Introduction multilevel models – a fuss over nothing.doc

Do multilevel models ever give different results?Or why bother with multilevel models?Kelvyn JonesCaroline WrightAndrew Bell HYPERLINK mailto:Kelvyn.jones@bristol.ac.uk Kelvyn.jones@bristol.ac.ukRevised and expanded 2nd version August 14th 2012.School of Geographical Sciencesand Centre for Multilevel ModellingUniversity of BristolVery Draft versionNot for citation without permission AbstractIt is sometimes said that multilevel models make no substantive difference to interpretation and represent something of a fuss over nothing. This paper demonstrates that this is not always the case with a simple example. It is shown that differences between a single-level and multilevel model will depend on the nature of the between and within group relations. We demonstrate the equivalence of the within-between model and the Mundlak model of contextual effects and argue that such models should be routinely used as the standard multilevel model conflates two potentially different relations in one term. We also consider the multilevel model as a measurement model and show how the multilevel property of precision weighted estimates can usefully be exploited as a simple way of dealing with measurement error in the calculation of group means. This results in less biased estimation of the contextual and between relations in a model of cross-level interactions. We provide an Appendix that gives a step-by-step demonstration of how these models can readily be specified, estimated, and displayed in the MLwiN software.KeywordsMultilevel models, within- and between- regressions, dependent data, exchangeability, shrinkage, measurement error precision-weighted estimation, group means, Mundlak specification, cross-level interactionContents TOC \o 1-3 \h \z \u HYPERLINK \l _Toc332906135 Introduction: multilevel models – a fuss over nothing? PAGEREF _Toc332906135 \h 4 HYPERLINK \l _Toc332906136 An example where the single and multilevel results diverge PAGEREF _Toc332906136 \h 5 HYPERLINK \