A Stratified Multi-proportions Randomized Response Model Lee, Gi-Sung; Park, Kyung-Soon;
We propose a multi-proportions randomized response model by stratified simple random sampling for surveys of sensitive issues of a polychotomous population composed of several stratum. We also systemize a theoretical validity to apply multi-proportions randomized response model (Abul-Ela et al.` model, Eriksson`s model) to stratified simple random sampling and derive the estimate and its dispersion matrix of the proportion of sensitive characteristic of population using the suggested model. Two types of sample allocations (proportional allocation and optimum allocation) are considered under the fixed cost. In efficiency, the Eriksson`s model by stratified sampling are compared to the Abul-Ela et al.` model.
multiproportions randomized response model;stratified random sampling;sample allocation;efficiency;
A multiplicative unrelated quantitative randomized response model, Korean Journal of Applied Statistics, 2016, 29, 5, 897
Abul-Ela, A.-L. A., Greenberg, B. G. and Horvitz, D. G. (1967). A multi-proportions randomized response model, Journal of the American Statistical Association, 62, 990-1008.
Ahn, S. C. and Lee, G. S. (2003). A stratified unrelated question model, Journal of the Korean Data Analysis Society, 5, 853-864.
Chaudhuri, A. and Mukerjee, R. (1988). Randomized Response: Theory and Techniques, Marcel Dekker, Inc., New York.
Eriksson, S. (1973). Randomized interviews for sensitive questions (Ph. D. thesis), University of Gothenburg.
Greenberg, B. G., Abul-Ela, A. A., Simmons, W. R. and Horvitz, D. G. (1969). The unrelated question randomized response model: Theoretical framework, Journal of the American Statistical Association, 64, 520-539.
Kim, J. M. and Warde, W. D. (2004). A stratifiedWarner's randomized response model, Journal of Statistical Planning and Inference, 120, 155-165.
Lee, G. S., Ryu, J. B., Hong, K. H. and Son, C. K. (2007). A study on two-stage cluster Mangat-Singh model, Journal of The Korean Data Analysis Society, 9, 1801-1810.
Warner, S. L. (1965). Randomized response; A survey technique for eliminating evasive answer bias, Journal of the American Statistical Association, 60, 63-69.