Journal of the Korean Data Analysis Society

Korean Data Analysis Society (한국자료분석학회)
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A Stratified Mixed Multiplicative Quantitative Randomize Response Model

층화 혼합 승법 양적속성 확률화응답모형

  • Lee, Gi-Sung (Department of Children Welfare, Woosuk University) ;
  • Hong, Ki-Hak (Department of Computer Science, Dongshin University) ;
  • Son, Chang-Kyoon (Department of Bigdata and Applied Statistics, Dongguk University)
  • 이기성 (우석대학교 아동복지학과) ;
  • 홍기학 (동신대학교 컴퓨터학과) ;
  • 손창균 (동국대학교 빅데이터.응용통계학과)
  • Received : 2018.11.20
  • Accepted : 2018.12.20
  • Published : 2018.12.31

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Abstract

We present a mixed multiplicative quantitative randomized response model which added a unrelated quantitative attribute and forced answer to the multiplicative model suggested by Bar-Lev et al. (2004). We also try to set up theoretical grounds for estimating sensitive quantitative attribute according to circumstances whether or not the information for unrelated quantitative attribute is known. We also extend it into the stratified mixed multiplicative quantitative randomized response model for stratified population along with two allocation methods, proportional and optimum allocation. We can see that the various quantitative randomized response models such as Eichhorn-Hayre's model (1983), Bar-Lev et al.'s model (2004), Gjestvang-Singh's model (2007) and Lee's model (2016a), are one of the special occasions of the suggested model. Finally, We compare the efficiency of our suggested model with Bar-Lev et al.'s (2004) and see that the bigger the value of $C_z$, the more the efficiency of the suggested model is obtained.

Lee(2016a)는 Bar-Lev et al.(2004)의 모형에 무관한 변수를 추가하여 민감한 변수, 변환된 변수 그리고 무관한 변수 중에서 확률장치에 의해 선택된 질문에 응답하도록 하는 승법 양적 확률화응답모형을 제안하였다. 본 연구에서는 Bar-Lev et al.(2004)이 제안한 강요 양적속성 승법모형에 무관한 변수와 강요응답을 새롭게 추가한 혼합 승법 양적속성 확률화응답모형을 제안하였다. 그리고 무관한 변수에 대한 정보를 아는 경우와 모르는 경우로 나누어 민감한 양적속성을 추정할 수 있는 이론적 체계를 구축하였다. 또한, 모집단이 층화되어 있을 때에도 제안한 모형의 적용이 가능하도록 층화 혼합 승법 양적속성 확률화응답모형으로 확장하였고 층화추출에 있어서 비례배분과 최적배분 문제를 다루었다. 마지막으로 기존의 승법모형인 Eichhorn-Hayre(1983) 모형, Bar-Lev et al.(2004) 모형, Gjestvang-Singh(2007) 모형, Lee(2016a) 모형이 제안한 혼합 승법 양적속성 확률화응답모형의 특수한 형태임을 확인할 수 있었고, Bar-Lev et al.(2004) 모형과의 효율성 비교 결과 $C_x$값이 작을수록 그리고 $C_z$값이 클수록 제안한 혼합 승법 양적속성 확률화응답모형이 Bar-Lev et al.(2004)의 모형보다 효율적이었다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. Ahn, S. C., Lee, G. S. (2003). A stratified unrelated question model, Journal of the Korean Data Analysis Society, 5(4B), 853-864. (in Korean).
  2. Ahn, S. C., Lee, G. S. (2004). A stratified discrete quantitative randomized response model, Journal of the Korean Data Analysis Society, 6(1B), 181-191. (in Korean).
  3. Bar-Lev, S. K., Bobovitch, E., Boukai, B. (2004). A note on randomized response models for quantitative data, Metrika, 60, 255-260. https://doi.org/10.1007/s001840300308
  4. Chaudhuri, A., Mukerjee, R. (1988). Randomized Response : Theory and Techniques, Marcel Dekker, Inc., New York.
  5. Cochran, W. G. (1977). Sampling Techniques, 3rd ed. John Wiley and Sons, New York.
  6. Greenberg, B. G., Kubler, R. R., Abernathy, J. R., Horvitz, D. G. (1971). Applications of the RR technique in obtaining quantitative data, Journal of the American Statistical Association, 66, 243-250. https://doi.org/10.1080/01621459.1971.10482248
  7. Eichhorn, B. H., Hayre, L. S. (1983). Scrambled randomized response methods for obtaining sensitive quantitative data, Journal of Statistical Planning and Inference, 7, 307-316. https://doi.org/10.1016/0378-3758(83)90002-2
  8. Gjestvang, C. R., Singh, S. (2007). Forced quantitative randomized response model : a new device, Metrika, 66, 243-257. https://doi.org/10.1007/s00184-006-0108-1
  9. Kim, J. M., Elam, M. E. (2005). A two-stage stratified Warner's randomized response model using optimal allocation, Metrika, 61(1), 1-7. https://doi.org/10.1007/s001840400319
  10. Kim, J. M., Warde, W. D. (2004). A stratified Warner's randomized response model, Journal of Statistical Planning and Inference, 120, 155-165. https://doi.org/10.1016/S0378-3758(02)00500-1
  11. Lee, G. S. (2016a). A multiplicative unrelated quantitative randomized response model, The Korean Journal of Applied Statistics, 29(5), 897-906. (in Korean). https://doi.org/10.5351/KJAS.2016.29.5.897
  12. Lee, G. S. (2016b). A quantitative unrelated randomized response model by replicated systematic sampling, Journal of the Korean Data Analysis Society, 18(3B), 1343-1354. (in Korean).
  13. Lee, G. S. (2017). A two-stage cluster multiplicative unrelated quantitative attribute randomized response model, Journal of the Korean Data Analysis Society, 19(4B), 1897-1906. (in Korean).
  14. Warner, S. L. (1965). Randomized response ; A survey technique for eliminating evasive answer bias, Journal of the American Statistical Association, 60, 63-69. https://doi.org/10.1080/01621459.1965.10480775