Seleção de modelos aditivos parcialmente lineares

Abstract

The covariates in a model may exhibit either a linear or a nonlinear relationship with the response variable, leading to different model configurations. By comparing the various possible combinations as the covariates are assigned to the parametric and nonparametric parts of the model, this study aims to select the most appropriate model—i.e., the one that provides the best fit to the analyzed data. The comparison process begins with an analysis of the second-order derivative curves for each covariate, identifying those that are likely to compose each part of the model. Then, the resulting models from different combinations are compared using techniques such as the likelihood ratio test and the Bayesian Information Criterion (BIC). This methodological approach has not yet been explored in any study, highlighting its significant contribution and advancement in the field. In this study, different categories of models are examined, ranging from Multiple Linear Regression Models to Additive Partial Linear Models (APLMs), the latter being the primary focus of this research. In addition to model selection, other important objectives were achieved for model construction, such as obtaining the penalized maximum likelihood estimators for Additive Partial Linear Models, constructing the curves related to the nonparametric part using P-splines, and determining the smoothing parameter through cross-validation. The simulation studies, as well as the real-data applications presented in this work, produced results that demonstrate the achievement of the objectives, offering valuable contributions to future research.