Multilevel Modeling

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Multilevel modeling, or hierarchical linear modeling, is especially useful when using clustered data (i.e. students that are clustered in schools) or analyzing within-person change using panel data. HLM takes into account the dependence of the residuals within groups or within the same person and adjusts the standard errors accordingly. Two main types of HLM include fixed effects, which allows the researcher to control for all unchanging unobserved variables, and random effects, which allows the researcher to control for characteristics that are observed at the higher level (i.e. the school).

Essential Reading:

Books

Bryk, Anthony S. and Stephen W. Raudenbush. (2002). Hierarchical Linear Models: applications and data analysis methods., 2nd Edition. Sage.
Kreft, I. and J. de Leeuw (1998). Introducing Multilevel Modelling. Sage.
Snijders, T.A.B. and R.J. Bosker (1999). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modelling. London: Sage.

Papers

Osgood, Wayne and Gail L. Smith. 1999. Applying Hierarchical Linear Modeling to Extended Longitudinal Evaluations: The Boys Town Follow-Up Study. Evaluation Review 19(1):3-38.
Qu, Annie (1997). "Comparison of PROC MIXED in SAS and HLM for Hierarchical Linear Models". Penn State Population Research Institute Statistics Core Report. Postscript or Adobe Acrobat
Schwartz, Jennifer and Jeff Ackerman. 2001. In search of a dependent variable: Comment on Avakame, 1998. Criminology 39(4): 969-980. This paper spells out the necessary data requirements, specifies the nature of an appropriate dependent variable, and presents an illustration of the types of research questions that would justify a hierarchical linear analysis.
Singer, Judith (1998). "Using SAS PROC MIXED to fit multilevel models, hierarchical models and individual growth models". Journal of Educational and Behavioral Statistics.
Johnson, David R. (1995). "Alternative Methods for the Quantitative analysis of Panel Data in Family Research: Pooled Time-Series Models." Journal of Marriage and Family 57: 1065-1077.

Tips, Tutorials and other materials

HLM software Scientific Software International

Hierarchical Linear Modeling with STATA PRI Workshop handout on using gllamm for generalized linear latent and mixed models.

Multi-level Modeling On March 23, 2006, Wayne Osgood spoke about his experiences with multi-level modeling using various packages.

Multilevel Modeling Newsgroup includes a searchable archives

Multilevel Models home page Producers of MLwiN software

Using Proc Mixed -- Judith D. Singer Essential reading for researchers using PROC MIXED to fit multilevel models, hierarchical models and individual growth models.

PRI Computer Core Help