Weighting Class Adjustments for Sample Survey

JONES, SHELTON MAURICE. Improved Variance Estimators Using Weighting Class Adjustments for Sample Survey Nonresponse. (Under the direction of Robert G. D. Steel.) In large-scale sample surveys, there will always be the problem of nonresponse. There are several imputation procedures designed to adjust for nonresponding sampling units. Among these are weighting class adjustments. One of the methods under discussion deals with weighting up responding information in class c to the total sample for the class by t Ic/t2c where: i) tIc is an estimator of the total number of eligibles in weighting class c, and ii) t 2c is an estimator of the total number of responding eligibles in weighting class c. When this is done the estimator is no longer unbiased and common variance formulas cannot be utilized efficiently. Emphasis is placed on estimating domain totals with two estimators. The first-order Taylor series approximation or linearization method is used to obtain variance estimates under the following conditions: Condition 1: When tIc and t 2c are generated from sample information but are treated as constants. Condition 2: When tIc and t 2c are generated from sample information and both treated as estimators. Condition 3: When tIc is assumed known from an external source and treated as a constant, whereas t 2c is treated as an estimator based on sample information. Condition 4: When tIc is assumed known from an external source and t 2c an estimator based on sample information but both are treated as constants. Variance estimates from many surveys have in the past relied on estimates that were based on Conditions I and 4. It has been shown, utilizing a simulation study, that variance estimates based on Conditions I and 4 are very erratic in accordance to variations among data, type of weighting class used and response rates. Conversely, when Conditions 2 and 3 are implemented the variance estimates are far more stable and reliable. IMPROVED VARIANCE ESTIMATORS USING WEIGHTING CLASS ADJUSTMENTS FOR SAMPLE SURVEY NONRESPONSE by Shelton Maurice Jones A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science DEPARTMENT OF STATISTICS