Τιμολόγηση νοσοκομειακών προγραμμάτων με την χρήση γενικευμένων γραμμικών μοντέλων

Αγρίτη, Βασιλική

Master Thesis

Author

Αγρίτη, Βασιλική

Date

2017-12

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Keywords

Λογιστική παλινδρόμηση ; Γραμμικά μοντέλα ; Κατανομή (Οικονομική θεωρία)

Abstract

The purpose of this thesis is to study the theory of generalized linear models by applying them to real data. To complete this thesis, insurance data were used after being collected and analyzed by Piet de Jong and Gillian Z. Heller for the need of the book Generalized Linear Models for Insurance Data. These data were reported in Australia during the period from July 1989 to the end of 1999. This thesis is divided into two parts. In the first part, we present the generalized linear models and their theoretical background in order to understand them and apply them. We mainly focus on response variables that are distinct and refer to binary data. In the second part we analyze the data using the statistical software package R. For the analysis needs, we will try to select the optimal model by applying the logistic regression to the data, where the response variable 'Claims' was transformed into a two-tier variable. As explanatory variables will be considered:  the degree of injury, as encoded, to a categorical variable with levels, 'low', 'severe' and 'death', - the categorical variable legal representation and - the variable settlement delay. Initially, the importance of entering the first variable will be tested, using Χ2 test, AIC criterion and BIC criterion, in order to examine whether the new variables improve the estimation. Subsequently, and after ending up to the optimal model selection with the above process, we will attempt to examine whether the selection of the above model is appropriate, using the Stepwise and Backwards method based on the AIC and BIC criteria. Finally, the interpretations of the selected models are made and compared with the results presented by de Jong and Heller.