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- Articles and reports: 12-001-X201500214230Description:
This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214237Description:
Careful design of a dual-frame random digit dial (RDD) telephone survey requires selecting from among many options that have varying impacts on cost, precision, and coverage in order to obtain the best possible implementation of the study goals. One such consideration is whether to screen cell-phone households in order to interview cell-phone only (CPO) households and exclude dual-user household, or to take all interviews obtained via the cell-phone sample. We present a framework in which to consider the tradeoffs between these two options and a method to select the optimal design. We derive and discuss the optimum allocation of sample size between the two sampling frames and explore the choice of optimum p, the mixing parameter for the dual-user domain. We illustrate our methods using the National Immunization Survey, sponsored by the Centers for Disease Control and Prevention.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214238Description:
Félix-Medina and Thompson (2004) proposed a variant of link-tracing sampling to sample hidden and/or hard-to-detect human populations such as drug users and sex workers. In their variant, an initial sample of venues is selected and the people found in the sampled venues are asked to name other members of the population to be included in the sample. Those authors derived maximum likelihood estimators of the population size under the assumption that the probability that a person is named by another in a sampled venue (link-probability) does not depend on the named person (homogeneity assumption). In this work we extend their research to the case of heterogeneous link-probabilities and derive unconditional and conditional maximum likelihood estimators of the population size. We also propose profile likelihood and bootstrap confidence intervals for the size of the population. The results of simulations studies carried out by us show that in presence of heterogeneous link-probabilities the proposed estimators perform reasonably well provided that relatively large sampling fractions, say larger than 0.5, be used, whereas the estimators derived under the homogeneity assumption perform badly. The outcomes also show that the proposed confidence intervals are not very robust to deviations from the assumed models.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214248Description:
Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214249Description:
The problem of optimal allocation of samples in surveys using a stratified sampling plan was first discussed by Neyman in 1934. Since then, many researchers have studied the problem of the sample allocation in multivariate surveys and several methods have been proposed. Basically, these methods are divided into two classes: The first class comprises methods that seek an allocation which minimizes survey costs while keeping the coefficients of variation of estimators of totals below specified thresholds for all survey variables of interest. The second aims to minimize a weighted average of the relative variances of the estimators of totals given a maximum overall sample size or a maximum cost. This paper proposes a new optimization approach for the sample allocation problem in multivariate surveys. This approach is based on a binary integer programming formulation. Several numerical experiments showed that the proposed approach provides efficient solutions to this problem, which improve upon a ‘textbook algorithm’ and can be more efficient than the algorithm by Bethel (1985, 1989).
Release date: 2015-12-17 - Articles and reports: 75-005-M2015002Description:
This report provides information to users who wish to compare employment and unemployment estimates from the Canadian surveys (LFS and SEPH) and American surveys (CPS and CES). The aspects covered include concepts, methods, seasonal adjustment, timeliness, revisions and main uses.
Release date: 2015-10-09 - Articles and reports: 12-001-X201500114149Description:
This paper introduces a general framework for deriving the optimal inclusion probabilities for a variety of survey contexts in which disseminating survey estimates of pre-established accuracy for a multiplicity of both variables and domains of interest is required. The framework can define either standard stratified or incomplete stratified sampling designs. The optimal inclusion probabilities are obtained by minimizing costs through an algorithm that guarantees the bounding of sampling errors at the domains level, assuming that the domain membership variables are available in the sampling frame. The target variables are unknown, but can be predicted with suitable super-population models. The algorithm takes properly into account this model uncertainty. Some experiments based on real data show the empirical properties of the algorithm.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114161Description:
A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114173Description:
Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse. By noting that for a particular survey variable, we just have observed and unobserved values, in this work we exploit the connection between unit and item nonresponse. In particular, we assume that the factors that drive unit response are the same as those that drive item response on selected variables of interest. Response probabilities are then estimated using a latent covariate that measures the will to respond to the survey and that can explain a part of the unknown behavior of a unit to participate in the survey. This latent covariate is estimated using latent trait models. This approach is particularly relevant for sensitive items and, therefore, can handle non-ignorable nonresponse. Auxiliary information known for both respondents and nonrespondents can be included either in the latent variable model or in the response probability estimation process. The approach can also be used when auxiliary information is not available, and we focus here on this case. We propose an estimator using a reweighting system based on the previous latent covariate when no other observed auxiliary information is available. Results on its performance are encouraging from simulation studies on both real and simulated data.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29
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- Articles and reports: 12-001-X201500214230Description:
This paper develops allocation methods for stratified sample surveys where composite small area estimators are a priority, and areas are used as strata. Longford (2006) proposed an objective criterion for this situation, based on a weighted combination of the mean squared errors of small area means and a grand mean. Here, we redefine this approach within a model-assisted framework, allowing regressor variables and a more natural interpretation of results using an intra-class correlation parameter. We also consider several uses of power allocation, and allow the placing of other constraints such as maximum relative root mean squared errors for stratum estimators. We find that a simple power allocation can perform very nearly as well as the optimal design even when the objective is to minimize Longford’s (2006) criterion.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214237Description:
Careful design of a dual-frame random digit dial (RDD) telephone survey requires selecting from among many options that have varying impacts on cost, precision, and coverage in order to obtain the best possible implementation of the study goals. One such consideration is whether to screen cell-phone households in order to interview cell-phone only (CPO) households and exclude dual-user household, or to take all interviews obtained via the cell-phone sample. We present a framework in which to consider the tradeoffs between these two options and a method to select the optimal design. We derive and discuss the optimum allocation of sample size between the two sampling frames and explore the choice of optimum p, the mixing parameter for the dual-user domain. We illustrate our methods using the National Immunization Survey, sponsored by the Centers for Disease Control and Prevention.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214238Description:
Félix-Medina and Thompson (2004) proposed a variant of link-tracing sampling to sample hidden and/or hard-to-detect human populations such as drug users and sex workers. In their variant, an initial sample of venues is selected and the people found in the sampled venues are asked to name other members of the population to be included in the sample. Those authors derived maximum likelihood estimators of the population size under the assumption that the probability that a person is named by another in a sampled venue (link-probability) does not depend on the named person (homogeneity assumption). In this work we extend their research to the case of heterogeneous link-probabilities and derive unconditional and conditional maximum likelihood estimators of the population size. We also propose profile likelihood and bootstrap confidence intervals for the size of the population. The results of simulations studies carried out by us show that in presence of heterogeneous link-probabilities the proposed estimators perform reasonably well provided that relatively large sampling fractions, say larger than 0.5, be used, whereas the estimators derived under the homogeneity assumption perform badly. The outcomes also show that the proposed confidence intervals are not very robust to deviations from the assumed models.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214248Description:
Unit level population models are often used in model-based small area estimation of totals and means, but the models may not hold for the sample if the sampling design is informative for the model. As a result, standard methods, assuming that the model holds for the sample, can lead to biased estimators. We study alternative methods that use a suitable function of the unit selection probability as an additional auxiliary variable in the sample model. We report the results of a simulation study on the bias and mean squared error (MSE) of the proposed estimators of small area means and on the relative bias of the associated MSE estimators, using informative sampling schemes to generate the samples. Alternative methods, based on modeling the conditional expectation of the design weight as a function of the model covariates and the response, are also included in the simulation study.
Release date: 2015-12-17 - Articles and reports: 12-001-X201500214249Description:
The problem of optimal allocation of samples in surveys using a stratified sampling plan was first discussed by Neyman in 1934. Since then, many researchers have studied the problem of the sample allocation in multivariate surveys and several methods have been proposed. Basically, these methods are divided into two classes: The first class comprises methods that seek an allocation which minimizes survey costs while keeping the coefficients of variation of estimators of totals below specified thresholds for all survey variables of interest. The second aims to minimize a weighted average of the relative variances of the estimators of totals given a maximum overall sample size or a maximum cost. This paper proposes a new optimization approach for the sample allocation problem in multivariate surveys. This approach is based on a binary integer programming formulation. Several numerical experiments showed that the proposed approach provides efficient solutions to this problem, which improve upon a ‘textbook algorithm’ and can be more efficient than the algorithm by Bethel (1985, 1989).
Release date: 2015-12-17 - Articles and reports: 75-005-M2015002Description:
This report provides information to users who wish to compare employment and unemployment estimates from the Canadian surveys (LFS and SEPH) and American surveys (CPS and CES). The aspects covered include concepts, methods, seasonal adjustment, timeliness, revisions and main uses.
Release date: 2015-10-09 - Articles and reports: 12-001-X201500114149Description:
This paper introduces a general framework for deriving the optimal inclusion probabilities for a variety of survey contexts in which disseminating survey estimates of pre-established accuracy for a multiplicity of both variables and domains of interest is required. The framework can define either standard stratified or incomplete stratified sampling designs. The optimal inclusion probabilities are obtained by minimizing costs through an algorithm that guarantees the bounding of sampling errors at the domains level, assuming that the domain membership variables are available in the sampling frame. The target variables are unknown, but can be predicted with suitable super-population models. The algorithm takes properly into account this model uncertainty. Some experiments based on real data show the empirical properties of the algorithm.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114161Description:
A popular area level model used for the estimation of small area means is the Fay-Herriot model. This model involves unobservable random effects for the areas apart from the (fixed) linear regression based on area level covariates. Empirical best linear unbiased predictors of small area means are obtained by estimating the area random effects, and they can be expressed as a weighted average of area-specific direct estimators and regression-synthetic estimators. In some cases the observed data do not support the inclusion of the area random effects in the model. Excluding these area effects leads to the regression-synthetic estimator, that is, a zero weight is attached to the direct estimator. A preliminary test estimator of a small area mean obtained after testing for the presence of area random effects is studied. On the other hand, empirical best linear unbiased predictors of small area means that always give non-zero weights to the direct estimators in all areas together with alternative estimators based on the preliminary test are also studied. The preliminary testing procedure is also used to define new mean squared error estimators of the point estimators of small area means. Results of a limited simulation study show that, for small number of areas, the preliminary testing procedure leads to mean squared error estimators with considerably smaller average absolute relative bias than the usual mean squared error estimators, especially when the variance of the area effects is small relative to the sampling variances.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114173Description:
Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse. By noting that for a particular survey variable, we just have observed and unobserved values, in this work we exploit the connection between unit and item nonresponse. In particular, we assume that the factors that drive unit response are the same as those that drive item response on selected variables of interest. Response probabilities are then estimated using a latent covariate that measures the will to respond to the survey and that can explain a part of the unknown behavior of a unit to participate in the survey. This latent covariate is estimated using latent trait models. This approach is particularly relevant for sensitive items and, therefore, can handle non-ignorable nonresponse. Auxiliary information known for both respondents and nonrespondents can be included either in the latent variable model or in the response probability estimation process. The approach can also be used when auxiliary information is not available, and we focus here on this case. We propose an estimator using a reweighting system based on the previous latent covariate when no other observed auxiliary information is available. Results on its performance are encouraging from simulation studies on both real and simulated data.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29
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