Imputation and Estimation Under Nonignorable Nonresponse for Household Surveys with Missing Covariate Information

• Activity Number: 290
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Anna Sikov*+ and Danny Pfeffermann
• Companies: Hebrew University of Jerusalem and University of Southampton/Hebrew University
• Keywords: Bootstrap ; Calibration ; Horvitz-Thompson type estimator ; Respondents distribution ; Nonrespondents distribution

Abstract

In this research we develop and apply new methods for handling not missing at random (NMAR)nonresponse. We assume a model for the outcome variable under complete response and a model for the response probability, which is allowed to depend on the outcome and auxiliary variables. The two models define the model holding for the outcomes observed for the responding units. Our methods utilize information on the population totals of some or all of the auxiliary variables in the two models, but we do not require that the auxiliary variables are observed for the nonresponding units. We develop an algorithm for estimating the parameters governing the two models and show how to estimate the distributions of the missing covariates and outcomes. We investigate conditions for the convergence of the algorithm for parameter estimation and develop conditions for the consistency and asymptotic normality of the estimators obtained by the application of this algorithm. We also consider several test statistics for testing the model fitted to the observed data and study their performance. The new developments are illustrated using real data set collected as part of the Household Expenditure Survey.