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- Articles and reports: 12-001-X202300200010Description: Sample coordination methods aim to increase (in positive coordination) or decrease (in negative coordination) the size of the overlap between samples. The samples considered can be from different occasions of a repeated survey and/or from different surveys covering a common population. Negative coordination is used to control the response burden in a given period, because some units do not respond to survey questionnaires if they are selected in many samples. Usually, methods for sample coordination do not take into account any measure of the response burden that a unit has already expended in responding to previous surveys. We introduce such a measure into a new method by adapting a spatially balanced sampling scheme, based on a generalization of Poisson sampling, together with a negative coordination method. The goal is to create a double control of the burden for these units: once by using a measure of burden during the sampling process and once by using a negative coordination method. We evaluate the approach using Monte-Carlo simulation and investigate its use for controlling for selection “hot-spots” in business surveys in Statistics Netherlands.Release date: 2024-01-03
- Articles and reports: 12-001-X202300100009Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.Release date: 2023-06-30
- Articles and reports: 12-001-X201900300001Description:
Standard linearization estimators of the variance of the general regression estimator are often too small, leading to confidence intervals that do not cover at the desired rate. Hat matrix adjustments can be used in two-stage sampling that help remedy this problem. We present theory for several new variance estimators and compare them to standard estimators in a series of simulations. The proposed estimators correct negative biases and improve confidence interval coverage rates in a variety of situations that mirror ones that are met in practice.
Release date: 2019-12-17 - Articles and reports: 12-001-X201900200007Description:
When fitting an ordered categorical variable with L > 2 levels to a set of covariates onto complex survey data, it is common to assume that the elements of the population fit a simple cumulative logistic regression model (proportional-odds logistic-regression model). This means the probability that the categorical variable is at or below some level is a binary logistic function of the model covariates. Moreover, except for the intercept, the values of the logistic-regression parameters are the same at each level. The conventional “design-based” method used for fitting the proportional-odds model is based on pseudo-maximum likelihood. We compare estimates computed using pseudo-maximum likelihood with those computed by assuming an alternative design-sensitive robust model-based framework. We show with a simple numerical example how estimates using the two approaches can differ. The alternative approach is easily extended to fit a general cumulative logistic model, in which the parallel-lines assumption can fail. A test of that assumption easily follows.
Release date: 2019-06-27 - Articles and reports: 12-001-X201800154929Description:
The U.S. Census Bureau is investigating nonrespondent subsampling strategies for usage in the 2017 Economic Census. Design constraints include a mandated lower bound on the unit response rate, along with targeted industry-specific response rates. This paper presents research on allocation procedures for subsampling nonrespondents, conditional on the subsampling being systematic. We consider two approaches: (1) equal-probability sampling and (2) optimized allocation with constraints on unit response rates and sample size with the objective of selecting larger samples in industries that have initially lower response rates. We present a simulation study that examines the relative bias and mean squared error for the proposed allocations, assessing each procedure’s sensitivity to the size of the subsample, the response propensities, and the estimation procedure.
Release date: 2018-06-21 - Articles and reports: 12-001-X201700114817Description:
We present research results on sample allocations for efficient model-based small area estimation in cases where the areas of interest coincide with the strata. Although model-assisted and model-based estimation methods are common in the production of small area statistics, utilization of the underlying model and estimation method are rarely included in the sample area allocation scheme. Therefore, we have developed a new model-based allocation named g1-allocation. For comparison, one recently developed model-assisted allocation is presented. These two allocations are based on an adjusted measure of homogeneity which is computed using an auxiliary variable and is an approximation of the intra-class correlation within areas. Five model-free area allocation solutions presented in the past are selected from the literature as reference allocations. Equal and proportional allocations need the number of areas and area-specific numbers of basic statistical units. The Neyman, Bankier and NLP (Non-Linear Programming) allocation need values for the study variable concerning area level parameters such as standard deviation, coefficient of variation or totals. In general, allocation methods can be classified according to the optimization criteria and use of auxiliary data. Statistical properties of the various methods are assessed through sample simulation experiments using real population register data. It can be concluded from simulation results that inclusion of the model and estimation method into the allocation method improves estimation results.
Release date: 2017-06-22 - 7. 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: 12-001-X201400214119Description:
When considering sample stratification by several variables, we often face the case where the expected number of sample units to be selected in each stratum is very small and the total number of units to be selected is smaller than the total number of strata. These stratified sample designs are specifically represented by the tabular arrays with real numbers, called controlled selection problems, and are beyond the reach of conventional methods of allocation. Many algorithms for solving these problems have been studied over about 60 years beginning with Goodman and Kish (1950). Those developed more recently are especially computer intensive and always find the solutions. However, there still remains the unanswered question: In what sense are the solutions to a controlled selection problem obtained from those algorithms optimal? We introduce the general concept of optimal solutions, and propose a new controlled selection algorithm based on typical distance functions to achieve solutions. This algorithm can be easily performed by a new SAS-based software. This study focuses on two-way stratification designs. The controlled selection solutions from the new algorithm are compared with those from existing algorithms using several examples. The new algorithm successfully obtains robust solutions to two-way controlled selection problems that meet the optimality criteria.
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-X201100211606Description:
This paper introduces a U.S. Census Bureau special compilation by presenting four other papers of the current issue: three papers from authors Tillé, Lohr and Thompson as well as a discussion paper from Opsomer.
Release date: 2011-12-21
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- Articles and reports: 12-001-X202300200010Description: Sample coordination methods aim to increase (in positive coordination) or decrease (in negative coordination) the size of the overlap between samples. The samples considered can be from different occasions of a repeated survey and/or from different surveys covering a common population. Negative coordination is used to control the response burden in a given period, because some units do not respond to survey questionnaires if they are selected in many samples. Usually, methods for sample coordination do not take into account any measure of the response burden that a unit has already expended in responding to previous surveys. We introduce such a measure into a new method by adapting a spatially balanced sampling scheme, based on a generalization of Poisson sampling, together with a negative coordination method. The goal is to create a double control of the burden for these units: once by using a measure of burden during the sampling process and once by using a negative coordination method. We evaluate the approach using Monte-Carlo simulation and investigate its use for controlling for selection “hot-spots” in business surveys in Statistics Netherlands.Release date: 2024-01-03
- Articles and reports: 12-001-X202300100009Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.Release date: 2023-06-30
- Articles and reports: 12-001-X201900300001Description:
Standard linearization estimators of the variance of the general regression estimator are often too small, leading to confidence intervals that do not cover at the desired rate. Hat matrix adjustments can be used in two-stage sampling that help remedy this problem. We present theory for several new variance estimators and compare them to standard estimators in a series of simulations. The proposed estimators correct negative biases and improve confidence interval coverage rates in a variety of situations that mirror ones that are met in practice.
Release date: 2019-12-17 - Articles and reports: 12-001-X201900200007Description:
When fitting an ordered categorical variable with L > 2 levels to a set of covariates onto complex survey data, it is common to assume that the elements of the population fit a simple cumulative logistic regression model (proportional-odds logistic-regression model). This means the probability that the categorical variable is at or below some level is a binary logistic function of the model covariates. Moreover, except for the intercept, the values of the logistic-regression parameters are the same at each level. The conventional “design-based” method used for fitting the proportional-odds model is based on pseudo-maximum likelihood. We compare estimates computed using pseudo-maximum likelihood with those computed by assuming an alternative design-sensitive robust model-based framework. We show with a simple numerical example how estimates using the two approaches can differ. The alternative approach is easily extended to fit a general cumulative logistic model, in which the parallel-lines assumption can fail. A test of that assumption easily follows.
Release date: 2019-06-27 - Articles and reports: 12-001-X201800154929Description:
The U.S. Census Bureau is investigating nonrespondent subsampling strategies for usage in the 2017 Economic Census. Design constraints include a mandated lower bound on the unit response rate, along with targeted industry-specific response rates. This paper presents research on allocation procedures for subsampling nonrespondents, conditional on the subsampling being systematic. We consider two approaches: (1) equal-probability sampling and (2) optimized allocation with constraints on unit response rates and sample size with the objective of selecting larger samples in industries that have initially lower response rates. We present a simulation study that examines the relative bias and mean squared error for the proposed allocations, assessing each procedure’s sensitivity to the size of the subsample, the response propensities, and the estimation procedure.
Release date: 2018-06-21 - Articles and reports: 12-001-X201700114817Description:
We present research results on sample allocations for efficient model-based small area estimation in cases where the areas of interest coincide with the strata. Although model-assisted and model-based estimation methods are common in the production of small area statistics, utilization of the underlying model and estimation method are rarely included in the sample area allocation scheme. Therefore, we have developed a new model-based allocation named g1-allocation. For comparison, one recently developed model-assisted allocation is presented. These two allocations are based on an adjusted measure of homogeneity which is computed using an auxiliary variable and is an approximation of the intra-class correlation within areas. Five model-free area allocation solutions presented in the past are selected from the literature as reference allocations. Equal and proportional allocations need the number of areas and area-specific numbers of basic statistical units. The Neyman, Bankier and NLP (Non-Linear Programming) allocation need values for the study variable concerning area level parameters such as standard deviation, coefficient of variation or totals. In general, allocation methods can be classified according to the optimization criteria and use of auxiliary data. Statistical properties of the various methods are assessed through sample simulation experiments using real population register data. It can be concluded from simulation results that inclusion of the model and estimation method into the allocation method improves estimation results.
Release date: 2017-06-22 - 7. 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: 12-001-X201400214119Description:
When considering sample stratification by several variables, we often face the case where the expected number of sample units to be selected in each stratum is very small and the total number of units to be selected is smaller than the total number of strata. These stratified sample designs are specifically represented by the tabular arrays with real numbers, called controlled selection problems, and are beyond the reach of conventional methods of allocation. Many algorithms for solving these problems have been studied over about 60 years beginning with Goodman and Kish (1950). Those developed more recently are especially computer intensive and always find the solutions. However, there still remains the unanswered question: In what sense are the solutions to a controlled selection problem obtained from those algorithms optimal? We introduce the general concept of optimal solutions, and propose a new controlled selection algorithm based on typical distance functions to achieve solutions. This algorithm can be easily performed by a new SAS-based software. This study focuses on two-way stratification designs. The controlled selection solutions from the new algorithm are compared with those from existing algorithms using several examples. The new algorithm successfully obtains robust solutions to two-way controlled selection problems that meet the optimality criteria.
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-X201100211606Description:
This paper introduces a U.S. Census Bureau special compilation by presenting four other papers of the current issue: three papers from authors Tillé, Lohr and Thompson as well as a discussion paper from Opsomer.
Release date: 2011-12-21
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