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- Articles and reports: 12-001-X20040016993Description:
The weighting cell estimator corrects for unit nonresponse by dividing the sample into homogeneous groups (cells) and applying a ratio correction to the respondents within each cell. Previous studies of the statistical properties of weighting cell estimators have assumed that these cells correspond to known population cells with homogeneous characteristics. In this article, we study the properties of the weighting cell estimator under a response probability model that does not require correct specification of homogeneous population cells. Instead, we assume that the response probabilities are a smooth but otherwise unspecified function of a known auxiliary variable. Under this more general model, we study the robustness of the weighting cell estimator against model misspecification. We show that, even when the population cells are unknown, the estimator is consistent with respect to the sampling design and the response model. We describe the effect of the number of weighting cells on the asymptotic properties of the estimator. Simulation experiments explore the finite sample properties of the estimator. We conclude with some guidance on how to select the size and number of cells for practical implementation of weighting cell estimation when those cells cannot be specified a priori.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - 3. Weighted estimation in multilevel ordinal and binary models in the presence of informative sampling designs ArchivedArticles and reports: 12-001-X20040016997Description:
Multilevel models are often fitted to survey data gathered with a complex multistage sampling design. However, if such a design is informative, in the sense that the inclusion probabilities depend on the response variable even after conditioning on the covariates, then standard maximum likelihood estimators are biased. In this paper, following the Pseudo Maximum Likelihood (PML) approach of Skinner (1989), we propose a probability weighted estimation procedure for multilevel ordinal and binary models which eliminates the bias generated by the informativeness of the design. The reciprocals of the inclusion probabilities at each sampling stage are used to weight the log likelihood function and the weighted estimators obtained in this way are tested by means of a simulation study for the simple case of a binary random intercept model with and without covariates. The variance estimators are obtained by a bootstrap procedure. The maximization of the weighted log likelihood of the model is done by the NLMIXED procedure of the SAS, which is based on adaptive Gaussian quadrature. Also the bootstrap estimation of variances is implemented in the SAS environment.
Release date: 2004-07-14
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- Articles and reports: 12-001-X20040016993Description:
The weighting cell estimator corrects for unit nonresponse by dividing the sample into homogeneous groups (cells) and applying a ratio correction to the respondents within each cell. Previous studies of the statistical properties of weighting cell estimators have assumed that these cells correspond to known population cells with homogeneous characteristics. In this article, we study the properties of the weighting cell estimator under a response probability model that does not require correct specification of homogeneous population cells. Instead, we assume that the response probabilities are a smooth but otherwise unspecified function of a known auxiliary variable. Under this more general model, we study the robustness of the weighting cell estimator against model misspecification. We show that, even when the population cells are unknown, the estimator is consistent with respect to the sampling design and the response model. We describe the effect of the number of weighting cells on the asymptotic properties of the estimator. Simulation experiments explore the finite sample properties of the estimator. We conclude with some guidance on how to select the size and number of cells for practical implementation of weighting cell estimation when those cells cannot be specified a priori.
Release date: 2004-07-14 - Articles and reports: 12-001-X20040016996Description:
This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.
Release date: 2004-07-14 - 3. Weighted estimation in multilevel ordinal and binary models in the presence of informative sampling designs ArchivedArticles and reports: 12-001-X20040016997Description:
Multilevel models are often fitted to survey data gathered with a complex multistage sampling design. However, if such a design is informative, in the sense that the inclusion probabilities depend on the response variable even after conditioning on the covariates, then standard maximum likelihood estimators are biased. In this paper, following the Pseudo Maximum Likelihood (PML) approach of Skinner (1989), we propose a probability weighted estimation procedure for multilevel ordinal and binary models which eliminates the bias generated by the informativeness of the design. The reciprocals of the inclusion probabilities at each sampling stage are used to weight the log likelihood function and the weighted estimators obtained in this way are tested by means of a simulation study for the simple case of a binary random intercept model with and without covariates. The variance estimators are obtained by a bootstrap procedure. The maximization of the weighted log likelihood of the model is done by the NLMIXED procedure of the SAS, which is based on adaptive Gaussian quadrature. Also the bootstrap estimation of variances is implemented in the SAS environment.
Release date: 2004-07-14
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