Compromise allocation in multivariate stratified sample surveys under two stage randomized response model

A general model for the randomized response (RR) method was introduced by Warner (J. Am. Stat. Assoc. 60:63–69, 1965) when a single-sensitive question is under study. However, since social surveys are often based on questionnaires containing more than one sensitive question, the analysis of multiple RR data is of considerable interest. In multivariate stratified surveys with multiple RR data the choice of optimum sample sizes from various strata may be viewed as a multiobjective nonlinear programming problem. The allocation thus obtained may be called a “compromise allocation” in sampling literature. This paper deals with the two-stage stratified Warner’s RR model applied to multiple sensitive questions. The problems of obtaining compromise allocations are formulated as multi-objective integer non linear programming problems with linear and quadratic cost functions as two separate problems. The solution to the formulated problems are achieved through goal programming technique. Numerical examples are presented to illustrate the computational details.

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