<- file stat 97refhlm.html -> Hierarchical models are "not necessarily linear".

Hierarchical Linear Models

=======================Les McLean, 23 May 1997==========sse Message-ID: <3385B923.231A@oise.utoronto.ca> From: Les McLean <lmclean@oise.utoronto.ca> Subject: More on Hierarchical Linear Models--a proper subset of multilevel models The well-deserved success of Bryk and Raudenbush's book and computer program have installed the acronym HLM in many people's statistical vocabulary, and sometimes in their toolbox. The list of reference books posted to edstat-l shows the vigour of this relatively new branch of statistics (Goldstein published the first book in 1987) and also signals a drawback of the term HLM. There is no requirement that multilevel models be linear! Hierarchical, yes--linear, no. Some computer programs only fit linear models, but that should not obscure the more general utility of the multilevel approach. Note that Hox's book is Applied Multilevel Analysis, Goldstein: Multilevel Statistical Models (now in 2nd. edition) and Longford: Random Coefficient Models. Unfortunately, much of our education and experience, and hence our thinking, has been limited to theory and practice of fitting and using linear models, and care must be taken not to let our intuition rule if we find ourselves fitting a non-linear model (logit models are common, for example, such as the item response model in measurement). Michael Cohen, in his post of 23 May, suggests reading the books in the order: Hox, B&R, Goldstein, and a beginner is well advised by this. If you are comfortable with complex regression models, however, and have fitted models with interaction terms, then moving directly to Goldstein will reward you with full generality. (As has been noted, the program MLn will handle any model for which you have adequate data.) Here's a tip for marvelously focusing your mind at the first appointment with multilevel models (you will soon see it is obvious): You will be fitting a familiar regression-like model (very familiar if the model is linear). You add a second "level" by writing a model for the error term! (and so on and so on, not quite infinitem). Try it. Not only will you like it, but when your data are hierarchical it is the only analysis available at the moment that can avoid misleading you badly. --

REFs HLM

=======================Bryan Griffin, 22 May 1997==========sse Message-ID: <3.0.32.19970522002702.00b99b78@gsvms2.cc.gasou.edu> From: "Bryan W. Griffin" <bwgriffin@gsvms2.cc.gasou.edu> >Date: 20 May 1997 09:57:54 GMT >From: ddusick@aol.com (Ddusick) >Subject: Hierarchical linear model > >Can someone give me a basic definition of 'hierarchical linear model', and >some recommendations on reading material? Thanks. Diane Hierarchical linear models (HLM) incorporate data from multiple levels in an attempt to determine the impact of individual and grouping factors upon some individual level outcome. For example, student achievement may be a function of student level characteristics (e.g., IQ, study habits), classroom level factors (e.g., instruction style, textbook), school level factors (e.g., wealth), and so on. HLMs, or multilevel models, can incorporate such factors in a manner better than ordinary least squares since HLMs take into account error structures at each level. There is software dedicated to estimating such models: VARCL, HLM, GENMOD, Mx, and MLn to name five. I know that three (MLn, HLM, and VARCL) are available commercially. Below are the web addresses for these three. http://www.ioe.ac.uk/multilevel/index.html http://www.educ.msu.edu/units/groups/LAMMP/ http://www.gamma.rug.nl/ I list six books on the topic. There are literally hundreds of articles available. 1. Bock, R. D. (ed.) (1989). Multilevel analysis of educational data. Academic Press. 2. Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models. Sage. 3. Goldstein, H. (1987). Multilevel models in educational and social research. Griffin & Co., and Oxford. 4. Goldstein, H. (1995). Multilevel statistical models (2nd ed.). Edward Arnold (Halstead and J. Wiley). 5. Longford, N. T. (1993). Random coefficient models. Oxford. 6. Raudenbush, S. W., & Willms, J. D. (eds.) (1991). Schools, classrooms, and pupils: International studies of schooling from a multilevel perspective. Academic Press.

REFs HLM

=======================Michael Cohen, 22 May 1997==========sse From: mcohen@cpcug.org (Michael Cohen) Subject: Re: Hierarchical linear model Message-ID: <5m1ujt$m1i$1@news2.digex.net> Ddusick (ddusick@aol.com) wrote: : Can someone give me a basic definition of 'hierarchical linear model', and : some recommendations on reading material? Thanks. Diane J. J. Hox (1995) Applied Multilevel Analysis. Amsterdam: TT-Publikaties. Anthony Bryk and Stephen Raudenbush (1992). Hierarchical Linear Models. Newbury Park CA: Sage Harvey Goldstein (1995). Multilevel Statistical Models (2nd ed.). London: Edward Arnold. Nicholas Longford (1993). Random Coefficient Models. Oxford: Clearendon Press. I suggest perhaps reading them in roughly the order given. I won't give a formal definition of HLM (see the books) but here's an example: Suppose we have data on students (gender, score on an assessment, etc.) but also data on their schools (school size, indicator of whether they offer calculus, etc.). To use ordinary least squares with these data as "independent" (exogenous) variables isn't right because of the correlations among students in the same school. HLM takes care of this properly. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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