A novel partially linear varying coefficient model with diagnostic analysis for the Birnbaum-Saunders distribution: application to real-world air pollution data

In recent years, semi-parametric modeling has proven successful in describing phenomena that necessitate the modeling of non-linear structures using both parametric and nonparametric components. Partially linear varying coefficient models have emerged as a valuable alternative for modeling the effect of nonlinear interactions between a response variable and a set of covariates across diverse phenomena. In this work, we propose a novel statistical model based on the reparameterized Birnbaum-Saunders distribution, where the systematic component allows the regression coefficients to vary smoothly with respect to certain covariates. To obtain the maximum penalized likelihood estimates of the model parameters, we propose Fisher scoring and weighted backfitting algorithms based on linear spline smoothing. We conduct residual and local influence analyses to assess the potential impact of individual observations on the model fit. Finally, we present a simulation study based on Monte Carlo experiments for evaluate de maximum penalized likelihood estimators, and provide an application of the proposed model to a real-world air pollution dataset, demonstrating its effectiveness in modeling real-world phenomena. The model has been fully implemented in the R programming language.