Hierarchical linear models and an application

Hierarchical linear models are the generalization of the regression approaches. These types of models are important because they can measure causation and be applied to the data having a hierarchical or clustered structure. When working on a data having a hierarchical cluster, multilevel regression models are preferred because of multicollinearity, which is one of the assumptions of classical linear regression model.While standards of attainments of young people which to constitute future of the community determine degree of development of community simultaneously, it also constitutes base of developed cultivated community for future. That's why, assessing the level of students? knowledge and determining the affects of students? achievement are very important. It is known that school types, region of the schools and student characteristics effect student achievement. Therefore parameters consisting of school types, region of the schools and student characteristics taken from Programme for International Student Assessment (PISA) 2003 data are used if they effect students' achievement in mathematics or not by using hierarchical linear models. Firstly, two and three level models were used for assessing the effects of student, school and region characteristics on mathematics achievement and secondly, two and three level models with ordinal and nominal dependent variables were used to determine success criteria and the level of success based on specific attributes for the students in the analysis. As a result of this study, factors effectings success in mathematics achievement and strategies to increase quality of education in secondary schools in Turkey will be determined.