Uma família de modelos de regressão com a distribuição original da variável resposta

Abstract

We know that statistic modeling by regression had a stronger impulse since generalized linear models (GLMs) development in 70 decade beginning of the XX century, proposed by Nelder e Wedderburn (1972). GLMs theory can be interpret like a traditional linear regression model generalization, where outcomes don't need necessary to assume a normal distribution, that is, any distribution belong to exponential distributions family. In binary logistic regression case, however, in many practice situations the outcomes response is originally from a discrete or continuous distribution, that is, the outcomes response has an original distribution that is not Bernoulli distribution and, although, because some purpose this variable was later dicothomized by an arbitrary cut of point C. In this work we propose a regression models family with original outcomes information, whose probability distribution or density function probability belong to exponential family. We present the models construction and development to each class, incorporating the original distribution outcomes response information. The proposed models are an extension of Suissa (1991) and Suissa and Blais (1995) works which present methods of estimating the risk of an event de_ned in a sample subspace of a continuous outcome variable. Simulation studies are presented in order to illustrate the performance of the developed methodology. For original normal outcomes we considered logistic, exponential, geometric, Poisson and lognormal models. For original exponential outcomes we considered logistic, normal, geometric, Poisson and lognormal models. In contribution to Suissa and Blais (1995) works we attribute two discrete outcomes for binary model, geometric and Poisson, and we also considered a normal distributions with multiplicative heteroscedastic structures continuous outcomes. In supplement we also propose the binary model with inated power series distributions outcomes considering a sample subspace of a zero inated geometric outcomes. We do several artificial data studies comparing the model of original distribution information regression model with usual regression model. Simulation studies are presented in order to illustrate the performance of the developed methodology. A real data set is analyzed by using the proposed models. Assuming a correct speci_ed distribution, the incorporation of this information about outcome response in the model produces more eficient likelihood estimates.