Háttértényezők hatásának vizsgálata hierarchikus lineáris modellekkel

Absztrakt

(Multivariate) linear regression represents a widespread tool of correlation analysis which can only be applied if the separate observations are mutually independent. If this condition is not fulfilled, the results of a linear regression may deviate significantly from the real values. In the case of dependent observations, hierarchical linear models can be applied, which provide a more accurate estimate than linear regression. The special features of hierarchical data structures have been taken into account in international educational research as far back as the 1970s and currently form an everyday part of data analysis. However, in Hungary they are still rarely applied. The aim of this study is to present the most basic hierarchical linear models – One-way ANOVA with Random Effects, Regression with Means-as-Outcomes, the Random Coefficients Regression Model, and Intercepts- and Slopes-as-Outcomes – and their potential educational applications with concrete examples. These models are illustrated through a secondary analysis of the TIMSS 2007 results, with an investigation of the influence of parents’ educational attainment and locality size on Hungarian students’ performance in mathematics in Year 8, i.e. how much of the variance is explained by these two variables. From a methodological point of view, the investigation focuses on the differences between applications of ordinary linear regression and hierarchical linear models while touching on the applicability of each and the quantitative and qualitative nature of the conclusions to be drawn.