A compositional methodology with external information for free time allocation preferences

The study of free-time activity preferences provides important information on the characteristics and inclinations of specific demographics. Correct modeling of these data can offer a useful insight in the definition of service demand and thus help define effective social strategies. Two important aspects need to be considered when analysing individual preferences on free time. The first difficulty, typical of optimal resource allocation, concerns the constrained nature of the data. There is a sum limit given by the total amount of free time available and, as a consequence, assigned values are not free to vary independently. Statistically this translates into a biased covariance structure. In this perspective the problem can be seen as compositional, which means that by definition these data only carry relative information and should be treated with ad-hoc tools. A second challenge consists in discerning the role that external factors play in determining preferences without, however, forcing the assumption that all information can be explained in this manner. In other words, there could be specific characteristics of the respondents (such as gender, education, etc. . . ) that influence part of the information, and should be considered, but are not able to explain the preference structure in its totality. This duality can be addressed with a methodology that combines together regression and multivariate analysis, proposed in literature as Principal Component Analysis with external information. The purpose of this work is thus to present an application that combines the compositional and external information approach to study free time allocation.