Weighting and estimation
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- Articles and reports: 12-001-X202300100005Description: Weight smoothing is a useful technique in improving the efficiency of design-based estimators at the risk of bias due to model misspecification. As an extension of the work of Kim and Skinner (2013), we propose using weight smoothing to construct the conditional likelihood for efficient analytic inference under informative sampling. The Beta prime distribution can be used to build a parameter model for weights in the sample. A score test is developed to test for model misspecification in the weight model. A pretest estimator using the score test can be developed naturally. The pretest estimator is nearly unbiased and can be more efficient than the design-based estimator when the weight model is correctly specified, or the original weights are highly variable. A limited simulation study is presented to investigate the performance of the proposed methods.Release date: 2023-06-30
- Articles and reports: 12-001-X201500114192Description:
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as K - composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), AK - composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial Qp defined in terms of the rotation pattern (Qp happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix S defined in terms of the rotation pattern and the roots of the polynomial Qp. In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Release date: 2015-06-29 - Articles and reports: 12-001-X201400214118Description:
Bagging is a powerful computational method used to improve the performance of inefficient estimators. This article is a first exploration of the use of bagging in survey estimation, and we investigate the effects of bagging on non-differentiable survey estimators including sample distribution functions and quantiles, among others. The theoretical properties of bagged survey estimators are investigated under both design-based and model-based regimes. In particular, we show the design consistency of the bagged estimators, and obtain the asymptotic normality of the estimators in the model-based context. The article describes how implementation of bagging for survey estimators can take advantage of replicates developed for survey variance estimation, providing an easy way for practitioners to apply bagging in existing surveys. A major remaining challenge in implementing bagging in the survey context is variance estimation for the bagged estimators themselves, and we explore two possible variance estimation approaches. Simulation experiments reveal the improvement of the proposed bagging estimator relative to the original estimator and compare the two variance estimation approaches.
Release date: 2014-12-19 - 4. 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-X201200111686Description:
We present a generalized estimating equations approach for estimating the concordance correlation coefficient and the kappa coefficient from sample survey data. The estimates and their accompanying standard error need to correctly account for the sampling design. Weighted measures of the concordance correlation coefficient and the kappa coefficient, along with the variance of these measures accounting for the sampling design, are presented. We use the Taylor series linearization method and the jackknife procedure for estimating the standard errors of the resulting parameter estimates. Body measurement and oral health data from the Third National Health and Nutrition Examination Survey are used to illustrate this methodology.
Release date: 2012-06-27 - 6. Statistical foundations of cell-phone surveys ArchivedArticles and reports: 12-001-X201000211382Description:
The size of the cell-phone-only population in the USA has increased rapidly in recent years and, correspondingly, researchers have begun to experiment with sampling and interviewing of cell-phone subscribers. We discuss statistical issues involved in the sampling design and estimation phases of cell-phone studies. This work is presented primarily in the context of a nonoverlapping dual-frame survey in which one frame and sample are employed for the landline population and a second frame and sample are employed for the cell-phone-only population. Additional considerations necessary for overlapping dual-frame surveys (where the cell-phone frame and sample include some of the landline population) are also discussed. We illustrate the methods using the design of the National Immunization Survey (NIS), which monitors the vaccination rates of children age 19-35 months and teens age 13-17 years. The NIS is a nationwide telephone survey, followed by a provider record check, conducted by the Centers for Disease Control and Prevention.
Release date: 2010-12-21 - 7. 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 - 8. Estimation of attributable number of deaths and standard errors from simple and complex sampled cohorts ArchivedArticles and reports: 11-522-X200600110400Description:
Estimates of the attributable number of deaths (AD) from all-causes can be obtained by first estimating population attributable risk (AR) adjusted for confounding covariates, and then multiplying the AR by the number of deaths determined from vital mortality statistics that occurred for a specific time period. Proportional hazard regression estimates of adjusted relative hazards obtained from mortality follow-up data from a cohort or a survey is combined with a joint distribution of risk factor and confounding covariates to compute an adjusted AR. Two estimators of adjusted AR are examined, which differ according to the reference population that the joint distribution of risk factor and confounders is obtained. The two types of reference populations considered: (i) the population that is represented by the baseline cohort and (ii) a population that is external to the cohort. Methods based on influence function theory are applied to obtain expressions for estimating the variance of the AD estimator. These variance estimators can be applied to data that range from simple random samples to (sample) weighted multi-stage stratified cluster samples from national household surveys. The variance estimation of AD is illustrated in an analysis of excess deaths due to having a non-ideal body mass index using data from the second National Health and Examination Survey (NHANES) Mortality Study and the 1999-2002 NHANES. These methods can also be used to estimate the attributable number of cause-specific deaths or incident cases of a disease and their standard errors when the time period for the accrual of is short.
Release date: 2008-03-17 - Articles and reports: 11-522-X200600110417Description:
The coefficients of regression equations are often parameters of interest for health surveys and such surveys are usually of complex design with differential sampling rates. We give estimators for the regression coefficients for complex surveys that are superior to ordinary expansion estimators under the subject matter model, but also retain desirable design properties. Theoretical and Monte Carlo properties are presented.
Release date: 2008-03-17 - Articles and reports: 11-522-X20050019461Description:
We propose a generalization of the usual coefficient of variation (CV) to address some of the known problems when used in measuring quality of estimates. Some of the problems associated with CV include interpretation when the estimate is near zero, and the inconsistency in the interpretation about precision when computed for different one-to-one monotonic transformations.
Release date: 2007-03-02
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- Articles and reports: 12-001-X202300100005Description: Weight smoothing is a useful technique in improving the efficiency of design-based estimators at the risk of bias due to model misspecification. As an extension of the work of Kim and Skinner (2013), we propose using weight smoothing to construct the conditional likelihood for efficient analytic inference under informative sampling. The Beta prime distribution can be used to build a parameter model for weights in the sample. A score test is developed to test for model misspecification in the weight model. A pretest estimator using the score test can be developed naturally. The pretest estimator is nearly unbiased and can be more efficient than the design-based estimator when the weight model is correctly specified, or the original weights are highly variable. A limited simulation study is presented to investigate the performance of the proposed methods.Release date: 2023-06-30
- Articles and reports: 12-001-X201500114192Description:
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as K - composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), AK - composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial Qp defined in terms of the rotation pattern (Qp happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix S defined in terms of the rotation pattern and the roots of the polynomial Qp. In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Release date: 2015-06-29 - Articles and reports: 12-001-X201400214118Description:
Bagging is a powerful computational method used to improve the performance of inefficient estimators. This article is a first exploration of the use of bagging in survey estimation, and we investigate the effects of bagging on non-differentiable survey estimators including sample distribution functions and quantiles, among others. The theoretical properties of bagged survey estimators are investigated under both design-based and model-based regimes. In particular, we show the design consistency of the bagged estimators, and obtain the asymptotic normality of the estimators in the model-based context. The article describes how implementation of bagging for survey estimators can take advantage of replicates developed for survey variance estimation, providing an easy way for practitioners to apply bagging in existing surveys. A major remaining challenge in implementing bagging in the survey context is variance estimation for the bagged estimators themselves, and we explore two possible variance estimation approaches. Simulation experiments reveal the improvement of the proposed bagging estimator relative to the original estimator and compare the two variance estimation approaches.
Release date: 2014-12-19 - 4. 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-X201200111686Description:
We present a generalized estimating equations approach for estimating the concordance correlation coefficient and the kappa coefficient from sample survey data. The estimates and their accompanying standard error need to correctly account for the sampling design. Weighted measures of the concordance correlation coefficient and the kappa coefficient, along with the variance of these measures accounting for the sampling design, are presented. We use the Taylor series linearization method and the jackknife procedure for estimating the standard errors of the resulting parameter estimates. Body measurement and oral health data from the Third National Health and Nutrition Examination Survey are used to illustrate this methodology.
Release date: 2012-06-27 - 6. Statistical foundations of cell-phone surveys ArchivedArticles and reports: 12-001-X201000211382Description:
The size of the cell-phone-only population in the USA has increased rapidly in recent years and, correspondingly, researchers have begun to experiment with sampling and interviewing of cell-phone subscribers. We discuss statistical issues involved in the sampling design and estimation phases of cell-phone studies. This work is presented primarily in the context of a nonoverlapping dual-frame survey in which one frame and sample are employed for the landline population and a second frame and sample are employed for the cell-phone-only population. Additional considerations necessary for overlapping dual-frame surveys (where the cell-phone frame and sample include some of the landline population) are also discussed. We illustrate the methods using the design of the National Immunization Survey (NIS), which monitors the vaccination rates of children age 19-35 months and teens age 13-17 years. The NIS is a nationwide telephone survey, followed by a provider record check, conducted by the Centers for Disease Control and Prevention.
Release date: 2010-12-21 - 7. 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 - 8. Estimation of attributable number of deaths and standard errors from simple and complex sampled cohorts ArchivedArticles and reports: 11-522-X200600110400Description:
Estimates of the attributable number of deaths (AD) from all-causes can be obtained by first estimating population attributable risk (AR) adjusted for confounding covariates, and then multiplying the AR by the number of deaths determined from vital mortality statistics that occurred for a specific time period. Proportional hazard regression estimates of adjusted relative hazards obtained from mortality follow-up data from a cohort or a survey is combined with a joint distribution of risk factor and confounding covariates to compute an adjusted AR. Two estimators of adjusted AR are examined, which differ according to the reference population that the joint distribution of risk factor and confounders is obtained. The two types of reference populations considered: (i) the population that is represented by the baseline cohort and (ii) a population that is external to the cohort. Methods based on influence function theory are applied to obtain expressions for estimating the variance of the AD estimator. These variance estimators can be applied to data that range from simple random samples to (sample) weighted multi-stage stratified cluster samples from national household surveys. The variance estimation of AD is illustrated in an analysis of excess deaths due to having a non-ideal body mass index using data from the second National Health and Examination Survey (NHANES) Mortality Study and the 1999-2002 NHANES. These methods can also be used to estimate the attributable number of cause-specific deaths or incident cases of a disease and their standard errors when the time period for the accrual of is short.
Release date: 2008-03-17 - Articles and reports: 11-522-X200600110417Description:
The coefficients of regression equations are often parameters of interest for health surveys and such surveys are usually of complex design with differential sampling rates. We give estimators for the regression coefficients for complex surveys that are superior to ordinary expansion estimators under the subject matter model, but also retain desirable design properties. Theoretical and Monte Carlo properties are presented.
Release date: 2008-03-17 - Articles and reports: 11-522-X20050019461Description:
We propose a generalization of the usual coefficient of variation (CV) to address some of the known problems when used in measuring quality of estimates. Some of the problems associated with CV include interpretation when the estimate is near zero, and the inconsistency in the interpretation about precision when computed for different one-to-one monotonic transformations.
Release date: 2007-03-02
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- Surveys and statistical programs – Documentation: 11-522-X19990015672Description:
Data fusion as discussed here means to create a set of data on not jointly observed variables from two different sources. Suppose for instance that observations are available for (X,Z) on a set of individuals and for (Y,Z) on a different set of individuals. Each of X, Y and Z may be a vector variable. The main purpose is to gain insight into the joint distribution of (X,Y) using Z as a so-called matching variable. At first however, it is attempted to recover as much information as possible on the joint distribution of (X,Y,Z) from the distinct sets of data. Such fusions can only be done at the cost of implementing some distributional properties for the fused data. These are conditional independencies given the matching variables. Fused data are typically discussed from the point of view of how appropriate this underlying assumption is. Here we give a different perspective. We formulate the problem as follows: how can distributions be estimated in situations when only observations from certain marginal distributions are available. It can be solved by applying the maximum entropy criterium. We show in particular that data created by fusing different sources can be interpreted as a special case of this situation. Thus, we derive the needed assumption of conditional independence as a consequence of the type of data available.
Release date: 2000-03-02
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