# Mat 6 spring 2012 - Mixed models

This course is concerned with statistical inference for linear and generalized linear mixed models. We will mainly consider frequentist likelihood based inference but if time allows we might also consider Bayesian inference and estimating equations. There will be a focus on theory but we will also consider data examples.

Project: my idea is that you should write an exposition of statistical inference for linear and generalized linear mixed models based on the course. Exercises posed in the course can e.g. be used as examples in the report. The report should be concise and theoretically oriented. You are welcome to use data examples for illustration but there will not be so much emphasis on elaborate data analyses.

The textbook for the course is

• Jiming Jiang (2007) Linear and generalized linear mixed models and their applications, Springer.
A useful reference regarding more practical aspects of fitting mixed models is
• J. J. Faraway (2006) Extending the linear model with R, Chapman and Hall/CRC, chapter 2 and 8.

1 Monday Feb 6: Read page 1-9 in Jiang (NB: sections 1.1.2 and 1.1.3 are too short and some details are not explained well). Handouts (with exercises). Data sets and R-scripts.

2 Wednesday Feb 8: Read Jiang pages 9-15, 25-26, 29-33. Handouts (with exercises).

3 Monday Feb 13: we continue with slides from Feb 8.

4 Wednesday Feb 15: we consider ANOVA for balanced designs and some examples of data analyses. Handouts (with exercises).

5 Monday Feb 27: we continue with slides from 4th lecture (starting with slide 10). Work on the exercises in week 8.

6 Monday March 5. No new material from Jiang. You may find helpful textbook material in Jesper Møller: Centrale statistiske modeller og likelihood baserede metoder, Section 5.1 and 5.2.1-5.2.3. Handouts.

7 Monday March 12. We finish the discussion of the two-way ANOVA and continue with inference for general linear mixed models. Read Jiang page 51-53, page 55-57 (until subsection 1.), 66-67, 70-72. Handouts.

8 Monday March 26. We consider asymptotic inference and prediction of random effects. Read Jiang 74-77 and 88-90. Handouts. R-code to simulation study. Some handwritten notes.

9 Tuesday April 10. We finish BLUE and BLUP for linear mixed models. Second we give a quick intro to logistic and Poisson regression. Handouts. Read Jiang 119-126.

10 Generalized linear mixed models, Laplace approximation and penalized quasi-likelihood estimation. Handouts. Jiang 127-132.

11 Penalized quasi-likelihood (Jiang 128-131). Handwritten notes.

12 Computation of likelihood functions for GLMMs using numerical integration and Monte Carlo approximation. The EM-algorithm. Handouts. Jiang 163-171. Exercise sheets: 6 and 7 (NB in this execise sheet, MM5 refers to the previous exercise sheet). Code is available in R-code 6, R-code 6 corrected, R-code 7, R-code 7 corrected. Gauss-Hermite schemes gh_5.txt and gh_10.txt are in the Data folder.

13 We finish material from last time and discuss various issues on pages 163-171 in Jiang. If time allows we also consider the Kalman-filter.

14-15 Student presentations on approximate F-tests based on paper by Halekoh and Højsgaard (and possibly also paper by Kenward and Roger). I do not expect that you will understand all the technical details in Halekoh and Højsgaard but try to understand and present the fundamental problems and ideas for solutions and also relate the material in the paper to what we have discussed during the course. You may also study the original paper by Kenward and Roger.

Emner der behandles til projekteksamen.