A Proposal for Setting-up Indicators in the Presence of Missing Data: the Case of Vulnerability Indicators

A procedure for the construction of an indicator in the presence of structured missing data is proposed. In particular, we face the problem of creating a ‘measure’ of the damage degree of valuable historical-architectonical buildings on the basis of the observation of several ordinal variables. Our proposal is the jointly use of Nonlinear PCA and an imputation method for missing data treatment. The adopted procedure can be generally applied when an indicator is needed on the basis of the observation of ordinal, but also nominal or numerical, variables, which are deeply interrelated and are affected by systematic missing data. It has the nice feature of treating missing data according to the relevance of variables affected by missing observations and, at the same time, it preserves all the properties of Nonlinear PCA without missing data. Furthermore, the method provides category quantifications and variable loadings that could be used for future inventory of buildings (in general of ‘units’) not included in the initial survey.