ABSTRACT
Hierarchical or multilevel regression modeling is an increasingly important tool in the analysis of complex data such as arise frequently in modern quantitative research. Hierarchical regression models are useful as soon as there is covariate information at different levels of variation. For example, in studying scholastic achievement we may have information about individual students (for example, family background), class-level information (characteristics of the teacher), and also information about the school (educational policy, type of neighborhood). Another situation in which hierarchical modeling arises naturally is in the analysis of data obtained by stratified or cluster sampling. A natural family of models is regression of y on indicator variables for strata or clusters, in addition to any measured covariates x. With cluster sampling, hierarchical modeling is in fact necessary in order to generalize to the unsampled clusters.
