Robust Analysis of a Nonlinear Model for Multilevel Educational Survey Data

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Abstract
A statistical model is proposed that describes the determination of an educational outcome variable as a nonlinear function of explanatory variables defined at different levels of a survey data hierarchy, say students and classes. The model hypothesizes that the student-level explanatory variables form a composite such that the intercept and slope in the regression of the outcome on the composite vary across classes systematically as functions of class-level variables and aggregates. A method is described for estimating the parameters of the model using robust techniques. The theoretical and practical derivation of the model is discussed, and an example is given.