Parameter estimation from incomplete data in binomial regression when the missing data mechanism is nonignorable.

We propose a method for estimating parameters in binomial regression models when the response variable is missing and the missing data mechanism is nonignorable. We assume throughout that the covariates are fully observed. Using a logit model for the missing data mechanism, we show how parameter estimation can be accomplished using the EM algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). An example from the Six Cities Study (Ware et al., 1984, American Review of Respiratory Diseases 129, 366-374) is presented to illustrate the method.

[1]  Nan M. Laird,et al.  Regression Analysis for Categorical Variables with Outcome Subject to Nonignorable Nonresponse , 1988 .

[2]  R. Little.  Models for Nonresponse in Sample Surveys , 1982 .

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

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

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

[6]  Lung-fei Lee,et al.  Identification and Estimation in Binary Choice Models with Limited (Censored) Dependent Variables , 1979 .

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

[8]  J. Ibrahim.  Incomplete Data in Generalized Linear Models , 1990 .

[9]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[10]  Robin Thompson,et al.  Composite Link Functions in Generalized Linear Models , 1981 .

[11]  M. Kenward,et al.  Informative dropout in longitudinal data analysis (with discussion) , 1994 .

[12]  R. Olsen,et al.  A Least Squares Correction for Selectivity Bias , 1980 .

[13]  D. Dockery,et al.  Passive smoking, gas cooking, and respiratory health of children living in six cities. , 2015, The American review of respiratory disease.

[14]  A. Ekholm,et al.  A MODEL FOR A BINARY RESPONSE WITH MISCLASSIFICATIONS , 1982 .

[15]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[16]  Erik V. Nordheim,et al.  Inference from Nonrandomly Missing Categorical Data: An Example from a Genetic Study on Turner's Syndrome , 1984 .

[17]  Donald B. Rubin,et al.  Multiple imputation in mixture models for nonignorable nonresponse with follow-ups , 1993 .