Modelo Binomial Semiparamétrico

Abstract

In several studies of interest variables may present linear and non-linear relationships with auxiliary variables. Therefore, the importance of working with semi-parametric models, where we both estimate the parameters for the parametric part and the non-parametric, the latter being estimated through a smooth curve proposed by Green and Silverman[7] (1994) and Eilers and Marx[4] (1996). In this work we assume that the response variable follows a Binomial distribution where the systematic component will have two compositions, one linear and one nonlinear. The parameters of the model are estimated using the Newton-Raphson method, with the aid of the score function and Fisher’s information matrix. The calculations were performed considering the three link functions, namely logit, probit and complement log-log. The smoothing parameter is obtained by minimizing the cross-validation function. Simulations and real data applications were performed using the R Core Team software[11] (2017) with the aid of algorithms made in this work that enabled the validation of the proposed model to be validated.