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- 1. Small area estimation under a two-level model ArchivedArticles and reports: 12-001-X200800110612Description:
Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.
Release date: 2008-06-26 - 2. Small area estimation under a restriction ArchivedArticles and reports: 12-001-X200800110619Description:
Small area prediction based on random effects, called EBLUP, is a procedure for constructing estimates for small geographical areas or small subpopulations using existing survey data. The total of the small area predictors is often forced to equal the direct survey estimate and such predictors are said to be calibrated. Several calibrated predictors are reviewed and a criterion that unifies the derivation of these calibrated predictors is presented. The predictor that is the unique best linear unbiased predictor under the criterion is derived and the mean square error of the calibrated predictors is discussed. Implicit in the imposition of the restriction is the possibility that the small area model is misspecified and the predictors are biased. Augmented models with one additional explanatory variable for which the usual small area predictors achieve the self-calibrated property are considered. Simulations demonstrate that calibrated predictors have slightly smaller bias compared to those of the usual EBLUP predictor. However, if the bias is a concern, a better approach is to use an augmented model with an added auxiliary variable that is a function of area size. In the simulation, the predictors based on the augmented model had smaller MSE than EBLUP when the incorrect model was used for prediction. Furthermore, there was a very small increase in MSE relative to EBLUP if the auxiliary variable was added to the correct model.
Release date: 2008-06-26 - 3. Network sampling with a bayesian approach ArchivedArticles and reports: 11-522-X20040018730Description:
This paper considers a link-tracing sampling design. It describes the Bayesian approach for the estimation of social network properties and gives an example.
Release date: 2005-10-27 - Articles and reports: 12-001-X20050018094Description:
Nested error regression models are frequently used in small-area estimation and related problems. Standard regression model selection criterion, when applied to nested error regression models, may result in inefficient model selection methods. We illustrate this point by examining the performance of the C_P statistic through a Monte Carlo simulation study. The inefficiency of the C_P statistic may, however, be rectified by a suitable transformation of the data.
Release date: 2005-07-21 - Surveys and statistical programs – Documentation: 89-552-M2005013Geography: CanadaDescription:
This report documents key aspects of the development of the International Adult Literacy and Life Skills Survey (ALL) - its theoretical roots, the domains selected for possible assessment, the approaches taken to assessment in each domain and the criteria that were employed to decide which domains were to be carried in the final design. As conceived, the ALL survey was meant to build on the success of the International Adult Literacy Survey (IALS) assessments by extending the range of skills assessed and by improving the quality of the assessment methods employed. This report documents several successes including: · the development of a new framework and associated robust measures for problem solving · the development of a powerful numeracy framework and associated robust measures · the specification of frameworks for practical cognition, teamwork and information and communication technology literacy The report also provides insight into those domains where development failed to yield approaches to assessment of sufficient quality, insight that reminds us that scientific advance in this domain is hard won.
Release date: 2005-03-24 - Articles and reports: 12-001-X20040016991Description:
In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - Surveys and statistical programs – Documentation: 81-595-M2003005Geography: CanadaDescription:
This paper develops technical procedures that may enable ministries of education to link provincial tests with national and international tests in order to compare standards and report results on a common scale.
Release date: 2003-05-29 - Articles and reports: 12-001-X20020026433Description:
Sitter and Skinner (1994) present a method which applies linear programming to designing surveys with multi-way stratification, primarily in situations where the desired sample size is less than or only slightly larger than the total number of stratification cells. The idea in their approach is simple, easily understood and easy to apply. However, the main practical constraint of their approach is that it rapidly becomes expensive in terms of magnitude of computation as the number of cells in the multi-way stratification increases, to the extent that it cannot be used in most realistic situations. In this article, we extend this linear programming approach and develop methods to reduce the amount of computation so that very large problems become feasible.
Release date: 2003-01-29 - Articles and reports: 11-522-X20010016236Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The Uniform Crime Reporting (UCR) Program has devoted a considerable amount of resources in a continuous effort to improve the quality of its data. In this paper, the authors introduce and discuss the use of the cross-ratios and chi-square measures to evaluate the rationality of the data. The UCR data is used to empirically illustrate this approach.
Release date: 2002-09-12
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- 1. Small area estimation under a two-level model ArchivedArticles and reports: 12-001-X200800110612Description:
Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.
Release date: 2008-06-26 - 2. Small area estimation under a restriction ArchivedArticles and reports: 12-001-X200800110619Description:
Small area prediction based on random effects, called EBLUP, is a procedure for constructing estimates for small geographical areas or small subpopulations using existing survey data. The total of the small area predictors is often forced to equal the direct survey estimate and such predictors are said to be calibrated. Several calibrated predictors are reviewed and a criterion that unifies the derivation of these calibrated predictors is presented. The predictor that is the unique best linear unbiased predictor under the criterion is derived and the mean square error of the calibrated predictors is discussed. Implicit in the imposition of the restriction is the possibility that the small area model is misspecified and the predictors are biased. Augmented models with one additional explanatory variable for which the usual small area predictors achieve the self-calibrated property are considered. Simulations demonstrate that calibrated predictors have slightly smaller bias compared to those of the usual EBLUP predictor. However, if the bias is a concern, a better approach is to use an augmented model with an added auxiliary variable that is a function of area size. In the simulation, the predictors based on the augmented model had smaller MSE than EBLUP when the incorrect model was used for prediction. Furthermore, there was a very small increase in MSE relative to EBLUP if the auxiliary variable was added to the correct model.
Release date: 2008-06-26 - 3. Network sampling with a bayesian approach ArchivedArticles and reports: 11-522-X20040018730Description:
This paper considers a link-tracing sampling design. It describes the Bayesian approach for the estimation of social network properties and gives an example.
Release date: 2005-10-27 - Articles and reports: 12-001-X20050018094Description:
Nested error regression models are frequently used in small-area estimation and related problems. Standard regression model selection criterion, when applied to nested error regression models, may result in inefficient model selection methods. We illustrate this point by examining the performance of the C_P statistic through a Monte Carlo simulation study. The inefficiency of the C_P statistic may, however, be rectified by a suitable transformation of the data.
Release date: 2005-07-21 - Articles and reports: 12-001-X20040016991Description:
In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - Articles and reports: 12-001-X20020026433Description:
Sitter and Skinner (1994) present a method which applies linear programming to designing surveys with multi-way stratification, primarily in situations where the desired sample size is less than or only slightly larger than the total number of stratification cells. The idea in their approach is simple, easily understood and easy to apply. However, the main practical constraint of their approach is that it rapidly becomes expensive in terms of magnitude of computation as the number of cells in the multi-way stratification increases, to the extent that it cannot be used in most realistic situations. In this article, we extend this linear programming approach and develop methods to reduce the amount of computation so that very large problems become feasible.
Release date: 2003-01-29 - Articles and reports: 11-522-X20010016236Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The Uniform Crime Reporting (UCR) Program has devoted a considerable amount of resources in a continuous effort to improve the quality of its data. In this paper, the authors introduce and discuss the use of the cross-ratios and chi-square measures to evaluate the rationality of the data. The UCR data is used to empirically illustrate this approach.
Release date: 2002-09-12 - Articles and reports: 11-522-X20010016252Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The use of sample co-ordination in business surveys is crucial because it provides a way of smoothing out the survey burden. In many co-ordination methodologies, the random numbers representing the units are permanent and the sample selection method varies. In the microstrata methodology, however, it is the selection function that is permanent. On the other hand, random numbers are systematically rearranged between units for different co-ordination purposes: smoothing out the burden, updating panels or minimizing the overlap between two surveys. These rearrangements are made in the intersections of strata, known as microstrata. This microstrata method has good, mathematical properties and demonstrates a general approach to sample co-ordination in which births, deaths and strata changes are automatically handled. There are no particular constraints on stratification and rotation rates of panels. Two software programs have been written to implement this method and its evolutions: SALOMON in 1998, and MICROSTRAT in 2001.
Release date: 2002-09-12 - Articles and reports: 11-522-X20010016306Description:
This paper discusses in detail issues dealing with the technical aspects of designing and conducting surveys. It is intended for an audience of survey methodologists.
The paper deals with concerns regarding the problem of automatic detection and correction of inconsistent or out-of-range data in a general process of statistical data collection. The proposed approach is capable of handling both qualitative and quantitative values. The purpose of this new approach is to overcome the computational limits of the Fellegi-Holt method, while maintaining its positive features. As customary, data records must respect a set of rules in order to be declared correct. By encoding the rules with linear inequalities, we develop mathematical models for the problems of interest. As a first relevant point, by solving a sequence of feasibility problems, the set of rules itself is checked for inconsistency or redundancy. As a second relevant point, imputation is performed by solving a sequence of set-covering problems.
Release date: 2002-09-12
Reference (3)
Reference (3) ((3 results))
- Surveys and statistical programs – Documentation: 89-552-M2005013Geography: CanadaDescription:
This report documents key aspects of the development of the International Adult Literacy and Life Skills Survey (ALL) - its theoretical roots, the domains selected for possible assessment, the approaches taken to assessment in each domain and the criteria that were employed to decide which domains were to be carried in the final design. As conceived, the ALL survey was meant to build on the success of the International Adult Literacy Survey (IALS) assessments by extending the range of skills assessed and by improving the quality of the assessment methods employed. This report documents several successes including: · the development of a new framework and associated robust measures for problem solving · the development of a powerful numeracy framework and associated robust measures · the specification of frameworks for practical cognition, teamwork and information and communication technology literacy The report also provides insight into those domains where development failed to yield approaches to assessment of sufficient quality, insight that reminds us that scientific advance in this domain is hard won.
Release date: 2005-03-24 - Surveys and statistical programs – Documentation: 81-595-M2003005Geography: CanadaDescription:
This paper develops technical procedures that may enable ministries of education to link provincial tests with national and international tests in order to compare standards and report results on a common scale.
Release date: 2003-05-29 - Surveys and statistical programs – Documentation: 75F0002M1995002Description:
This paper presents the Survey of Labour and Income Dynamics (SLID) coding structure for the major fields of study for postsecondary graduates. It uses data collected in the 1991 Census of Population.
Release date: 1995-12-30
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