Correcting measurement errors with Bayesian networks when the variables are continuous and discrete

Measurement error is the difference between a feature value provided by the respondent and the corresponding true but unknown value. Measurement error is one of the main nonsampling error sources. Object-oriented Bayesian networks (OOBNs) have been recently proposed to model and correct measurement errors. In particular, the measurement error in a categorical variable is described by a mixed measurement model implemented in a BN. We apply this model to 2008 Survey on Household Income and Wealth (SHIW), conducted by Banca d’Italia. In particular, financial assets in SHIW are affected by misreporting of financial amounts with a prevalence of underreporting. The measurement error model is estimated using a validation sample. Specifically, the probability of an error is estimated from the validation sample using a BN model. The variables are mixed continuous and discrete. Hence, we need to discretize before learning the BN. This is a challenging problem since discretization should be performed accounting for the association structure; otherwise, if the continuous variables are independently discretized, their relation structure could be dramatically altered. Here we propose a methodology to learn the network while discretizing. Once the error probability is estimated, the overall measurement error model is implemented and microdata are imputed