SMOOTH TRANSITION LOGISTIC REGRESSION MODEL TREE / MODELO DE REGRESSÃO LOGÍSTICA COM TRANSIÇÃO SUAVE ESTRUTURADO POR ÁRVORE (STLR-TREE)
AUTOR(ES)
RODRIGO PINTO MOREIRA
DATA DE PUBLICAÇÃO
2008
RESUMO
The main goal of this work is to adapt the STR-Tree model, which is the combination of a Smooth Transition with Regression model with Classi cation and Regression Tree (CART), in order to use it in Classification. Some changes were made in its structural form and in the estimation. Due to the fact we are doing binary dependent variables classification, is necessary to use the techniques employed in Logistic Regression, so the estimation of the linear part will be made by Maximum Likelihood. Thus the model, which is nonlinear parametric and structured by a decision tree, where each terminal node represents a regime that have their parameters estimated in the same way as in a Logistic Regression, is called Smooth Transition Logistic Regression Tree (STLR-Tree). The inclusion of the regimes, determined by the splitting of the tree s nodes, is based on Lagrange Multipliers tests, which for the Gaussian cases uses the Residual Sum-of-squares in their test statistic, here are replaced by the Deviance function, which is equivalent to the case of non-Gaussian models, that has the distribution of the dependent variable in the exponential family. After applying the model in two datasets chosen from the bibliography comparing with other methods of classi cation such as: Generalized Additive Models (GAM), Logistic Regression, Neural Networks, Discriminant Analyses, k-Nearest Neighbor (k-NN) and Classification and Regression Trees (CART). It can be seen, verifying in the Classification Tables (Confusion Matrices) that STLR-Tree showed the second best result for the overall rate of correct classification in three of the four applications shown, being in all of them, behind only from GAM.
ASSUNTO(S)
classificacao classification logistic regression nonlinear models regressao logistica modelos nao-lineares
