An overview of multilevel regression

Due to the inherently hierarchical nature of many natural phenomena, data collected rests in nested entities. As an example, students are nested in schools, school are nested in districts, districts are nested in counties, and counties are nested within states. Multilevel models provide a statistical framework for investigating and drawing conclusions regarding the influence of factors at differing hierarchical levels of analysis. The work in this paper serves as an introduction to multilevel models and their comparison to Ordinary Least Squares (OLS) regression. We overview three basic model structures: variable intercept model, variable slope model, and hierarchical linear model and illustrate each model with an example of student data. Then, we contrast the three multilevel models with the OLS model and present a method for producing confidence intervals for the regression coefficients.