Bootstrapping within the Multilevel/Hierarchical Linear Modeling Framework: A Primer for Use with SAS and SPLUS

Abstract

Nested data structure obtained from a cluster sampling design often calls for hierarchical linear modeling (HLM) analysis. Such data structure warrants some special considerations when the bootstrap technique is applied. This paper presents some discussions and examples for applying the bootstrap method within the framework of hierarchical linear modeling. A two-level dataset (about 900 students nested under 20 schools) extracted from the High School and Beyond (HSB) was used for illustration. Bootstrap resampling was implemented in both SAS and S-PLUS, and a hierarchical linear model with one Level-1 predictor (student SES), and one Level-2 predictor (type of schools, Catholic or public) was applied.