From GLM to GAMLSS

• Grant number: 11/14439-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2011
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Silvia Lopes de Paula Ferrari
• Grantee: Julio Adolfo Zucon Trecenti
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The regression analysis, a statistical technique used to measure the relationship between variables, has been one of the most active areas in Statistics, as well as one of the most frequently used tool to analyse data. In the early 1970s, the field of regression analysis gained further recognition by the study of the generalized linear models, denoted here by GLM, by John Robert Nelder and Wedderburn, which opened a wide range of possibilities for the normal linear models.The GLM extend the normal linear models allowing the dependent variable to have a distribution in a sub-class of the exponential family. With the development of technology and computing power, the GLM have been widely used in several practical problems. However, there are still some restrictions, such as the GLM do not accommodate distributions outside the exponential family, and require a fully parametric formulation. A very broad class of regression models was proposed by Robert Rigby and Mikis Stasinopoulos in 2001, namely the generalized additive models for location, scale and shape, denoted here by GAMLSS. These models involve parametric and non-parametric components. This proposal for a scientific initiation to the student Julio Adolfo Zucon Trecenti aims to draw a line between the two classes of models mentioned above, passing through the generalized additive models. Theoretical, practical and computational issues of the models will be taken into account.