Three Methods of Estimating a Model of Group Effects

Abstract

Three methods of estimating a model of school effects, involving either contextual or structural variables, are compared. The comparison shows that two methods, ordinary least squares and an approach based on the analysis of covariance, produce unbiased estimators under a given set of assumptions. The third method, based on a residualized input-output approach, produces biased estimators. When the model involves only contextual variables, the first two methods result in the same estimators. These results are presented using a matrix algebra formulation: they apply to the case where the model contains one or more covariates, and one or more school level variables. The relative advantages of the first two methods are considered, and it is suggested that in most situations the ordinary least squares approach is preferable.