How Do Extreme Schools Change the Interpretation of Results in School Effectiveness Research? Effects of Outlying Second-Level Variables in HLM.

This study examined the robustness of the estimation of fixed-effects in multilevel analysis, as might occur in the conduct of school-effects studies with outlying schools. Outlying values for both intercepts and slopes for individual schools were modeled separately to determine the effects of extreme values of second-level variables on the fixed-effect parameter estimation. A total of seven data sets were generated for the simulation. Under the conditions investigated in this study, adding a cluster of outlying schools had little effect on the estimation of gamma 10 and gamma 11. However, the standard error of gamma 01 increased, thereby increasing the conservativeness of the test of significance of gamma 01. This occurred for clusters of outlying slopes, intercepts, or a combination of both. Introducing a single outlying school also increased the standard error of gamma 01, the effects being more dramatic when the outlier was an extreme slope. (Author/SLD) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Multilevel Outliers 1 How do Extreme Schools Change the Interpretation of Results in SchoolEffectiveness Research? : Effects of Outlying Second-Level Variables in HLM. Janet K. Sheehan & Tianqi Han Northern Illinois University U.S. DEPARTMENT OF EDUCATION of Educational Research and Improvement ED ATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY J 4A) E7 TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This paper was presented at the Annual Meeting of the American Educational Research Association, New York, NY, April, 1996 BEST COPY AVAILABLE 2 Multilevel Outliers 2 Abstract This study examined the robustness of the estimation of fixed-effects in multilevel analysis, as might occur when conducting school-effects studies with outlying schools. Outlying values for both intercepts and slopes for individual schools were modeled separately to determine the effects of extreme values of second-level variables on the fixed-effect parameter estimation. Under the conditions investigated in this study, adding a cluster of outlying schools had little effect on the estimation of yio and yii, however the standard error of ym increased, thereby increasing the conservativeness of the test of significance of ym. This occurred for clusters of outlying slopes, intercepts, or a combination of both. Introducing a single outlying school also increased the standard error of yoi, the effects being more dramatic when the outlier was an extreme slope.This study examined the robustness of the estimation of fixed-effects in multilevel analysis, as might occur when conducting school-effects studies with outlying schools. Outlying values for both intercepts and slopes for individual schools were modeled separately to determine the effects of extreme values of second-level variables on the fixed-effect parameter estimation. Under the conditions investigated in this study, adding a cluster of outlying schools had little effect on the estimation of yio and yii, however the standard error of ym increased, thereby increasing the conservativeness of the test of significance of ym. This occurred for clusters of outlying slopes, intercepts, or a combination of both. Introducing a single outlying school also increased the standard error of yoi, the effects being more dramatic when the outlier was an extreme slope.