Γραμμικά μοντέλα για τον συντελεστή συσχέτισης του Pearson
Linear models for Pearson correlation coefficient
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Abstract
In statistical analysis, the correlation coefficient is typically treated as a fixed parameter and used as a measure for inference regarding the linear relationship between two variables. This approach limits the ability to incorporate additional explanatory variables that may influence the dependence between the two response variables. In the present thesis, the subject of modeling the Pearson correlation coefficient is examined by incorporating explanatory variables within a regression framework. Since the correlation coefficient is bounded within the interval (-1,1), the use of an appropriate link function is required, as the classical linear model is not suitable. The aim of this study is to investigate and compare various link functions for modeling the correlation coefficient under different conditions.
The thesis consists of six chapters. Chapter 1 presents the theoretical framework of generalized linear models, with particular emphasis on the four link functions considered (tanh, logit, probit and complementary log-log). Chapter 2 introduces the Pearson correlation coefficient and discusses its theoretical background. Chapter 3 describes the methodology and the structure of the proposed models for statistical analysis. Chapter 4 presents the results of a simulation study, as well as the comparison of the models under different constraint intervals of the correlation coefficient, namely, the interval (0,1) and its natural range (-1,1), and for different distributions of the response variables whose correlation is being modeled, i.e. the bivariate normal distribution and the bivariate binary distribution. Chapter 5 presents the results of applying the models to real data. Finally, Chapter 6 summarizes the main conclusions following the overall comparison of the models discusses the limitations of the study. The statistical analysis is conducted using the R programming language.
Postgraduate Studies Programme
Εφαρμοσμένη ΣτατιστικήDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
118Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα