  Small area models are mixed effects regression models that link the small
areas and borrow strength from similar domains. When the auxiliary variables
used in the models are measured with error, small area estimators that ignore
the measurement error may be worse than direct estimators. Alternative small
area estimators accounting for measurement error have been proposed in the
literature but only for continuous auxiliary variables. Adopting a Bayesian
approach, we extend the unit-level model in order to account for measurement
error in both continuous and categorical covariates. For the discrete variables
we model the misclassification probabilities and estimate them jointly with all
the unknown model parameters. We test our model through a simulation study
exploring different scenarios. The impact of the proposed model is emphasized
through application to data from the Ethiopia Demographic and Health Survey
where we focus on the women's malnutrition issue, a dramatic problem in
developing countries and an important indicator of the socio-economic progress
of a country.
