Έλεγχοι καλής προσαρμογής σε λογιστικά μοντέλα παλινδρόμησης

The aim of this dissertation is to investigate the goodness-of-fit tests for the multinomial logistic regression model. A new approach which can be used to assess goodness-of-fit for all three types of logistic regression models - binary, multinomial, ordinal - will be examined and elaborated. Moreover, in case that the tests indicate lack of fit, the types of subjects that are not modelled well can be easily identified through the contigency table. This thesis consists of six chapters. In Chapter 1, we introduce the basic theory of the binary logistic model. In Chapter 2, we study the goodness-of-fit tests, which have been proposed for the binary logistic model and we mention some limitations that make these tests inproper. In Chapter 3, we introduce the multinomial logistic model and the proposed goodness-of-fit test for this case. Furthermore, a new strategy based on partitioning in the covariate space according to popular clustering methods is analyzed in order to implement a classic Pearson's Chi-Square goodness-of-fit test. In Chapter 4, simulation studies are carried out in R in order to investigate the power of the proposed tests and the Hosmer-Lemeshow test to detect the omission of a quadratic and an interaction term from the true logistic model. In Chapter 5, the application on a real dataset was performed to illustrate the use of goodness-of-fit test for multinomial logistic regression and we drew certain conclusions about the particular application in conjuction with the results of the simulation study. Finally, in Chapter 6, we state overall inferences and concerns that have arisen during our study in logistic regression models.