Generalized Partially Functional Linear Model with Interaction between Functional Predictors

This paper proposes a generalized partially functional linear model with interaction terms. It is suitable for cases where the response variable is scalar, and the predictor variables include a mix of functional and scalar types, while considering the correlations among functional predictor variables. The model uses principal component analysis for dimensionality reduction, employs maximum likelihood estimation to obtain parameter values, proves the asymptotic properties of the estimates, and validates the model’s accuracy through data simulation experiments. Finally, the proposed model was applied to investigate the influence of air quality, climate factors, and medical and social indicators, along with their interactions, on cancer incidence, which is a binary response.