Multiple imputation for nonignorable missing data

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.

[1]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[2]  Jae Kwang Kim,et al.  A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data , 2011 .

[3]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[4]  Peter E. Rossi,et al.  Bayesian analysis of dichotomous quantal response models , 1984 .

[5]  James R Carpenter,et al.  Sensitivity analysis after multiple imputation under missing at random: a weighting approach , 2007, Statistical methods in medical research.

[6]  Jae Kwang Kim.  Parametric fractional imputation for missing data analysis , 2011 .

[7]  William S. Reece,et al.  Imputation of Missing Values When the Probability of Response Depends on the Variable Being Imputed , 1982 .

[8]  D. Rubin.  Multiple imputation for nonresponse in surveys , 1989 .

[9]  Michael Peress.  Correcting for Survey Nonresponse Using Variable Response Propensity , 2010 .

[10]  Sylvie Chevret,et al.  A multiple imputation approach for MNAR mechanisms compatible with Heckman's model , 2016, Statistics in medicine.

[11]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[12]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[13]  Gabriele B. Durrant,et al.  Using data augmentation to correct for non‐ignorable non‐response when surrogate data are available: an application to the distribution of hourly pay , 2006 .

[14]  D. Rubin.  Formalizing Subjective Notions about the Effect of Nonrespondents in Sample Surveys , 1977 .

[15]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[16]  Jae Kwang Kim,et al.  An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse , 2014 .

[17]  Roderick J. A. Little,et al.  Modeling the Drop-Out Mechanism in Repeated-Measures Studies , 1995 .

[18]  R. Little,et al.  Pattern-mixture models for multivariate incomplete data with covariates. , 1996, Biometrics.

[19]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[20]  Roderick J. A. Little,et al.  An analysis of nonignorable nonresponse to income in a survey with a rotating panel design , 2011 .

[21]  Phillip S. Kott,et al.  Using Calibration Weighting to Adjust for Nonresponse Under a Plausible Model (with full appendices) , 2007 .

[22]  Jae Kwang Kim,et al.  A semi-parametric estimation of mean functionals with non-ignorable missing data , 2010 .

[23]  H. Boshuizen,et al.  Multiple imputation of missing blood pressure covariates in survival analysis. , 1999, Statistics in medicine.

[24]  Ted Chang,et al.  Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse , 2010 .

[25]  Jun Shao,et al.  Estimation With Survey Data Under Nonignorable Nonresponse or Informative Sampling , 2002 .

[26]  P. Kott.  Using Calibration Weighting to Adjust for Nonresponse and Coverage Errors , 2006 .

[27]  Jae Kwang Kim,et al.  A Propensity-score-adjustment Method for Nonignorable Nonresponse , 2016 .

[28]  D. Rubin,et al.  Multiple Imputation for Interval Estimation from Simple Random Samples with Ignorable Nonresponse , 1986 .

[29]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .