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- Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19 - 2. Fractional hot deck imputation for robust inference under item nonresponse in survey sampling ArchivedArticles and reports: 12-001-X201400214091Description:
Parametric fractional imputation (PFI), proposed by Kim (2011), is a tool for general purpose parameter estimation under missing data. We propose a fractional hot deck imputation (FHDI) which is more robust than PFI or multiple imputation. In the proposed method, the imputed values are chosen from the set of respondents and assigned proper fractional weights. The weights are then adjusted to meet certain calibration conditions, which makes the resulting FHDI estimator efficient. Two simulation studies are presented to compare the proposed method with existing methods.
Release date: 2014-12-19 - Articles and reports: 12-002-X201400111901Description:
This document is for analysts/researchers who are considering doing research with data from a survey where both survey weights and bootstrap weights are provided in the data files. This document gives directions, for some selected software packages, about how to get started in using survey weights and bootstrap weights for an analysis of survey data. We give brief directions for obtaining survey-weighted estimates, bootstrap variance estimates (and other desired error quantities) and some typical test statistics for each software package in turn. While these directions are provided just for the chosen examples, there will be information about the range of weighted and bootstrapped analyses that can be carried out by each software package.
Release date: 2014-08-07 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114000Description:
We have used the generalized linearization technique based on the concept of influence function, as Osier has done (Osier 2009), to estimate the variance of complex statistics such as Laeken indicators. Simulations conducted using the R language show that the use of Gaussian kernel estimation to estimate an income density function results in a strongly biased variance estimate. We are proposing two other density estimation methods that significantly reduce the observed bias. One of the methods has already been outlined by Deville (2000). The results published in this article will help to significantly improve the quality of information on the precision of certain Laeken indicators that are disseminated and compared internationally.
Release date: 2014-06-27 - 6. Theoretical and empirical properties of model assisted decision-based regression estimators ArchivedArticles and reports: 12-001-X201400114004Description:
In 2009, two major surveys in the Governments Division of the U.S. Census Bureau were redesigned to reduce sample size, save resources, and improve the precision of the estimates (Cheng, Corcoran, Barth and Hogue 2009). The new design divides each of the traditional state by government-type strata with sufficiently many units into two sub-strata according to each governmental unit’s total payroll, in order to sample less from the sub-stratum with small size units. The model-assisted approach is adopted in estimating population totals. Regression estimators using auxiliary variables are obtained either within each created sub-stratum or within the original stratum by collapsing two sub-strata. A decision-based method was proposed in Cheng, Slud and Hogue (2010), applying a hypothesis test to decide which regression estimator is used within each original stratum. Consistency and asymptotic normality of these model-assisted estimators are established here, under a design-based or model-assisted asymptotic framework. Our asymptotic results also suggest two types of consistent variance estimators, one obtained by substituting unknown quantities in the asymptotic variances and the other by applying the bootstrap. The performance of all the estimators of totals and of their variance estimators are examined in some empirical studies. The U.S. Annual Survey of Public Employment and Payroll (ASPEP) is used to motivate and illustrate our study.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114029Description:
Fay and Train (1995) present a method called successive difference replication that can be used to estimate the variance of an estimated total from a systematic random sample from an ordered list. The estimator uses the general form of a replication variance estimator, where the replicate factors are constructed such that the estimator mimics the successive difference estimator. This estimator is a modification of the estimator given by Wolter (1985). The paper furthers the methodology by explaining the impact of the row assignments on the variance estimator, showing how a reduced set of replicates leads to a reasonable estimator, and establishing conditions for successive difference replication to be equivalent to the successive difference estimator.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114030Description:
The paper reports the results of a Monte Carlo simulation study that was conducted to compare the effectiveness of four different hierarchical Bayes small area models for producing state estimates of proportions based on data from stratified simple random samples from a fixed finite population. Two of the models adopted the commonly made assumptions that the survey weighted proportion for each sampled small area has a normal distribution and that the sampling variance of this proportion is known. One of these models used a linear linking model and the other used a logistic linking model. The other two models both employed logistic linking models and assumed that the sampling variance was unknown. One of these models assumed a normal distribution for the sampling model while the other assumed a beta distribution. The study found that for all four models the credible interval design-based coverage of the finite population state proportions deviated markedly from the 95 percent nominal level used in constructing the intervals.
Release date: 2014-06-27 - 9. Estimating relative survival for cancer: An analysis of bias introduced by outdated life tables ArchivedArticles and reports: 82-003-X201400211903Geography: CanadaDescription:
Based on data from the Canadian Cancer Registry, this study examines the impact of using historical rather than current life tables to estimate expected survival in calculations of relative survival ratios. Results are presented by sex, age group, and survival duration.
Release date: 2014-02-19 - 10. Estimation and replicate variance estimation of deciles for complex survey data from positively skewed populations ArchivedArticles and reports: 12-001-X201300211868Description:
Thompson and Sigman (2000) introduced an estimation procedure for estimating medians from highly positively skewed population data. Their procedure uses interpolation over data-dependent intervals (bins). The earlier paper demonstrated that this procedure has good statistical properties for medians computed from a highly skewed sample. This research extends the previous work to decile estimation methods for a positively skewed population using complex survey data. We present three different interpolation methods along with the traditional decile estimation method (no bins) and evaluate each method empirically, using residential housing data from the Survey of Construction and via a simulation study. We found that a variant of the current procedure using the 95th percentile as a scaling factor produces decile estimates with the best statistical properties.
Release date: 2014-01-15
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- Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19 - 2. Fractional hot deck imputation for robust inference under item nonresponse in survey sampling ArchivedArticles and reports: 12-001-X201400214091Description:
Parametric fractional imputation (PFI), proposed by Kim (2011), is a tool for general purpose parameter estimation under missing data. We propose a fractional hot deck imputation (FHDI) which is more robust than PFI or multiple imputation. In the proposed method, the imputed values are chosen from the set of respondents and assigned proper fractional weights. The weights are then adjusted to meet certain calibration conditions, which makes the resulting FHDI estimator efficient. Two simulation studies are presented to compare the proposed method with existing methods.
Release date: 2014-12-19 - Articles and reports: 12-002-X201400111901Description:
This document is for analysts/researchers who are considering doing research with data from a survey where both survey weights and bootstrap weights are provided in the data files. This document gives directions, for some selected software packages, about how to get started in using survey weights and bootstrap weights for an analysis of survey data. We give brief directions for obtaining survey-weighted estimates, bootstrap variance estimates (and other desired error quantities) and some typical test statistics for each software package in turn. While these directions are provided just for the chosen examples, there will be information about the range of weighted and bootstrapped analyses that can be carried out by each software package.
Release date: 2014-08-07 - Articles and reports: 12-001-X201400111886Description:
Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114000Description:
We have used the generalized linearization technique based on the concept of influence function, as Osier has done (Osier 2009), to estimate the variance of complex statistics such as Laeken indicators. Simulations conducted using the R language show that the use of Gaussian kernel estimation to estimate an income density function results in a strongly biased variance estimate. We are proposing two other density estimation methods that significantly reduce the observed bias. One of the methods has already been outlined by Deville (2000). The results published in this article will help to significantly improve the quality of information on the precision of certain Laeken indicators that are disseminated and compared internationally.
Release date: 2014-06-27 - 6. Theoretical and empirical properties of model assisted decision-based regression estimators ArchivedArticles and reports: 12-001-X201400114004Description:
In 2009, two major surveys in the Governments Division of the U.S. Census Bureau were redesigned to reduce sample size, save resources, and improve the precision of the estimates (Cheng, Corcoran, Barth and Hogue 2009). The new design divides each of the traditional state by government-type strata with sufficiently many units into two sub-strata according to each governmental unit’s total payroll, in order to sample less from the sub-stratum with small size units. The model-assisted approach is adopted in estimating population totals. Regression estimators using auxiliary variables are obtained either within each created sub-stratum or within the original stratum by collapsing two sub-strata. A decision-based method was proposed in Cheng, Slud and Hogue (2010), applying a hypothesis test to decide which regression estimator is used within each original stratum. Consistency and asymptotic normality of these model-assisted estimators are established here, under a design-based or model-assisted asymptotic framework. Our asymptotic results also suggest two types of consistent variance estimators, one obtained by substituting unknown quantities in the asymptotic variances and the other by applying the bootstrap. The performance of all the estimators of totals and of their variance estimators are examined in some empirical studies. The U.S. Annual Survey of Public Employment and Payroll (ASPEP) is used to motivate and illustrate our study.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114029Description:
Fay and Train (1995) present a method called successive difference replication that can be used to estimate the variance of an estimated total from a systematic random sample from an ordered list. The estimator uses the general form of a replication variance estimator, where the replicate factors are constructed such that the estimator mimics the successive difference estimator. This estimator is a modification of the estimator given by Wolter (1985). The paper furthers the methodology by explaining the impact of the row assignments on the variance estimator, showing how a reduced set of replicates leads to a reasonable estimator, and establishing conditions for successive difference replication to be equivalent to the successive difference estimator.
Release date: 2014-06-27 - Articles and reports: 12-001-X201400114030Description:
The paper reports the results of a Monte Carlo simulation study that was conducted to compare the effectiveness of four different hierarchical Bayes small area models for producing state estimates of proportions based on data from stratified simple random samples from a fixed finite population. Two of the models adopted the commonly made assumptions that the survey weighted proportion for each sampled small area has a normal distribution and that the sampling variance of this proportion is known. One of these models used a linear linking model and the other used a logistic linking model. The other two models both employed logistic linking models and assumed that the sampling variance was unknown. One of these models assumed a normal distribution for the sampling model while the other assumed a beta distribution. The study found that for all four models the credible interval design-based coverage of the finite population state proportions deviated markedly from the 95 percent nominal level used in constructing the intervals.
Release date: 2014-06-27 - 9. Estimating relative survival for cancer: An analysis of bias introduced by outdated life tables ArchivedArticles and reports: 82-003-X201400211903Geography: CanadaDescription:
Based on data from the Canadian Cancer Registry, this study examines the impact of using historical rather than current life tables to estimate expected survival in calculations of relative survival ratios. Results are presented by sex, age group, and survival duration.
Release date: 2014-02-19 - 10. Estimation and replicate variance estimation of deciles for complex survey data from positively skewed populations ArchivedArticles and reports: 12-001-X201300211868Description:
Thompson and Sigman (2000) introduced an estimation procedure for estimating medians from highly positively skewed population data. Their procedure uses interpolation over data-dependent intervals (bins). The earlier paper demonstrated that this procedure has good statistical properties for medians computed from a highly skewed sample. This research extends the previous work to decile estimation methods for a positively skewed population using complex survey data. We present three different interpolation methods along with the traditional decile estimation method (no bins) and evaluate each method empirically, using residential housing data from the Survey of Construction and via a simulation study. We found that a variant of the current procedure using the 95th percentile as a scaling factor produces decile estimates with the best statistical properties.
Release date: 2014-01-15
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