Calibration of multiple-choice questionnaires to assess quantitative indicators

Area of Science:

• Multivariate statistical analysis
• Psychometrics
• Building conservation science

Background:

• Assessing measurement instruments for complex phenomena requires robust methodologies.
• Existing methods may not fully capture the nuances of ordinal data in real-world applications.
• Quantifying the state of decay in historical buildings presents unique challenges.

Purpose of the Study:

• To propose and evaluate a combined approach using Rasch analysis and Nonlinear Principal Component Analysis (PCA).
• To develop a reliable continuous indicator for the state of decay in historical Italian buildings.
• To explore the synergistic potential of integrating latent factor methods.

Main Methods:

• Rasch analysis was employed for questionnaire calibration, variable selection, and category reduction.
• Nonlinear PCA was utilized for optimal scaling of variable categories and computation of a continuous decay indicator.
• The methods were applied to a case study of Italian buildings of architectural and historical interest.

Main Results:

• The combined approach successfully calibrated measurement instruments and quantified building decay.
• A continuous indicator was generated, suitable for independent use in future building inventories.
• The study analyzed the similarities and diverse potentialities of the integrated techniques.

Conclusions:

• The synergistic use of Rasch analysis and Nonlinear PCA offers a powerful framework for assessing measurement instruments.
• This integrated methodology provides a reliable and objective method for quantifying building decay.
• The developed indicator has practical applications in heritage building conservation and inventory management.