Multilevel Model Analysis in Hierarchical Data Structure: An Application to Educational Data

Moursellas Andreas
Supervisor: I. Panaretos
 

FIRST PAGES

Table of contents
List of tables
List of figures

CHAPTER 1
INTRODUCTION

1.1 The Scope of the Thesis
1.2 The Structure of the Thesis

INITIAL CONCEPTS OF HIERARCHICAL DATA STRUCTURE

2.1 Types of variables in hierarchical data structure
2.2 Arias with hierarchical data structure
2.3 Possible approaches for hierarchical data structure - Traditional models to random coefficient models

    2.3.1 Models and formulae

    2.3.2 Total of pooled regression

    2.3.3 Aggregate regression

    2.3.4 The contextual model

    2.3.5 The Cronbach model

    2.3.6 Analysis of Covariance (ANCOVA)

    2.3.7 Moving from one single-level to multilevel-model techniques

    2.3.8 Assumptions and Differences for the Linear Models - A brief summary

2.4 Conclusions of the chapter

3.1 The basic two-level model - The formulas

   3.1.1 The 2-level model and basic notation

   3.1.2 Parameter estimation for the variance components model

   3.1.3 The general 2-level model including random coefficients

   3.1.4 Parameter estimates - Possible Approaches - Algorithms

   3.1.5 Estimating the residuals

   3.1.6 Hypothesis testing and confidence intervals

3.2 Extensions of the 2-level linear model

   3.2.1 The three-level linear model

   3.2.2 Cross-Classified models

   3.2.3 Models for discrete response data - The proportions as responses case

   3.2.4 Multivariate multilevel models - The basic 2-level multivariate model

3.3 Conclusions of the chapter

4.1 Applications in Education

4.2 Applications in various areas

   4.2.1 Spatial Statistics

    4.2.2 Health Statistics

    4.2.3 Repeated measures

    4.2.4 Survey research

4.3 Conclusions of the chapter