GENERALIZED ADDITIVE MIXED MODELS WITH P-SPLINES APPLIED TO SUGARCANE PRODUCTION IN THE STATE OF SÃO PAULO

In this paper, we apply the generalized additive mixed models with the use of the P-\textit{splines} technique as mixed models, which will be adopted in a problem of the agro-environmental area, in this case on the average levels of sugarcane production, which is influenced by changes in climatic variables such as temperature and precipitation which were measured over 10 years in each mesoregion of the state of São Paulo. The reason for using this approach as a smoothing method is that the tendency of these climate covariates is not known on its most, but it is known that they directly influence the response variable. Besides allowing for the inclusion of fixed and random effects in the models to be proposed, these models allow for the inclusion of an autoregressive process AR(1) as a correlation structure in the residuals.