, and describe the specifics of the rounding guidelines. More importantly, this paper will suggest several approaches to assist researchers in following these protocols more effectively and efficiently.

    Release date: 2006-07-18

  • Technical products: 12-002-X20060019254
    Description:

    This article explains how to append census area-level summary data to survey or administrative data. It uses examples from datasets present in Statistics Canada Research Data Centres, but the methods also apply to external datasets. Four examples illustrate common situations faced by researchers: (1) when the survey (or administrative) and census data both contain the same level of geographic identifiers, coded to the same year standard ("vintage") of census geography; (2) when the two files contain geographic identifiers of the same vintage, but at different levels of census geography; (3) when the two files contain data coded to different vintages of census geography; (4) when the survey data are lacking in geographic identifiers, and those identifiers must first be generated from postal codes present on the file. The examples are shown using SAS syntax, but the principles apply to other programming languages or statistical packages.

    Release date: 2006-07-18

  • Classification: 82-225-X20060099205
    Description:

    The Death Clearance Overview document describes the Death Clearance module of the Canadian Cancer Registry, its structure, its function and its role in the operation of the national cancer registry. Inputs and outputs are listed and briefly described, as well as the different steps constituting the Death Clearance process.

    Release date: 2006-07-07

  • Technical products: 21-601-M2006079
    Description:

    The findings in this working paper highlight the importance of public support in addressing the capital requirements of functional food and nutraceutical firms and underscore the considerable burden in this respect borne by smaller sized firms.

    Release date: 2006-06-15

  • Technical products: 75F0002M2006001
    Description:

    A Preliminary interview of background information is collected for all respondents aged 16 and over, who enter the sample for the Survey of Labour and Income Dynamics (SLID). For the majority of the longitudinal respondents, this occurs when a new panel is introduced and the preliminary information is collected during the first Labour interview. However, all persons living with a longitudinal respondent are also interviewed for SLID. Thus Preliminary interviews are conducted for new household members during their first Labour interview after they join the household. Longitudinal persons who have turned 16 while their household is in the SLID sample are then eligible for SLID interviews so they are asked the Preliminary interview questions during their first Labour interview.

    The purpose of this document is to present the questions, possible responses and question flows for the 2005 Preliminary questionnaire (for the 2004 reference year).

    Release date: 2006-04-06

  • Technical products: 75F0002M2006003
    Description:

    The Survey of Income and Labour Dynamics (SLID) interview is conducted using computer-assisted interviewing (CAI). CAI is paperless interviewing. This document is therefore a written approximation of the CAI interview, or the questionnaire.

    In previous years, SLID conducted a Labour interview each January and a separate Income interview in May. In 2005 (reference year 2004) the two interviews were combined and collected in one interview in January.

    A labour and income interview is collected for all respondents 16 years of age and over. Respondents have the option of answering income questions during the interview, or of giving Statistics Canada permission to use their income tax records.

    In January 2005, data was collected for reference year 2004 from panels 3 and 4. Panel 3, in its sixth and final year, consisted of approximately 17,000 households and panel 4, in its third year, also consisted of approximately 17,000 households.

    This document outlines the structure of the January 2005 Labour and Income interview (for the 2004 reference year) including question wording, possible responses, and flows of questions.

    Release date: 2006-04-06

  • Technical products: 75F0002M2006005
    Description:

    The Survey of Labour and Income Dynamics (SLID) is a longitudinal survey initiated in 1993. The survey was designed to measure changes in the economic well-being of Canadians as well as the factors affecting these changes.

    Sample surveys are subject to errors. As with all surveys conducted at Statistics Canada, considerable time and effort is taken to control such errors at every stage of the Survey of Labour and Income Dynamics. Nonetheless errors do occur. It is the policy at Statistics Canada to furnish users with measures of data quality so that the user is able to interpret the data properly. This report summarizes a set of quality measures that has been produced in an attempt to describe the overall quality of SLID data. Among the measures included in the report are sample composition and attrition rates, sampling errors, coverage errors in the form of slippage rates, response rates, tax permission and tax linkage rates, and imputation rates.

    Release date: 2006-04-06

  • Technical products: 75F0002M2006002
    Description:

    In previous years, the Survey of Labour and Income Dynamics (SLID) conducted a Labour interview each January and a separate Income interview in May. In 2005 (reference year 2004) the two interviews were combined and collected in one interview in January.

    The data are collected using computer-assisted interviewing. Thus there are no paper questionnaires required for data collection. The questions, responses and interview flow for Labour and Income are documented in other SLID research papers. This document presents the information for the 2005 Entry Exit portion of the Labour Income interview (for the 2004 reference year).

    The Entry Exit Component consists of five separate modules. The Entry module is the first set of data collected. It is information collected to update the place of residence, housing conditions and expenses, as well as the household composition. For each person identified in Entry, the Demographics module collects (or updates) the person's name, date of birth, sex and marital status. Then the Relationships module identifies (or updates) the relationship between each respondent and every other household member. The Exit module includes questions on who to contact for the next interview and the names, phone numbers and addresses of two contacts to be used only if future tracing of respondents is required. An overview of the Tracing component is also included in this document.

    Release date: 2006-03-27

  • Index and guides: 92-134-X
    Description:

    This document summarizes the results of content analyses of the 2004 Census Test. The first section briefly explains the context of the content analyses by describing the nature of the sample, its limitations and the strategies used to evaluate data quality. The second section provides an overview of the results for questions that have not changed since the 2001 Census by describing the similarities between 2001 and 2004 distributions and non-response rates. The third section evaluates data quality of new census questions or questions that have changed substantially: same-sex married couples, ethnic origins, levels of schooling, location where highest diploma was obtained, school attendance, permission to access income tax files, and permission to make personal data publicly available 92 years after the census. The last section summarizes the overall results for questions whose content was coded and evaluated as part of the 2004 test, namely industry, occupation and place of work variables.

    Release date: 2006-03-21

  • Surveys and statistical programs – Documentation: 71F0031X2006003
    Description:

    This paper introduces and explains modifications made to the Labour Force Survey estimates in January 2006. Some of these modifications include changes to the population estimates, improvements to the public and private sector estimates and historical updates to several small Census Agglomerations (CA).

    Release date: 2006-01-25

Date modified: