Imputation and estimation under nonignorable nonresponse for household surveys with missing covariate information

Abstract

In this paper 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, which can be tested. 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, which are then used for imputing the missing values for
the nonresponding units and for estimating population means and the variances of the estimators.
We also consider several test statistics for testing the model fitted to the observed data and study
their performance, thus validating the proposed procedure. The new developments are illustrated
using simulated data and a real data set collected as part of the Household Expenditure Survey
carried out by the Israel Central Bureau of Statistics in 2005.

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