title: Multicollinearity in hierarchical linear models.
abstract: This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model.
authors.affiliation: Department of Mathematics, Computer Science and Information System, Northwest Missouri State University, USA.
authors.forename: Han
authors.initials: H
authors.lastname: Yu
authors.affiliation: Department of Criminal Justice, The University of Toledo, USA.
authors.forename: Shanhe
authors.initials: S
authors.lastname: Jiang
authors.affiliation: Department of Sociology, Duke University, USA. Electronic address: kland@soc.duke.edu.
authors.forename: Kenneth C
authors.initials: KC
authors.lastname: Land
mesh_terms: D006801:Humans; D016014:Linear Models; D008962:Models, Theoretical; D012044:Regression Analysis; D012107:Research Design; D012942:Social Sciences / Q000379:methods*
keywords: Covariate pool; Hierarchical linear models; Multicollinearity; Singular value decomposition; Top-down diagnosis