Modelos aditivos parcialmente lineares multivariados

Abstract

In the present work, Multivariate Partially Linear Additive Models are presented, that is, models that encompass both linear and nonlinear relationships between the response variable and the explanatory variables. As it is a multivariate model, the response variable is presented as a vector of variables. The objective of the work is to study such models and implement an algorithm that allows for the estimation of the parameters. To describe the non-parametric components, B-Splines are used. In order to obtain the estimators of the model parameters, the penalized maximum likelihood method is used, and the smoothing parameters, given by lambda, are chosen through the Cross Validation method. Through the penalized likelihood function, we also obtain the information matrix, which will provide the standard deviation estimates of the parameter estimators. When the information matrix is not invertible, we apply the bootstrap method. Finally, to evaluate the proposed model, simulation studies were carried out, and an application was made to a dataset from the 2003 edition of PISA, an assessment conducted every three years by the Organisation for Economic Co-operation and Development (OECD) that measures the performance of 15-year-old students in reading, mathematics, and science.