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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 - 3. Chi-squared tests in dual frame surveys ArchivedArticles and reports: 12-001-X201400214096Description:
In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald’s test (Wald 1943), Rao-Scott first-order and second-order corrected tests (Rao and Scott 1981) from a single survey to a dual frame survey and derive the asymptotic distributions. Simulation studies show that both Rao-Scott type corrected tests work well and thus are recommended for use in dual frame surveys. An example is given to illustrate the usage of the developed tests.
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: 11-522-X201300014276Description:
In France, budget restrictions are making it more difficult to hire casual interviewers to deal with collection problems. As a result, it has become necessary to adhere to a predetermined annual work quota. For surveys of the National Institute of Statistics and Economic Studies (INSEE), which use a master sample, problems arise when an interviewer is on extended leave throughout the entire collection period of a survey. When that occurs, an area may cease to be covered by the survey, and this effectively generates a bias. In response to this new problem, we have implemented two methods, depending on when the problem is identified: If an area is ‘abandoned’ before or at the very beginning of collection, we carry out a ‘sub-allocation’ procedure. The procedure involves interviewing a minimum number of households in each collection area at the expense of other areas in which no collection problems have been identified. The idea is to minimize the dispersion of weights while meeting collection targets. If an area is ‘abandoned’ during collection, we prioritize the remaining surveys. Prioritization is based on a representativeness indicator (R indicator) that measures the degree of similarity between a sample and the base population. The goal of this prioritization process during collection is to get as close as possible to equal response probability for respondents. The R indicator is based on the dispersion of the estimated response probabilities of the sampled households, and it is composed of partial R indicators that measure representativeness variable by variable. These R indicators are tools that we can use to analyze collection by isolating underrepresented population groups. We can increase collection efforts for groups that have been identified beforehand. In the oral presentation, we covered these two points concisely. By contrast, this paper deals exclusively with the first point: sub-allocation. Prioritization is being implemented for the first time at INSEE for the assets survey, and it will be covered in a specific paper by A. Rebecq.
Release date: 2014-10-31 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - 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 - 8. The influence of sampling method and interviewers on sample realization in the European Social Survey ArchivedArticles and reports: 12-001-X201400114001Description:
This article addresses the impact of different sampling procedures on realised sample quality in the case of probability samples. This impact was expected to result from varying degrees of freedom on the part of interviewers to interview easily available or cooperative individuals (thus producing substitutions). The analysis was conducted in a cross-cultural context using data from the first four rounds of the European Social Survey (ESS). Substitutions are measured as deviations from a 50/50 gender ratio in subsamples with heterosexual couples. Significant deviations were found in numerous countries of the ESS. They were also found to be lowest in cases of samples with official registers of residents as sample frame (individual person register samples) if one partner was more difficult to contact than the other. This scope of substitutions did not differ across the ESS rounds and it was weakly correlated with payment and control procedures. It can be concluded from the results that individual person register samples are associated with higher sample quality.
Release date: 2014-06-27 - 9. A nonparametric method to generate synthetic populations to adjust for complex sampling design features ArchivedArticles and reports: 12-001-X201400114003Description:
Outside of the survey sampling literature, samples are often assumed to be generated by simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.
Release date: 2014-06-27 - 10. Joint determination of optimal stratification and sample allocation using genetic algorithm ArchivedArticles and reports: 12-001-X201300211884Description:
This paper offers a solution to the problem of finding the optimal stratification of the available population frame, so as to ensure the minimization of the cost of the sample required to satisfy precision constraints on a set of different target estimates. The solution is searched by exploring the universe of all possible stratifications obtainable by cross-classifying the categorical auxiliary variables available in the frame (continuous auxiliary variables can be transformed into categorical ones by means of suitable methods). Therefore, the followed approach is multivariate with respect to both target and auxiliary variables. The proposed algorithm is based on a non deterministic evolutionary approach, making use of the genetic algorithm paradigm. The key feature of the algorithm is in considering each possible stratification as an individual subject to evolution, whose fitness is given by the cost of the associated sample required to satisfy a set of precision constraints, the cost being calculated by applying the Bethel algorithm for multivariate allocation. This optimal stratification algorithm, implemented in an R package (SamplingStrata), has been so far applied to a number of current surveys in the Italian National Institute of Statistics: the obtained results always show significant improvements in the efficiency of the samples obtained, with respect to previously adopted stratifications.
Release date: 2014-01-15
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Articles and reports (10)
Articles and reports (10) ((10 results))
- 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 - 3. Chi-squared tests in dual frame surveys ArchivedArticles and reports: 12-001-X201400214096Description:
In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald’s test (Wald 1943), Rao-Scott first-order and second-order corrected tests (Rao and Scott 1981) from a single survey to a dual frame survey and derive the asymptotic distributions. Simulation studies show that both Rao-Scott type corrected tests work well and thus are recommended for use in dual frame surveys. An example is given to illustrate the usage of the developed tests.
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: 11-522-X201300014276Description:
In France, budget restrictions are making it more difficult to hire casual interviewers to deal with collection problems. As a result, it has become necessary to adhere to a predetermined annual work quota. For surveys of the National Institute of Statistics and Economic Studies (INSEE), which use a master sample, problems arise when an interviewer is on extended leave throughout the entire collection period of a survey. When that occurs, an area may cease to be covered by the survey, and this effectively generates a bias. In response to this new problem, we have implemented two methods, depending on when the problem is identified: If an area is ‘abandoned’ before or at the very beginning of collection, we carry out a ‘sub-allocation’ procedure. The procedure involves interviewing a minimum number of households in each collection area at the expense of other areas in which no collection problems have been identified. The idea is to minimize the dispersion of weights while meeting collection targets. If an area is ‘abandoned’ during collection, we prioritize the remaining surveys. Prioritization is based on a representativeness indicator (R indicator) that measures the degree of similarity between a sample and the base population. The goal of this prioritization process during collection is to get as close as possible to equal response probability for respondents. The R indicator is based on the dispersion of the estimated response probabilities of the sampled households, and it is composed of partial R indicators that measure representativeness variable by variable. These R indicators are tools that we can use to analyze collection by isolating underrepresented population groups. We can increase collection efforts for groups that have been identified beforehand. In the oral presentation, we covered these two points concisely. By contrast, this paper deals exclusively with the first point: sub-allocation. Prioritization is being implemented for the first time at INSEE for the assets survey, and it will be covered in a specific paper by A. Rebecq.
Release date: 2014-10-31 - Articles and reports: 11-522-X201300014286Description:
The Étude Longitudinale Française depuis l’Enfance (ELFE) [French longitudinal study from childhood on], which began in 2011, involves over 18,300 infants whose parents agreed to participate when they were in the maternity hospital. This cohort survey, which will track the children from birth to adulthood, covers the many aspects of their lives from the perspective of social science, health and environmental health. In randomly selected maternity hospitals, all infants in the target population, who were born on one of 25 days distributed across the four seasons, were chosen. This sample is the outcome of a non-standard sampling scheme that we call product sampling. In this survey, it takes the form of the cross-tabulation between two independent samples: a sampling of maternity hospitals and a sampling of days. While it is easy to imagine a cluster effect due to the sampling of maternity hospitals, one can also imagine a cluster effect due to the sampling of days. The scheme’s time dimension therefore cannot be ignored if the desired estimates are subject to daily or seasonal variation. While this non-standard scheme can be viewed as a particular kind of two-phase design, it needs to be defined within a more specific framework. Following a comparison of the product scheme with a conventional two-stage design, we propose variance estimators specially formulated for this sampling scheme. Our ideas are illustrated with a simulation study.
Release date: 2014-10-31 - 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 - 8. The influence of sampling method and interviewers on sample realization in the European Social Survey ArchivedArticles and reports: 12-001-X201400114001Description:
This article addresses the impact of different sampling procedures on realised sample quality in the case of probability samples. This impact was expected to result from varying degrees of freedom on the part of interviewers to interview easily available or cooperative individuals (thus producing substitutions). The analysis was conducted in a cross-cultural context using data from the first four rounds of the European Social Survey (ESS). Substitutions are measured as deviations from a 50/50 gender ratio in subsamples with heterosexual couples. Significant deviations were found in numerous countries of the ESS. They were also found to be lowest in cases of samples with official registers of residents as sample frame (individual person register samples) if one partner was more difficult to contact than the other. This scope of substitutions did not differ across the ESS rounds and it was weakly correlated with payment and control procedures. It can be concluded from the results that individual person register samples are associated with higher sample quality.
Release date: 2014-06-27 - 9. A nonparametric method to generate synthetic populations to adjust for complex sampling design features ArchivedArticles and reports: 12-001-X201400114003Description:
Outside of the survey sampling literature, samples are often assumed to be generated by simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.
Release date: 2014-06-27 - 10. Joint determination of optimal stratification and sample allocation using genetic algorithm ArchivedArticles and reports: 12-001-X201300211884Description:
This paper offers a solution to the problem of finding the optimal stratification of the available population frame, so as to ensure the minimization of the cost of the sample required to satisfy precision constraints on a set of different target estimates. The solution is searched by exploring the universe of all possible stratifications obtainable by cross-classifying the categorical auxiliary variables available in the frame (continuous auxiliary variables can be transformed into categorical ones by means of suitable methods). Therefore, the followed approach is multivariate with respect to both target and auxiliary variables. The proposed algorithm is based on a non deterministic evolutionary approach, making use of the genetic algorithm paradigm. The key feature of the algorithm is in considering each possible stratification as an individual subject to evolution, whose fitness is given by the cost of the associated sample required to satisfy a set of precision constraints, the cost being calculated by applying the Bethel algorithm for multivariate allocation. This optimal stratification algorithm, implemented in an R package (SamplingStrata), has been so far applied to a number of current surveys in the Italian National Institute of Statistics: the obtained results always show significant improvements in the efficiency of the samples obtained, with respect to previously adopted stratifications.
Release date: 2014-01-15
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