Germán Rodríguez
Multilevel Models Princeton University

Pop 510 Syllabus

1: Introduction to Multilevel Models

The statistical analysis of clustered data. Random and fixed effects. Within-group and between-group variance. The intra-class correlation. Maximum likelihood and empirical Bayes estimates. A quick review of available software: MLwin, HLM, Stata and R. School effects in language scores.

2: Two-Level Models: Random Intercepts and Slopes

Random intercept models. Estimation using maximum likelihood (ML) and restricted maximum likelihood (REML). Likelihood ratio and Wald tests. Bayes estimates of group intercepts. Fixed and random-effect models revisited. Random slope models. Comparisons with group-specific regressions. Longitudinal and growth curve models.

3: Three Level Models: Nested and Crossed Effects

Three-level models. Modeling random intercepts and random slopes. Cross-level interactions. The issue of centering. Fitting more complex models. Crossed effects. The general linear mixed model.

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.

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.

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.


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 A 4th edition was published by Wiley in 2010 as a "print-on-demand" book.

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

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. (2012). Multilevel and longitudinal modeling using Stata. Third Edition Volume I: Continuous Responses. Volume II: Categorical Responses, Counts and Survival. Stata Press. (1st Edition 2005, 2nd Edition 2008.)

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 at, home of MLwiN, has a large collection of resources on multilevel modelling, including an online course!

The latest news from the home of HLM, the program produced by Stephen Raudenbush's group, will be found at Note that they have a free student edition of HLM 6.