Understanding HLM Models and Type VI Errors: The Need for Reflection

Abstract

This article presents a framework for two common hierarchical linear models (HLM), instructions to run them in Statistical Package for the Social Sciences (SPSS), and a comparison between SPSS 21.0 linear mixed models (LMM) and HLM 7.0 output. Discussions topics include centering in hierarchical modeling, a comparison of SPSS output for the default restricted maximum likelihood and maximum likelihood solutions, a comparison of SPSS output for HLM and ordinary least squares (OLS) multiple linear regression (MLR) with person vectors output on mean square errors and R², and a comparison of R² and R² changes. Correlated residuals between SPSS LMM and OLS MLR provide a context for considering hypothesis testing, research questions, and the choice of statistical tests. Finally, this article addresses the complexity of developing multi-level linear research questions and determining which statistical techniques are appropriate for answering those questions so Type VI errors can be avoided.