Modelos de superfície de resposta para dados de contagem com medidas repetidas - Silva, Francinilton Arruda da (2018)
The Response Surface Methodology (RSM) aims to determine the levels of factors (quantitative) that optimize a quantitative response of interest, in order to obtain the coordinates of the stationary point (minimum or maximum) of the model, identifying the optimum conditions of the same. The models are usually adjusted by means of a second-order linear model, based on a continuous response (with Normal distribution), and the entire estimation procedure is based on the classical regression model. In the absence of this premise, which occurs when the response is characterized by counting data, it is used the transformation methods in the response, which can cause problems in the accuracy of the point estimate of the stationary point. In general, counting data are modeled using the Poisson distribution associated with regression models, a particular case of Generalized Linear Models (GLMs). In addition, there are situations in which data are taken over time, presenting a longitudinal structure. In this case, it is considered the existence of correlation in the same experimental unit over time and, in 1986, Liang and Zeger proposed Generalized Estimation Equations (GEEs), as an extension of the GLMs, to analyze longitudinal data. The proposal of this work describes the RSM for longitudinal counting data, through the GEEs, studying their properties, estimation and inferences. A study of the stationary point precision is carried out by means of the point and interval estimation of the stationary point, using the following methods: inverse binding function, delta method and residual bootstrap method, comparing the impact of these approaches with that of the distribution response Normal. For that, we used simulated data sets.