Dipartimento di Scienze Statistiche

       Functional logistic regression is a scalar-on-function regression method for a binary response variable, introduced in the 1990s. Unlike classical logistic regression, it allows the predictor to be a function, typically a curve observed over time or another continuous domain, rather than a finite set of scalar covariates, making it a natural tool whenever the explanatory information is inherently functional. Estimating this model is far from straightforward. When the functional predictor is approximated through basis expansion methods, severe multicollinearity emerges among the resulting coefficients, which makes the estimates unstable and the model difficult to interpret. In this talk we review some of the main solutions proposed in the literature to overcome this problem, ranging from penalized and regularized approaches to dimension-reduction techniques such as functional principal component analysis. We also present several related regression frameworks, including the PC-ARIMA logit model and the multiresponse logit model, discussing how they extend the basic formulation to more complex settings, such as time-dependent structures and multiple categorical outcomes. Throughout the seminar, we will also present concrete applications drawn from scientific papers published in the field, illustrating how these methods perform on real data and highlighting their practical relevance across different domains.