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Nonresponse in surveys with callbacks

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A class of models is considered for the response-nonresponseof individuals who are given repeated opportunities to respond toa survey questionnaire. From an error-free list of sampling units,a probability sample of units is selected to estimate the univariatepopulation mean Y. Associated with each unit is a response(' )probability q(,k), where 0 < q(,k) (LESSTHEQ) 1. The sampled units which do not initially respond to the survey are recontacted on a second call. On the r('th) call, r = 1,2,..., R, those units are recontacted which have not furnished a response by the (r-1)('st) call;Assuming the population is partitioned into K categories, models are developed from the described survey situation whose parameters include f(,k)and q(,k) (k = 1,2,..., K), where f(,k) is the population proportion of units in the k('th) category, and q(,k) is the response probability of a unit in the k('th) category. It is assumed that the units in a part of the population will never respond to any call of the survey. Various allocations of units in this part of the population to the K categories are discussed and appropriate models are described. Explicit expressions for the maximum likelihood estimates of the parameters in these models are given;For the estimation of Y, we use the estimator(' );(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);where f(,k) is the maximum likelihood estimate of f(,k) and y(,k) is the(' )sample mean of Y for units in the k('th) category over all calls. Thisestimator is consistent for fixed K, and also consistent for sequences of samples in which K is allowed to increase to infinity. The asymptotic variance of the estimator of(' )Y and a consistent estimate of the asymptotic variance are given for fixed K;The model is extended to the sample designs of stratified random sampling, and two stage sampling with random sampling at the second stage. Estimators of the number of units in the k('th) category, k = 1,2,..., K, for the population are produced for these designs. Consistent estimators of the covariance matrix are given. Estimators of the population total of Y are constructed and variances and consistent estimators of the variances are given;An example is given to illustrate the major features of the method.