Aspectos teóricos dos modelos GAMLSS e aplicação a dados longitudinais

Abstract

he assumption of normality of errors is commonly considered when using linear regression models (LRM). Although other models have emerged to deal with this limitation, such as generalized linear models (GLMs) and generalized aditives models (GAMs), they are still restricted to the linear exponential family. In order to overcome such limitations, the generalized additive model for location, scale and shape (GAMLSS) was proposed, which is capable of modeling data with, theoretically, any distribution. Even with all this flexibility, GAMLSS still has a little expressive use compared to other models that deal with distributions different from the normal (such as GLMs and GAMs). This expressiveness is even lower when it comes to the class of models with latent variables (mixed models). In this work, a theoretical framework on this class of models is presented and an application is made to a dataset of longitudinal nature of pollen production. Using the gamlss package implemented in the R software, one can see the enormous flexibility of GAMLSS (given the large number of distributions available in the package and the ability to explicitly model different types of parameters, for example). The use of the GAMLSS model with generalized gamma marginal distribution showed a good fit to the pollen production data, being able to deal with the asymmetry of the data. The modeling of pollen production data via mixed linear models (MLM) violated some assumptions (such as normality of residuals and homogeneity of variance). On the other hand, the use of GAMLSS showed a good fit without violating assumptions, suggesting that this class of models is able to provide more reliable inferences and estimates. However, the absence of influence analysis tools (largely abundant in MLM) is still a limitation of GAMLSS.