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.
Marella, D., Mezzini, M., Vicard, P. (2014). Correcting measurement errors with Bayesian networks when the variables are continuous and discrete. In 7th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computational and Methodological Statistics (ERCIM 2014).