Analysis

Description: Many studies face the problem of comparing estimates obtained with different survey methodology, including differences in frames, measurement instruments, and modes of delivery. The problem arises in multimode surveys and in surveys that are redesigned. Major redesign of survey processes could affect survey estimates systematically, and it is important to quantify and adjust for such discontinuities between the designs to ensure comparability of estimates over time. We propose a small area estimation approach to reconcile two sets of survey estimates, and apply it to two surveys in the Marine Recreational Information Program (MRIP), which monitors recreational fishing along the Atlantic and Gulf coasts of the United States. We develop a log-normal model for the estimates from the two surveys, accounting for temporal dynamics through regression on population size and state-by-wave seasonal factors, and accounting in part for changing coverage properties through regression on wireless telephone penetration. Using the estimated design variances, we develop a regression model that is analytically consistent with the log-normal mean model. We use the modeled design variances in a Fay-Herriot small area estimation procedure to obtain empirical best linear unbiased predictors of the reconciled estimates of fishing effort (requiring predictions at new sets of covariates), and provide an asymptotically valid mean square error approximation.

Description:

Auxiliary information is often used to improve the precision of survey estimators of finite population means and totals through ratio or linear regression estimation techniques. Resulting estimators have good theoretical and practical properties, including invariance, calibration and design consistency. However, it is not always clear that ratio or linear models are good approximations to the true relationship between the auxiliary variables and the variable of interest in the survey, resulting in efficiency loss when the model is not appropriate. In this article, we explain how regression estimation can be extended to incorporate semiparametric regression models, in both simple and more complicated designs. While maintaining the good theoretical and practical properties of the linear models, semiparametric models are better able to capture complicated relationships between variables. This often results in substantial gains in efficiency. The applicability of the approach for complex designs using multiple types of auxiliary variables will be illustrated by estimating several acidification-related characteristics for a survey of lakes in the Northeastern US.

Description:

Classical results in finite population sampling tell us that systematic sampling is the most efficient equal-probability one-per-stratum design for certain kinds of autocorrelated superpopulations, but stratified simple random sampling may be much better than systematic sampling if the superpopulation is a trend with uncorrelated errors. What if the superpopulation consists of a trend plus autocorrelated errors? Intuitively, some sort of “compromise” between the two designs might be better than either. Such compromise designs are constructed in this paper and are shown to be examples of Markov chain designs, a wide class of methods for one-per-stratum selection from a finite population. These designs include as special cases systematic sampling, balanced systematic sampling and stratified simple random sampling with one sampling unit per stratum. First and second-order inclusion probabilities are derived for Markov chain designs, yielding the Horvitz-Thompson estimator and its variance. Efficiency of the Horvitz-Thompson estimator is evaluated using superpopulation models. Numerical examples show that new designs considered here can be more efficient than standard designs for superpopulations consisting of trend plus autocorrelated errors. An example of the implementation of Markov chain designs for the 1992 National Resources Inventory in Alaska is given.

Description: Many studies face the problem of comparing estimates obtained with different survey methodology, including differences in frames, measurement instruments, and modes of delivery. The problem arises in multimode surveys and in surveys that are redesigned. Major redesign of survey processes could affect survey estimates systematically, and it is important to quantify and adjust for such discontinuities between the designs to ensure comparability of estimates over time. We propose a small area estimation approach to reconcile two sets of survey estimates, and apply it to two surveys in the Marine Recreational Information Program (MRIP), which monitors recreational fishing along the Atlantic and Gulf coasts of the United States. We develop a log-normal model for the estimates from the two surveys, accounting for temporal dynamics through regression on population size and state-by-wave seasonal factors, and accounting in part for changing coverage properties through regression on wireless telephone penetration. Using the estimated design variances, we develop a regression model that is analytically consistent with the log-normal mean model. We use the modeled design variances in a Fay-Herriot small area estimation procedure to obtain empirical best linear unbiased predictors of the reconciled estimates of fishing effort (requiring predictions at new sets of covariates), and provide an asymptotically valid mean square error approximation.

Description:

Auxiliary information is often used to improve the precision of survey estimators of finite population means and totals through ratio or linear regression estimation techniques. Resulting estimators have good theoretical and practical properties, including invariance, calibration and design consistency. However, it is not always clear that ratio or linear models are good approximations to the true relationship between the auxiliary variables and the variable of interest in the survey, resulting in efficiency loss when the model is not appropriate. In this article, we explain how regression estimation can be extended to incorporate semiparametric regression models, in both simple and more complicated designs. While maintaining the good theoretical and practical properties of the linear models, semiparametric models are better able to capture complicated relationships between variables. This often results in substantial gains in efficiency. The applicability of the approach for complex designs using multiple types of auxiliary variables will be illustrated by estimating several acidification-related characteristics for a survey of lakes in the Northeastern US.

Description:

Classical results in finite population sampling tell us that systematic sampling is the most efficient equal-probability one-per-stratum design for certain kinds of autocorrelated superpopulations, but stratified simple random sampling may be much better than systematic sampling if the superpopulation is a trend with uncorrelated errors. What if the superpopulation consists of a trend plus autocorrelated errors? Intuitively, some sort of “compromise” between the two designs might be better than either. Such compromise designs are constructed in this paper and are shown to be examples of Markov chain designs, a wide class of methods for one-per-stratum selection from a finite population. These designs include as special cases systematic sampling, balanced systematic sampling and stratified simple random sampling with one sampling unit per stratum. First and second-order inclusion probabilities are derived for Markov chain designs, yielding the Horvitz-Thompson estimator and its variance. Efficiency of the Horvitz-Thompson estimator is evaluated using superpopulation models. Numerical examples show that new designs considered here can be more efficient than standard designs for superpopulations consisting of trend plus autocorrelated errors. An example of the implementation of Markov chain designs for the 1992 National Resources Inventory in Alaska is given.