Variable selection in small area model with measurement error in covariates

Model based small area estimation relies on mixed effects regression models that link the small areas and borrow strength from similar domains. The variability of the random effects, while accounting for lack of fit, affects uncer- tainty of both point and interval estimators of small area means. In the presence of good covariates, small variation of the random small area effects is expected, but when measurement error is present it has been proved that parameter esti- mates may be dramatically biased and the variability of the random effects and, consequently, of the small area means significantly increases. Adopting a fully Bayesian approach, we model the measurement error through a mixture that al- lows us, using spike and slab priors, to infer the presence or not of measurement error in the covariates. We empirically evaluate the accuracy of the estimates in different simulation scenario. We also apply the proposed procedure to the well known Battese data and to data from the 2010 Italian household budget survey (Banca d’Italia, Indagine sui bilanci delle famiglie italiane).