The See-Saw Effect: a multilevel problem?

Abstract

Studies of school effectiveness often use measures of association, such as regression weights and correlation coefficients. These statistics are used to estimate the size of the change or “effect” that would occur in one variable (for example reading ability) given a particular change in another variable (for example sex and sex ratio). In this paper we explore the limitations of regression coefficients for use in a contextual analysis, in which both individual and contextual variables are included as independent variables. In our example “individual sex” and a context variable “sex ratio of the schoolclass” are regressors, and reading ability is the dependent variable. Our conclusion is that researchers should be careful making interpretations of effects from multiple regression analysis, when dealing with aggregate data. Even in the case (as in our example) when individual and contextual variables are made orthogonal to avoid multicollinearity, interpretation of the effects of the aggregate variable is problematical.