Multiple imputation for nonignorable missing data

다국어 초록 (Multilingual Abstract)

Multiple imputation is a popular technique for analyzing incomplete data. Missing at random mechanism is often assumed when multiple imputation is performed, assuming that the response mechanism does not depend on the missing variable. However, the assumption of ignorable nonresponse may lead to largely biased estimates when in fact the missingness is nonignorable. In this paper, we propose a multiple imputation method in the presence of nonignorable nonresponse. In the proposed method, we take the selection model approach and specify the response model and the respondents’ outcome model to capture the joint model of the study variable and the response indicator. The proposed data augmentation algorithm uses the respondents’ outcome model and incorporates a semiparametric estimation of the respondents’ outcome model. The proposed multiple imputation method performs well if the specified response model is correct. Limited simulation studies are presented to check the performance of the proposed multiple imputation method.

참고문헌 (Reference)

1 Durrant, G. B., "Using data augmentation to correct for non-ignorable non-response when surrogate data are available : an application to the distribution of hourly pay" 169 : 605-623, 2006

2 Chang, T., "Using calibration weighting to adjust for nonresponse under a plausible model" 95 : 555-571, 2008

3 Kott, P. S., "Using calibration weighting to adjust for nonresponse and coverage errors" 105 : 1265-1275, 2010

4 Tanner, M. A., "The calculation of posterior distributions by data augmentation" 82 (82): 528-540, 1987

5 Little,R.J.A, "Statistical Analysis With Missing Data" Wiley 2002

6 Carpenter, J. R., "Sensitivity analysis after multiple imputation under missing at random : a weighting approach" 16 : 259-275, 2007

7 Gelfand, A. E., "Sampling based approaches to calculating marginal densities" 85 : 398-409, 1990

8 Heckman, J. J., "Sample Selection Bias as a Specification error" 47 (47): 153-161, 1979

9 Riddles, M. K., "Propensity-score-adjustment method for nonignorable nonresponse" 215-245, 2016

10 Little, R. J. A., "Pattern-mixture models for multivariate incomplete data with covariates" 52 : 98-111, 1996

11 Kim, J. K., "Parametric fractional imputation for missing data analysis" 98 : 119-132, 2011

12 Van Buuren, S., "Multiple imputation of missing blood pressure covariates in survival analysis" 18 (18): 681-694, 1999

13 Rubin, D. B., "Multiple imputation for interval estimation from simple random sample with ignorable nonresponse" 81 : 366-374, 1986

14 Rubin, D. B., "Multiple Imputation for Nonresponse in Surveys" Wiley 1987

15 Little, R. J. A., "Modeling the drop-out mechanism in longitudinal studies" 90 : 1112-1121, 1995

16 Greenlees, J. S., "Imputation of missing values when the probability of response depends on the variable being imputed" 77 : 251-261, 1982

17 Rubin, D. B., "Formalizing subjective notions about the effect of nonrespondents in sample surveys" 72 : 538-543, 1977

18 Qin, J., "Estimation with survey data under nonignorable nonresponse or informative sampling" 97 : 193-200, 2002

19 Silverman, B. W., "Density Estimation for Statistics and Data Analysis" Chapman & Hall/CRC 1986

20 Peress, M., "Correcting for survey nonresponse using variable response propensity" 105 : 1418-1430, 2010

21 Zellner, A., "Bayesian analysis of dichotomous quantal response models" 25 : 365-393, 1984

22 Box, G. E. P., "Bayesian Inference in Statistical Analysis" Wiley 1992

23 Wang, S., "An instrument variable approach for identification and estimation with nonignorable nonresponse" 24 : 1097-1116, 2014

24 Giusti, C., "An analysis of nonignorable nonresponse to income in a survey with a rotating panel design" 27 : 211-229, 2011

25 Gilks, W. R., "Adaptive rejection sampling for Gibbs sampling" 41 : 337-348, 1992

26 Kim, J. K., "A semi-parametric estimation of mean functionalswith non-ignorable missing data" 106 : 157-165, 2011

27 Galimard, J. -E., "A multiple imputation approach for mnar mechanisms compatible with Heckman’s model" 35 : 2907-2920, 2016