Full text
| |
| Author(s): |
Mayara Caroline Maioli
Total Authors: 1
|
| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2018-03-08 |
| Examining board members: |
Caio Lucidius Naberezny Azevedo;
Filidor Edilfonso Vilca Labra;
Carlos Alberto Ribeiro Diniz
|
| Advisor: | Caio Lucidius Naberezny Azevedo |
| Abstract | |
Situations where the response variable is either continuous or binary are quite common in several fields of knowledge. Although there are several models for these situations, in many cases, characteristics such as asymmetry and heavy tails, are not properly treated. In addition, bivariate responses, containing one continuous and one discrete variable, are common in many real problems, which may also exhibit asymmetry and heavy tails. The most common approach in the bivariate case is to model each variable separately, ignoring the potential correlation between them, or to decompose the joint distribution into the marginal distribution of the binary variable and the conditional distribution of the continuous variable, given the binary variable. The decomposition into the marginal distribution of the continuous variable and the conditional distribution of the binary variable, given the continuous variable, it is also possible. In this project we developed: a class of linear regression models based on the skew scale mixture of normal distributions under the centered parameterization (SSMNC), a class of regression models for binary data with link function associated with some SSMNC distribution, and a class of mixed regression models for bivariate continuous and binary data, in which both the continuous response and the link function for the binary response, belong to the SSMNC class. To introduce the dependency structure between the two response variables, we consider a common random effects structure, whose distributions also belong to the SSMNC class. We developed estimation procedures under the Bayesian paradigm, also, diagnostic tools, including residual analysis and influence measures, as well as model comparison measures. We performed simulation studies, considering different scenarios of interest, in order to evaluate the performance of estimates and diagnostic measures. The proposed methodologies were illustrated with both data from simulation studies and with real data sets (AU) | |
| FAPESP's process: | 15/25867-2 - Mixed regression models for bivariate skew continuous and binary data |
| Grantee: | Mayara Caroline Maioli |
| Support Opportunities: | Scholarships in Brazil - Master |