모의실험을 기반으로 성향점수 추정을 위한 최적 세부 층 개수 결정에 관한 연구
A study on determining the optimal number of strata for propensity score estimation by simulation studies
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
다수의 무응답이 표본조사에서 발생하고 있으며 무응답 메커니즘에 따라 무응답 처리 방법이 달라진다. 무응답 메커니즘은 MCAR, MAR 그리고 MNAR로 나누어지며 흔히 MAR 무응답에서는보조변수를 독립변수로 한 로지스틱 회귀모형을 이용하여 응답확률(response probability) 또는성향점수(propensity score)를 추정한 후 무응답을 처리한다. 반면 MNAR 무응답인 경우는 성향점수가 관심변수의 함수이지만 무응답이 관심변수에서 발생하기 때문에 관심변수를 독립변수로사용하여 성향점수를 추정하는 것은 불가능하다. 이에 MNAR 무응답임에도 보조변수를 독립변수로 사용한 모형을 이용하여 성향점수를 추정한다. 이 경우 정확한 성향점수가 얻어지지 않기때문에 추정된 성향점수를 이용한 성향점수 보정(propensity score adjusted: PSA)추정량은 편향이발생하고 추정의 정확성이 떨어진다. 최근 MNAR 무응답에서 정확성 향상을 위해 사후층화를이용한 성향점수 추정법이 개발되었다. 또한, Min과 Shin (2018)은 사후층화를 위해 지수 응답확률모형과 초모집단 모형의 오차가 정규분포인 경우에서의 최적 세부 층 개수와 경계를 제안하였다. 본 연구에서는 로그-정규분포, 감마분포를 포함한 다양한 초모집단 분포와 다양한 응답확률 모형에서 사용할 수 있는 최적 세부 층 개수를 모의실험을 통해 제안하였다.
Abstract
A large number of non-responses occur in sample surveys, and the method of handling non-response depends on the non-response mechanisms. Nonresponse mechanisms are divided into MCAR, MAR, and MNAR. Commonly, for MAR nonresponse, the response probability or propensity score is estimated using a logistic regression model with auxiliary variables as independent variables. On the other hand, for MNAR nonresponse, the propensity score is a function of the variable of interest, but since nonresponse occurs in the variable of interest, it is impossible to estimate the propensity score using a model that uses the variable of interest. Therefore, for MNAR nonresponse, the propensity score is estimated using a model in which the auxiliary variable is an independent variable. In this case, since an accurate propensity score can not be obtained, the propensity score adjusted(PSA) estimator using the estimated propensity score is biased and the accuracy of the estimate is reduced. To solve this problem, a propensity score estimation method using post-stratification was developed, and Min and Shin (2018) proposed the optimal number of substrata and boundaries under the assumption of an exponential response probability model and a normally distributed super-population model. In this study, we proposed through simulation the optimal number of substrata that can be used in various distributions and response probability models, including log-normal distribution and gamma distribution.
참고문헌 (13)
- Bethlehem, J., "Working with response probabilities", Journal of Official Statistics, 36, pp.647~674 (2020)
- Chung, H. Y., "Estimation using informative sampling technique when response rate follows exponential function of variable of interest", The Korean Journal of Applied Statistics, 30, pp.993~1004 (2017)
- Chung, H. Y., "A study on non-response bias adjusted estimation for take-all stratum", The Korean Journal of Applied Statistics, 33, pp.409~420 (2020)
- Chung, H. Y., "A response probability estimation for non-ignorable non-response", Communications for Statistical Applications and Methods, 29, pp.263~275 (2022)
- Da Silva, D. N., "Nonparametric propensity weighting for survey nonresponse through local polynomial regression", Survey Methodology, 35(2), pp.165~176 (2009)
- Kim, J. K., "Some theory for propensity-score-adjustment estimators in survey sampling", Survey Methodology, 38, pp.157~165 (2012)
- Lee, M. -H., "Bias corrected imputation method for non-ignorable non-response", The Korean Journal of Applied Statistics, 35, pp.485~499 (2022)
- Min, J. -W., "A study on the determination of substrata using the information of exponential response rate by simulation studies", The Korean Journal of Applied Statistics, 31, pp.621~636 (2018)
- Pfeffermann, D, "Parametric distributions of complex survey data under informative probability sampling", Statistica Sinica, 8, pp.1087~1114 (1998)
- Pfeffermann, D., "Multi-level modelling under informative sampling", Biometika, 93, pp.943~959 (2006)
- Riddles, M. K., "A propensity-score-adjustment method for nonignorable nonresponse", Journal of Survey Statistics and Methodology, 4, pp.215~245 (2016)
- Rosenbaum, P. R., "The central role of the propensity score in observational studies for casual effects", Biometrika, 70, pp.41~55 (1983)
- Yeo, L., "A study to improve the accuracy of the naive propensity score adjusted estimator using double post-stratification method", The Korean Journal of Applied Statistics, 36, pp.547~559 (2023)