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  • Articles and reports: 12-001-X202200100008
    Description:

    The Multiple Imputation of Latent Classes (MILC) method combines multiple imputation and latent class analysis to correct for misclassification in combined datasets. Furthermore, MILC generates a multiply imputed dataset which can be used to estimate different statistics in a straightforward manner, ensuring that uncertainty due to misclassification is incorporated when estimating the total variance. In this paper, it is investigated how the MILC method can be adjusted to be applied for census purposes. More specifically, it is investigated how the MILC method deals with a finite and complete population register, how the MILC method can simultaneously correct misclassification in multiple latent variables and how multiple edit restrictions can be incorporated. A simulation study shows that the MILC method is in general able to reproduce cell frequencies in both low- and high-dimensional tables with low amounts of bias. In addition, variance can also be estimated appropriately, although variance is overestimated when cell frequencies are small.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100100004
    Description:

    Multiple data sources are becoming increasingly available for statistical analyses in the era of big data. As an important example in finite-population inference, we consider an imputation approach to combining data from a probability survey and big found data. We focus on the case when the study variable is observed in the big data only, but the other auxiliary variables are commonly observed in both data. Unlike the usual imputation for missing data analysis, we create imputed values for all units in the probability sample. Such mass imputation is attractive in the context of survey data integration (Kim and Rao, 2012). We extend mass imputation as a tool for data integration of survey data and big non-survey data. The mass imputation methods and their statistical properties are presented. The matching estimator of Rivers (2007) is also covered as a special case. Variance estimation with mass-imputed data is discussed. The simulation results demonstrate the proposed estimators outperform existing competitors in terms of robustness and efficiency.

    Release date: 2021-06-24

  • Articles and reports: 12-001-X202100100009
    Description:

    Predictive mean matching is a commonly used imputation procedure for addressing the problem of item nonresponse in surveys. The customary approach relies upon the specification of a single outcome regression model. In this note, we propose a novel predictive mean matching procedure that allows the user to specify multiple outcome regression models. The resulting estimator is multiply robust in the sense that it remains consistent if one of the specified outcome regression models is correctly specified. The results from a simulation study suggest that the proposed method performs well in terms of bias and efficiency.

    Release date: 2021-06-24

  • Articles and reports: 12-001-X202000100006
    Description:

    In surveys, logical boundaries among variables or among waves of surveys make imputation of missing values complicated. We propose a new regression-based multiple imputation method to deal with survey nonresponses with two-sided logical boundaries. This imputation method automatically satisfies the boundary conditions without an additional acceptance/rejection procedure and utilizes the boundary information to derive an imputed value and to determine the suitability of the imputed value. Simulation results show that our new imputation method outperforms the existing imputation methods for both mean and quantile estimations regardless of missing rates, error distributions, and missing-mechanisms. We apply our method to impute the self-reported variable “years of smoking” in successive health screenings of Koreans.

    Release date: 2020-06-30

  • Articles and reports: 12-001-X201900200001
    Description:

    Development of imputation procedures appropriate for data with extreme values or nonlinear relationships to covariates is a significant challenge in large scale surveys. We develop an imputation procedure for complex surveys based on semiparametric quantile regression. We apply the method to the Conservation Effects Assessment Project (CEAP), a large-scale survey that collects data used in quantifying soil loss from crop fields. In the imputation procedure, we first generate imputed values from a semiparametric model for the quantiles of the conditional distribution of the response given a covariate. Then, we estimate the parameters of interest using the generalized method of moments (GMM). We derive the asymptotic distribution of the GMM estimators for a general class of complex survey designs. In simulations meant to represent the CEAP data, we evaluate variance estimators based on the asymptotic distribution and compare the semiparametric quantile regression imputation (QRI) method to fully parametric and nonparametric alternatives. The QRI procedure is more efficient than nonparametric and fully parametric alternatives, and empirical coverages of confidence intervals are within 1% of the nominal 95% level. An application to estimation of mean erosion indicates that QRI may be a viable option for CEAP.

    Release date: 2019-06-27

  • Articles and reports: 12-001-X201900100009
    Description:

    The demand for small area estimates by users of Statistics Canada’s data has been steadily increasing over recent years. In this paper, we provide a summary of procedures that have been incorporated into a SAS based production system for producing official small area estimates at Statistics Canada. This system includes: procedures based on unit or area level models; the incorporation of the sampling design; the ability to smooth the design variance for each small area if an area level model is used; the ability to ensure that the small area estimates add up to reliable higher level estimates; and the development of diagnostic tools to test the adequacy of the model. The production system has been used to produce small area estimates on an experimental basis for several surveys at Statistics Canada that include: the estimation of health characteristics, the estimation of under-coverage in the census, the estimation of manufacturing sales and the estimation of unemployment rates and employment counts for the Labour Force Survey. Some of the diagnostics implemented in the system are illustrated using Labour Force Survey data along with administrative auxiliary data.

    Release date: 2019-05-07

  • Articles and reports: 12-001-X201700114823
    Description:

    The derivation of estimators in a multi-phase calibration process requires a sequential computation of estimators and calibrated weights of previous phases in order to obtain those of later ones. Already after two phases of calibration the estimators and their variances involve calibration factors from both phases and the formulae become cumbersome and uninformative. As a consequence the literature so far deals mainly with two phases while three phases or more are rarely being considered. The analysis in some cases is ad-hoc for a specific design and no comprehensive methodology for constructing calibrated estimators, and more challengingly, estimating their variances in three or more phases was formed. We provide a closed form formula for the variance of multi-phase calibrated estimators that holds for any number of phases. By specifying a new presentation of multi-phase calibrated weights it is possible to construct calibrated estimators that have the form of multi-variate regression estimators which enables a computation of a consistent estimator for their variance. This new variance estimator is not only general for any number of phases but also has some favorable characteristics. A comparison to other estimators in the special case of two-phase calibration and another independent study for three phases are presented.

    Release date: 2017-06-22

  • Articles and reports: 11-633-X2017006
    Description:

    This paper describes a method of imputing missing postal codes in a longitudinal database. The 1991 Canadian Census Health and Environment Cohort (CanCHEC), which contains information on individuals from the 1991 Census long-form questionnaire linked with T1 tax return files for the 1984-to-2011 period, is used to illustrate and validate the method. The cohort contains up to 28 consecutive fields for postal code of residence, but because of frequent gaps in postal code history, missing postal codes must be imputed. To validate the imputation method, two experiments were devised where 5% and 10% of all postal codes from a subset with full history were randomly removed and imputed.

    Release date: 2017-03-13

  • Articles and reports: 12-001-X201600214661
    Description:

    An example presented by Jean-Claude Deville in 2005 is subjected to three estimation methods: the method of moments, the maximum likelihood method, and generalized calibration. The three methods yield exactly the same results for the two non-response models. A discussion follows on how to choose the most appropriate model.

    Release date: 2016-12-20

  • Articles and reports: 12-001-X201600214676
    Description:

    Winsorization procedures replace extreme values with less extreme values, effectively moving the original extreme values toward the center of the distribution. Winsorization therefore both detects and treats influential values. Mulry, Oliver and Kaputa (2014) compare the performance of the one-sided Winsorization method developed by Clark (1995) and described by Chambers, Kokic, Smith and Cruddas (2000) to the performance of M-estimation (Beaumont and Alavi 2004) in highly skewed business population data. One aspect of particular interest for methods that detect and treat influential values is the range of values designated as influential, called the detection region. The Clark Winsorization algorithm is easy to implement and can be extremely effective. However, the resultant detection region is highly dependent on the number of influential values in the sample, especially when the survey totals are expected to vary greatly by collection period. In this note, we examine the effect of the number and magnitude of influential values on the detection regions from Clark Winsorization using data simulated to realistically reflect the properties of the population for the Monthly Retail Trade Survey (MRTS) conducted by the U.S. Census Bureau. Estimates from the MRTS and other economic surveys are used in economic indicators, such as the Gross Domestic Product (GDP).

    Release date: 2016-12-20
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  • Articles and reports: 12-001-X202200100008
    Description:

    The Multiple Imputation of Latent Classes (MILC) method combines multiple imputation and latent class analysis to correct for misclassification in combined datasets. Furthermore, MILC generates a multiply imputed dataset which can be used to estimate different statistics in a straightforward manner, ensuring that uncertainty due to misclassification is incorporated when estimating the total variance. In this paper, it is investigated how the MILC method can be adjusted to be applied for census purposes. More specifically, it is investigated how the MILC method deals with a finite and complete population register, how the MILC method can simultaneously correct misclassification in multiple latent variables and how multiple edit restrictions can be incorporated. A simulation study shows that the MILC method is in general able to reproduce cell frequencies in both low- and high-dimensional tables with low amounts of bias. In addition, variance can also be estimated appropriately, although variance is overestimated when cell frequencies are small.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X202100100004
    Description:

    Multiple data sources are becoming increasingly available for statistical analyses in the era of big data. As an important example in finite-population inference, we consider an imputation approach to combining data from a probability survey and big found data. We focus on the case when the study variable is observed in the big data only, but the other auxiliary variables are commonly observed in both data. Unlike the usual imputation for missing data analysis, we create imputed values for all units in the probability sample. Such mass imputation is attractive in the context of survey data integration (Kim and Rao, 2012). We extend mass imputation as a tool for data integration of survey data and big non-survey data. The mass imputation methods and their statistical properties are presented. The matching estimator of Rivers (2007) is also covered as a special case. Variance estimation with mass-imputed data is discussed. The simulation results demonstrate the proposed estimators outperform existing competitors in terms of robustness and efficiency.

    Release date: 2021-06-24

  • Articles and reports: 12-001-X202100100009
    Description:

    Predictive mean matching is a commonly used imputation procedure for addressing the problem of item nonresponse in surveys. The customary approach relies upon the specification of a single outcome regression model. In this note, we propose a novel predictive mean matching procedure that allows the user to specify multiple outcome regression models. The resulting estimator is multiply robust in the sense that it remains consistent if one of the specified outcome regression models is correctly specified. The results from a simulation study suggest that the proposed method performs well in terms of bias and efficiency.

    Release date: 2021-06-24

  • Articles and reports: 12-001-X202000100006
    Description:

    In surveys, logical boundaries among variables or among waves of surveys make imputation of missing values complicated. We propose a new regression-based multiple imputation method to deal with survey nonresponses with two-sided logical boundaries. This imputation method automatically satisfies the boundary conditions without an additional acceptance/rejection procedure and utilizes the boundary information to derive an imputed value and to determine the suitability of the imputed value. Simulation results show that our new imputation method outperforms the existing imputation methods for both mean and quantile estimations regardless of missing rates, error distributions, and missing-mechanisms. We apply our method to impute the self-reported variable “years of smoking” in successive health screenings of Koreans.

    Release date: 2020-06-30

  • Articles and reports: 12-001-X201900200001
    Description:

    Development of imputation procedures appropriate for data with extreme values or nonlinear relationships to covariates is a significant challenge in large scale surveys. We develop an imputation procedure for complex surveys based on semiparametric quantile regression. We apply the method to the Conservation Effects Assessment Project (CEAP), a large-scale survey that collects data used in quantifying soil loss from crop fields. In the imputation procedure, we first generate imputed values from a semiparametric model for the quantiles of the conditional distribution of the response given a covariate. Then, we estimate the parameters of interest using the generalized method of moments (GMM). We derive the asymptotic distribution of the GMM estimators for a general class of complex survey designs. In simulations meant to represent the CEAP data, we evaluate variance estimators based on the asymptotic distribution and compare the semiparametric quantile regression imputation (QRI) method to fully parametric and nonparametric alternatives. The QRI procedure is more efficient than nonparametric and fully parametric alternatives, and empirical coverages of confidence intervals are within 1% of the nominal 95% level. An application to estimation of mean erosion indicates that QRI may be a viable option for CEAP.

    Release date: 2019-06-27

  • Articles and reports: 12-001-X201900100009
    Description:

    The demand for small area estimates by users of Statistics Canada’s data has been steadily increasing over recent years. In this paper, we provide a summary of procedures that have been incorporated into a SAS based production system for producing official small area estimates at Statistics Canada. This system includes: procedures based on unit or area level models; the incorporation of the sampling design; the ability to smooth the design variance for each small area if an area level model is used; the ability to ensure that the small area estimates add up to reliable higher level estimates; and the development of diagnostic tools to test the adequacy of the model. The production system has been used to produce small area estimates on an experimental basis for several surveys at Statistics Canada that include: the estimation of health characteristics, the estimation of under-coverage in the census, the estimation of manufacturing sales and the estimation of unemployment rates and employment counts for the Labour Force Survey. Some of the diagnostics implemented in the system are illustrated using Labour Force Survey data along with administrative auxiliary data.

    Release date: 2019-05-07

  • Articles and reports: 12-001-X201700114823
    Description:

    The derivation of estimators in a multi-phase calibration process requires a sequential computation of estimators and calibrated weights of previous phases in order to obtain those of later ones. Already after two phases of calibration the estimators and their variances involve calibration factors from both phases and the formulae become cumbersome and uninformative. As a consequence the literature so far deals mainly with two phases while three phases or more are rarely being considered. The analysis in some cases is ad-hoc for a specific design and no comprehensive methodology for constructing calibrated estimators, and more challengingly, estimating their variances in three or more phases was formed. We provide a closed form formula for the variance of multi-phase calibrated estimators that holds for any number of phases. By specifying a new presentation of multi-phase calibrated weights it is possible to construct calibrated estimators that have the form of multi-variate regression estimators which enables a computation of a consistent estimator for their variance. This new variance estimator is not only general for any number of phases but also has some favorable characteristics. A comparison to other estimators in the special case of two-phase calibration and another independent study for three phases are presented.

    Release date: 2017-06-22

  • Articles and reports: 11-633-X2017006
    Description:

    This paper describes a method of imputing missing postal codes in a longitudinal database. The 1991 Canadian Census Health and Environment Cohort (CanCHEC), which contains information on individuals from the 1991 Census long-form questionnaire linked with T1 tax return files for the 1984-to-2011 period, is used to illustrate and validate the method. The cohort contains up to 28 consecutive fields for postal code of residence, but because of frequent gaps in postal code history, missing postal codes must be imputed. To validate the imputation method, two experiments were devised where 5% and 10% of all postal codes from a subset with full history were randomly removed and imputed.

    Release date: 2017-03-13

  • Articles and reports: 12-001-X201600214661
    Description:

    An example presented by Jean-Claude Deville in 2005 is subjected to three estimation methods: the method of moments, the maximum likelihood method, and generalized calibration. The three methods yield exactly the same results for the two non-response models. A discussion follows on how to choose the most appropriate model.

    Release date: 2016-12-20

  • Articles and reports: 12-001-X201600214676
    Description:

    Winsorization procedures replace extreme values with less extreme values, effectively moving the original extreme values toward the center of the distribution. Winsorization therefore both detects and treats influential values. Mulry, Oliver and Kaputa (2014) compare the performance of the one-sided Winsorization method developed by Clark (1995) and described by Chambers, Kokic, Smith and Cruddas (2000) to the performance of M-estimation (Beaumont and Alavi 2004) in highly skewed business population data. One aspect of particular interest for methods that detect and treat influential values is the range of values designated as influential, called the detection region. The Clark Winsorization algorithm is easy to implement and can be extremely effective. However, the resultant detection region is highly dependent on the number of influential values in the sample, especially when the survey totals are expected to vary greatly by collection period. In this note, we examine the effect of the number and magnitude of influential values on the detection regions from Clark Winsorization using data simulated to realistically reflect the properties of the population for the Monthly Retail Trade Survey (MRTS) conducted by the U.S. Census Bureau. Estimates from the MRTS and other economic surveys are used in economic indicators, such as the Gross Domestic Product (GDP).

    Release date: 2016-12-20
Reference (7)

Reference (7) ((7 results))

  • Surveys and statistical programs – Documentation: 71F0031X2005002
    Description:

    This paper introduces and explains modifications made to the Labour Force Survey estimates in January 2005. Some of these modifications include the adjustment of all LFS estimates to reflect population counts based on the 2001 Census, updates to industry and occupation classification systems and sample redesign changes.

    Release date: 2005-01-26

  • Surveys and statistical programs – Documentation: 92-397-X
    Description:

    This report covers concepts and definitions, the imputation method and data quality for this variable. The 2001 Census collected information on three types of unpaid work performed during the week preceding the Census: looking after children, housework and caring for seniors. The 2001 data on unpaid work are compared with the 1996 Census data and with the data from the General Social Survey (use of time in 1998). The report also includes historical tables.

    Release date: 2005-01-11

  • Surveys and statistical programs – Documentation: 92-388-X
    Description:

    This report contains basic conceptual and data quality information to help users interpret and make use of census occupation data. It gives an overview of the collection, coding (to the 2001 National Occupational Classification), edit and imputation of the occupation data from the 2001 Census. The report describes procedural changes between the 2001 and earlier censuses, and provides an analysis of the quality level of the 2001 Census occupation data. Finally, it details the revision of the 1991 Standard Occupational Classification used in the 1991 and 1996 Censuses to the 2001 National Occupational Classification for Statistics used in 2001. The historical comparability of data coded to the two classifications is discussed. Appendices to the report include a table showing historical data for the 1991, 1996 and 2001 Censuses.

    Release date: 2004-07-15

  • Surveys and statistical programs – Documentation: 92-398-X
    Description:

    This report contains basic conceptual and data quality information intended to facilitate the use and interpretation of census class of worker data. It provides an overview of the class of worker processing cycle including elements such as regional office processing, and edit and imputation. The report concludes with summary tables that indicate the level of data quality in the 2001 Census class of worker data.

    Release date: 2004-04-22

  • Surveys and statistical programs – Documentation: 85-602-X
    Description:

    The purpose of this report is to provide an overview of existing methods and techniques making use of personal identifiers to support record linkage. Record linkage can be loosely defined as a methodology for manipulating and / or transforming personal identifiers from individual data records from one or more operational databases and subsequently attempting to match these personal identifiers to create a composite record about an individual. Record linkage is not intended to uniquely identify individuals for operational purposes; however, it does provide probabilistic matches of varying degrees of reliability for use in statistical reporting. Techniques employed in record linkage may also be of use for investigative purposes to help narrow the field of search against existing databases when some form of personal identification information exists.

    Release date: 2000-12-05

  • Surveys and statistical programs – Documentation: 75F0002M1998012
    Description:

    This paper looks at the work of the task force responsible for reviewing Statistics Canada's household and family income statistics programs, and at one of associated program changes, namely, the integration of two major sources of annual income data in Canada, the Survey of Consumer Finances (SCF) and the Survey of Labour and Income Dynamics (SLID).

    Release date: 1998-12-30

  • Surveys and statistical programs – Documentation: 75F0002M1997006
    Description:

    This report documents the edit and imputation approach taken in processing Wave 1 income data from the Survey of Labour and Income Dynamics (SLID).

    Release date: 1997-12-31
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