NSF-CBMS Regional Conference on Generalized Linear Mixed Models and Related Topics
June 8-12, 1999, University of Florida

Outline of Lectures

Day 1

Lecture I

1. Chestnut Leaf Blight - introduction.
   1. Why is Chestnut Leaf Blight important?
   2. Control by hypovirulence.
   3. Questions of interest.
2. Probit regression analysis of individual gene effects.
   1. Model.
   2. Estimation and tests by ML.
   3. Results.
3. Subpopulation effects.
   1. What are subpopulations and what effect would they have?
   2. Fixed or random?
   3. Consequences of assuming a random factor
   4. Likelihood
   5. Test of no other gene effect.
   6. Prediction of subpopulation values.
4. Rest of conference.
   1. References.
   2. Outline.

Lecture II

1. Example: Propranolol and high blood pressure.
2. Fixed and random factors.
3. Best linear unbiased prediction.
4. Estimation and testing.
   1. ML estimation.
   2. REML estimation.
   3. Likelihood inference.
   4. Generalized estimating equations.

Lecture III

1. Generalized linear models.
   1. Example: Potato flour dilutions.
   2. Modelling approach.
   3. Transforming versus linking
   4. Estimation and testing
2. Generalized linear mixed models.
   1. Basic ideas.
   2. Modelling.
   3. Estimation and testing.
   4. Best prediction.

Day 2

Lecture IV

1. Inference primarily about fixed effects.
   1. Chestnut blight (gene effects).
   2. Progabide and seizures.
2. Inference primarily about random effects.
   1. Chesnut blight (subpopulation effects).
   2. Potomac River Fever.
3. Prediction.
   1. Neo-tropical migrants.
   2. Small domain estimation.
4. Is everything a GLMM?
   1. Photosynthesis in corn.

Lecture V

1. "Convenient" models.
   1. Beta-binomial.
   2. Poisson-gamma.
   3. Others
2. Marginal models
3. Conditional inference
4. Need for flexible general approaches

Day 3

Lecture VI

1. Simulation based methods.
2. Approximating the likelihood directly.
3. Approximate ingredients of likelihood estimation.
   1. EM.
   2. Newton-Raphson.
   3. Stochastic approximation.
4. Methods of approximation
   1. Gibbs.
   2. Metropolis-Hastings.
   3. Independence sampler.
   4. "Smooth" approximation.
   5. Variance reduction techniques.
5. Approximating tests.
   1. Gibbs.
   2. Likelihood ratio.
   3. Score tests.

Lecture VII

1. Generalized estimating equations.
   1. Marginal versus conditional models.
   2. GEEs for conditional models: mean structure.
   3. GEEs for correlation structure.
   4. Relation to the dispersion-mean model.
2. Penalized quasi-likelihood.
   1. Joint maximization.
   2. Hierarchical likelihood.
   3. Conditional moments.

Day 4

Lecture VIII

1. Estimating equations.
2. What is REML for GLMMs?
   1. Based on residuals.
   2. Marginal likelihood.
   3. Equate observed and expected BLUPs.
3. BLUP methods.
   1. Approximate.
   2. "Exact".
   3. Tweedie models.
4. Composite and working likelihoods.

Day 5

Lecture IX

1. Choice of link function and link diagnostics.
2. Choice of random effects distribution and diagnostics.
3. Outlier detection and residual analysis.
4. Small sample adjustments.
5. Prediction intervals and estimation of prediction error.

Lecture X

1. Additive and nonparametric components.
2. Exact small sample inference.
3. SAS Proc GENMIX.
4. Concluding remarks.