Pop 510a Syllabus
Week 1: Introduction to Multilevel Models
The statistical analysis of clustered data. Random and fixed effects. Working with aggregate data. Ecological correlation. Random-intercept models. Within-group and between-group variance. The intra-class correlation. Random-slope models. Heteroscedasticity. Estimation and testing: ML, and REML.
A quick review of available software: MlWin, HLM and Stata. Fitting random-intercept and random slope models. Scores in a language test and verbal IQ.
Week 2: The Hierarchical Linear Model
The general hierarchical linear model. Level-specific models. Modeling random intercepts and random slopes. Cross-level interactions. The issue of centering. Should we center on the grand mean, group means or not at all? Three level models.
Fitting more complex models. Fitted trajectories. variance plots.
Week 3: Testing and Model Specification
Tests for fixed effects. Tests for the variances of the random effects. Tests at the boundary of the parameter space. Explained variance in multilevel models. Residuals and influence in multilevel models.
Week 4: Multilevel Generalized Linear Models
A random-intercept logit model. Approximate methods of estimation. Marginal quasi-likelihood (MQL). Penalized quasi-likelihood (PQL). Bootstrapping for bias reduction. Quadrature methods. Adaptive Gaussian quadrature. Applications to ordered logit models.
Review of procedures used in WLwiN, HLM, MIXOR and Stata. Fitting a random-intercept logit model. Application to prenatal care in Guatemala.
Week 5: Bayesian Estimation in Hierarchical Models
The Bayesian approach. Monte Carlo Markov Chain. Gibbs sampling. The Metropolis algorithm. Testing for convergence.
The BUGS package. Fitting random-intercept and random-slopes models using BUGS. MCMC in MLwiN.
Week 6: Multilevel Survival Models
A multilevel extension of shared frailty models. Relationship with generalized linear multilevel models (GLMM). Converting multilevel results into fitted survival probabilities.
An application to child survival in Kenya.
Bibliography
de Leeuw J. and Meijer, E. Editors (2008). Handbook of Multilevel Analysis. New York: Springer-Verlag.
Gelman, A., and J. Hill. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press
Goldstein, H. (2003). Multilevel Statistical Models, 3rd Edition. London: Edward Arnold. The 2nd edition, published in 1995 but including recent corrections, is available free in electronic form at http://www.soziologie.uni-halle.de/langer/multilevel/books/goldstein.pdf.
Hox, J. J. (2002). Multilevel Analysis: Techniques and Applications. Mahwah, NJ: Lawrence Erlbaum Associates. An earlier (1996) book by the same author, Applied Multilevel Analysis, Amsterdam: TT-Publicaties, is available online at www.geocities.com/joophox/publist/amaboek.pdf
Kreft, Ita G. G. and de Leeuw, Jan (1998). Introducing Multilevel Modeling. Newbury Park: Sage Publications.
Leyland, A. H., and H. Goldstein. (2001). Multilevel Modelling of Health Statistics. New York: Wiley
Longford, N. T.. (1993) Random Coefficient Models. Oxford: Clarendon Press.
Rabe-Hesketh, S., and A. Skrondal. (2008). Multilevel and longitudinal modeling using Stata. 2nd Edition. STATA. Stata Press
Raudenbush, S. W. and Bryk, A.S. (2001). Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park: SAGE Publications. An earlier book by these authors is Bryk, A. S. and Raudenbush, S. W. (1992). Hierarchical Linear Models. Newbury Park: Sage Publications.
Snijders, T. and Bosker, R. (1999). Multilevel Analysis: An introduction to basic and advanced multilevel modeling. Thousand Oaks, California: Sage Publications.
Useful Links
The Centre for Multilevel Modelling at Bristol University directed by Harvey Goldstein and home of MLwiN: http://www.cmm.bristol.ac.uk/Multilevel Modelling Newsletter. It also includes a more complete list of books on multilevel modelling.
The latest news from the home of HLM, the program produced by Stephen Raudenbush's group, http://www.ssicentral.com/hlm. Note that they have a free student edition of HLM 6.