Analyzing Multilevel Data in the Presence of Heterogeneous Within-Class Regressions

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Abstract
The concerns of this investigation are multiple sources of complications in the analysis of multilevel educational data. The focus is on problems that arise when within-group regressions of outcome on input are related to teacher/ school characteristics. Single-level and multilevel analytical approaches are applied to hypothetical data for which the relationship between teacher/class quality and the heterogeneity of within-class slopes is varied systematically. It is shown that single-level analyses and the proposed multilevel approaches can all yield mislèading estimates of teacher/class effects on mean class outcomes. However, selected multilevel methods provide some indication of misspecification and can identify the direction of the bias in estimating teacher/class effects on mean class outcomes.