Multi-Level Statistical Models

Fri. 1-2, Rm.   MTH 2400                                                Fall '09

Organizational Meeting was held   Wed., Sept. 9, 1pm, MTH 2400

All Future Meetings will be held   Fridays 1-2pm, MTH 2400

Eric Slud,   Paul Smith,        Statistics Program , Math Department       

Interested participants should get in touch with either of us at   or

Reading list

Schedule of Talks

RIT Focus:   to understand and work with Statistical Computing tools for (Frequentist and Bayesian) data analysis using mixed effect and multilevel and hierarchical linear and generalized-linear models. We will read papers and textbook chapters to understand the interplay between fixed-effect models, random-effect models, and mixed-effect models with multiple random-effect levels. Issues of model identifiability, consistent estimation and random-effect prediction underlie the use of multilevel-model statistical software, and lead naturally to a discussion of hierarchical models and Bayesian tools, including the Gibbs Sampler and MCMC/Bugs. The computational problems arising in likelihood calculations for multilevel models are known to be formidable, and we will discuss various frequentist and Bayesian computational approaches, implemented primarily in R and SAS.

Prerequisites:   Participants should have had some upper-level course in Mathematical Statistics (at the level of Stat 420 or higher) and some introduction to Statistical Computing (at the level of Stat 430 for SAS or Stat 705 for R, but other Stat computing languages would also be OK). Some familiarity with linear or GLM models would be helpful.

Topics by Keyword:

  • specification of identifiable multilevel statistical models,
                   estimation, prediction of random effects, goodness of fit
  • Markov Chain Monte Carlo & Gibbs Sampler,
                   methods and diagnostics for convergence
  • random-effect Generalized Linear Models
                   Laplace Method, penalized quasi-likelihood, adaptive Gaussian quadrature,
  • SAS PROC MIXED and GLIMMIX, R functions lmer, glmmPQL, MCMCglmm
  • meta-analysis via random-effect models,
  • hierarchical models and Bayesian analysis and interpretation,
                   posterior predictive checks, simulated posterior quantities
  • biased sampling & survey-weighted multilevel models

  • Reading List   (Still under construction)

          Online Talks & Slides

    To see a series of two "Minicourse" lectures I gave several years ago (in 2004) on
    Markov Chain Monte Carlo, click for Lecture 1 and Lecture 2 .


    Gelman, A. and Hill, J. (2007) Data Analysis using Regression and Multilevel/Hierarchical Models, Cambridge.

    Hartung, J., Knapp, G., and Sinha, Bimal (2008), Statistical Meta-Analysis with Applications, New York: Wiley.

    McCulloch, C. and Searle, S. (2001) Generalized, Linear and Mixed Models, Wiley.

    Meng, X., Shao, Q.-M., and Ibrahim, J. (2001), Monte-Carlo Methods in Bayesian Computation, Springer-Verlag.

    Pinheiro, J. and Bates, D. (2000), Mixed-Effects Models in S and S-PLUS, Springer-Verlag.

           Miscellaneous Papers & Reports

    Breslow, N. and Clayton, D. (1993), Approximate Inference in Generalized Linear Mixed Models, Jour. of Amer. Statist. Assoc.

    Casella, G. and George, E. (1992), Explaining the Gibbs Sampler, Amer. Statistician 46, 167-173.

    Ghosh M., and Rao J.N.K. (1994), Small Area Estimation: An Appraisal, Statistical Science, 9, 55-93.

    Jiang, Jiming (1999), Conditional inference about generalized linear mixed models. Ann. Statist. 27, 1974-2007.

    Moura and Holt (1999), Small Area Estimation Using Multilevel Models, Survey Methodology , 25, 73-80.

    Slud, E. (2000), Accurate Calculation and Maximization of Log-Likelihood for Mixed Logistic Regression, Census SAIPE Tech Rep.

    Schedule of Talks ---