Sample allocation problem in multi-objective multivariate stratified sample surveys under two stage randomized response model

Abstract

Warner (1965) introduced the randomized response model as an alternative survey technique for socially undesirable or incriminating behaviour questions in order to reduce response error, protect a respondent’s privacy, and increase response rates. In multivariate stratified surveys with multiple randomised response data the choice of optimum sample sizes from various strata may be viewed as a multi-objective nonlinear programming problem. The allocation thus obtained may be called a “compromise allocation” in sampling literature.

In this paper, we have formulated two stage stratified Warner’s Randomised Response model (RRM) as a multi-objective integer non-liner optimization problem. In this problem of RRM we have minimized the square root of coefficient of variations instead of variations for different characteristics because the coefficient of variation is unit free, subject to the linear and quadratic cost constraint. The multi-objective optimization problem of RRM has been solved by lexicographic goal programming integrated with fixed priority - distance method. The solution obtained by lexicographic goal programming Integrated with fixed priority - distance have been compared with various existing approaches namely the value function approach, goal programming techniques,  - constraint method and distance-based method and Khuri & Cornel distance based method. A numerical example is also been presented to illustrate the computational details.

https://doi.org/10.28919/jmcs/3376