종단자료 결측치의 대체방법 비교 = A Comparison of Imputation Methods for Incomplete Longitudinal Data

다국어 초록 (Multilingual Abstract)

This paper compared the Complete Case analysis (CC) method with 10 different imputation methods: the last observation carried forward imputation, the within-class mean imputation, the within-class random imputation, the regression imputation, the stochastic regression imputation, the sequential mean imputation and 4 multiple imputation methods, the within-class random multiple imputation, the stochastic regression multiple imputation, the sequential mean multiple imputation, and PROC MI (SAS procedure). We not only introduced the theoretical principles for each method, but also compared the performance of each method using data generated from the Korean Education and Employment Panel (KEEP) data for continuous, ordinal, and binary outcome variables.
When the outcome variable was continuous, the PROC MI method performed better than the other methods based on the bias of population mean estimate and coverage probability. When the outcome variables were ordinal or binary, Paik's (1997) Seq_MI method performed better than the other methods. The results of this research showed that Paik's method, intended to be used under monotone missing pattern conditions, performed well even under arbitrary missing pattern conditions.

국문 초록 (Abstract)

이 연구에서는 한국교육고용패널(KEEP) 자료의 기준년도 자료와 1차, 2차, 3차 추수조사 자료를 이용하여 결측치에 대한 대체방법들이 연속형과 순서형, 이분형 등 세 가지 종속변수별로 비교되었다. 비교된 대체방법들은 이월대체, 집단내 평균대체, 집단내 확률대체, 회귀대체, 확률 회귀대체, 순차적 평균대체 등의 여섯 가지 단일대체 방법들과 집단내 확률대체, 확률 회귀대체, 순차적 평균대체, PROC MI 등의 네 가지 다중대체 방법들이었으며, 비교의 결과는 종속변수의 특징에 관계없이 PROC MI와 Paik(1997)의 순차적 평균대체를 사용하는 다중대체 방법이 다른 방법들보다 효과적이었다. PROC MI는 순서형 변수와 이분형 변수의 임의 결측유형에서는 사용할 수 없기 때문에 Paik(1997)의 순차적 평균대체를 이용한 다중대체 방법이 대부분의 실험조건에서 전반적으로 효과적인 대체결과를 가지는 것으로 나타났다.

참고문헌 (Reference)

1 강민아, "행정학 및 정책학 조사연구에서 결측치 발생과 처리 방법에 대한 고찰" 한국행정학회 40 (40): 31-52, 2006

2 김덕준, "행정조사분석에서의 결측치 처리방법: NORM을 활용한 다중대체방법을 중심으로" 한국국정관리학회 17 (17): 107-128, 2007

3 심정숙, "한국복지패널에서 패널무응답 대체방법 연구" 480-493, 2008

4 이규민, "한국교육종단연구의 표본설계 자료의 질관리 및 분석방안 연구" 한국교육개발원 2007

5 신택수, "잠재성장 모델 하에서 다양한 결측치 분석 기법 비교" 한국교육평가학회 19 (19): 193-214, 2006

6 신형원, "범주형 자료의 결측치 추정방법 성능 비교" 한국통계학회 15 (15): 4-44, 2002

7 김규성, "무응답 대체방법과 대체효과" 1 (1): 1-19, 2000

8 김진, "농가경제조사에 대한 대체법 비교" 통계청 9 (9): 133-145, 2004

9 Yang,S, "comparison of imputation methods for incomplete longitudinal data" Sungkyunkwan University 2008

10 Kalton,G., "The treatment of missing survey data," 12 : 1-16, 1986

11 Paik,M.C, "The Generalized estimating equation approach when data are not missing completely at random" 92 : 1320-1329, 1997

12 Little,R.J.A.,, "Statistical Analysis with Missing Data,2nd edition" Wiley 2002

13 SAS Institute Inc, "SAS/STAT Software,Version"

14 Schafer,J.L, "Multiple imputation:a primer," 8 : 3-15, 1999

15 Rubin,D.B, "Multiple Imputation for Nonresponse in Surveys," John Wiley and Sons 1987

16 Fichman,M., "Multiple Imputation for Missing Data:Making the most of What You Know," 6 (6): 282-308, 2003

17 Little,R.J.A, "Modeling the dropout mechanism in repeated measures studies" 90 : 1112-11121, 1995

18 Demirtas,H, "Modeling incomplete longitudinal data" 3 : 305-321, 2004

19 Hogan,J.W., "Model-based approaches to analysing incomplete longitudinal and failure time data" 16 : 239-258, 1997

20 Schafer,J.L, "Missing data:Our view of the State of the Art" 7 (7): 147-177, 2002

21 Peugh,J.L.,, "Missing data in Educational Research: A review of reporting practices and suggestions for improvement" 74 (74): 525-556, 2004

22 Croninger,R.G, "Missing data and institutional research" 127 : 33-48, 2005

23 Allison,P.D, "Missing Data,Sage University Paper Series on Quantitative Applications inthe Social Sciences" Sage Publications. 7-136, 2002

24 Hedeker,D, "Longitudinal Data Analysis" John Wiley and Sons 2005

25 Rubin,D.B, "Inference and missing data" 63 : 581-592, 1976

26 Gornbein,J.A, "Incomplete data in repeated measures analysis," 1 : 275-295, 1992

27 Saunders,J.A., "Imputing Missing Data: A comparison of Methods for social Work Researchers" 30 (30): 19-31, 2006

28 Bokossa,M.C., "Imputation of test scores in the National Education Longitudinal Study of 1988, U.S. Department of Education, National Center of Education Statistics" Government Printing Office 2001

29 Engels,J.M, "Imputation of missing longitudinal data:a comparison of methods," 56 : 968-976, 2003

30 Winglee,M, "Handling item nonresponse in the U.S.Component of the IEA Reading Literacy Study" 26 (26): 343-359, 2001

31 Hogan,J.W, "Handling drop-out in longitudinal studies" 23 : 1455-1497, 2004

32 Hu, M., "Evaluation of Some Popular ImputationAlgorithms, Proceeding of the Survey Research Methods Section" 308-313, 1998

33 Allison,P.D, "Estimation of Linear Models with Incomplete Data,In Sociological Methodology" 71-103, 1987

34 Davey,A, "Correcting for selective nonresponse in the National Longitudinal Survey of Youth using multiple imputation," 36 (36): 500-519, 2000

35 강신수, "Comparison of Five Single Imputation Methods in General Missing Pattern" 한국데이터정보과학회 15 (15): 945-955, 2004

36 강신수, "Comparison of EM and Multiple Imputation Methods with Traditional Methods in Monotone Missing Pattern" 한국데이터정보과학회 16 (16): 95-106, 2005

37 Breiman,L, "Classification and regression tree, Monterey" Wadsworth and Brooks 1984

38 Twisk,J, "Attrition in longitudinal studies: How to deal with missing data" 55 (55): 329-337, 2002

39 Molenberghs, G, "Analyzing incomplete longitudinal clinical trial data" 5 (5): 445-464, 2004

40 Diggle,P.J, "Analysis of Longitudinal Data,2nd edition," Oxford University Press 2002

41 Hu,M, "A study of Imputation Algorithms"

42 Pigott,T.D, "A review of methods for missing data" 7 (7): 353-383, 2001

43 Ambler,G.,, "A comparison of imputation techniques for handling missingpredictor values in a risk model with a binary outcomes" 16 : 277-298, 2007