From multiple choice questionnaires to synthetic indicators: jointly use of Rasch analysis and NonLinear PCA

The jointly use of two latent factors methods is proposed to assess a measurement instrument for underlying phenomena. In particular the decay status of valuable Italian buildings is quantified on the basis of a wide set of observed categorical variables. At the purpose, Rasch analysis is used to properly calibrate the data, to discard non informative variables and redundant categories. As a second step, an optimal scaling technique, Nonlinear PCA, is applied to quantify variable categories and to compute a quantitative decay indicator, which could be independently used for units of future inventory. On the overall, similarities and different capabilities of the two techniques are analyzed and discussed.