Random Coefficient Models for Multilevel Analysis

We propose a possible statistical model for both contextual analysis and slopes as outcomes analysis. These techniques have been used in multilevel analysis for quite some time, but a precise specification of the regression models has not been given before. We formalize them by proposing a random coefficient regression model, and we investigate its statistical properties in some detail. Various estimation methods are reviewed and applied to a Dutch school-career example. This paper was published previously in Journal of Educational Statistics, 11, 1986, 57–85. I corrected some typos, otherwise it’s a faithful reproduction. In recent years there has been an increasing awareness that many, if not most, problems in educational research have multilevel characteristics (Burstein, 1980b, Oosthoek & Van den Eeden, 1984). To make this statement a bit more precise, we introduce some terminology. Date: August 26, 2006.