Statistics 4C03/6C03

Generalized Linear Models

Dr P.D.M. Macdonald

2006-2007

Announcements

Calendar Description & Course Outline

STATS 4C03/6C03: Generalized Linear Models

Normal linear model, exponential family, iteratively-reweighted least squares, logistic regression, Poisson regression and log-linear models, other families of GLMs, analysis of deviance and model checking, residual analysis.

Course Outline

Timetable

Tuesday 08:30-09:20, Thursday 13:30-15:20, in HH-207.

Textbooks

Dobson, A.J. (2002) An Introduction to Generalized Linear Models, Second Edition, Chapman & Hall.
Dobson's text gives very a accessible account of the theory and is aimed at anyone who needs to use GLMs to analyse data. This is the required course text.

McCullagh, P. & Nelder, J.A. (1989) Generalized Linear Models, Second Edition, Chapman & Hall.
This is the authoritative original monograph on the topic; everything is there, but it is not always easy to follow.

McCulloch, C.E. & Searle, S.R. (2001) Generalized, Linear and Mixed Models, Wiley.
This text gives a concise and thorough account of the theory while putting GLMs in the broader context of mixed models.

Course Notes

• SAS code for examples from a first course in statistics
• Gamma MLE by nlm() and by Fisher Scoring
• Drawing ellipses in R
• Plotting gamma 2-parameter confidence regions
• Studying the sampling distribution of gamma MLE
• Wald and likelihood ratio tests for a gamma shape parameter
• Wald and likelihood ratio tests for a gamma mean
• Plotting inverse Gaussian 2-parameter confidence regions
• Wald and likelihood ratio tests for an inverse Gaussian mean
• Simulation of inverse Gaussian confidence regions

Computing Resources

• R for Beginners - an introduction to R, in pdf format - and other online manuals
• Download R - an open code language and environment for statistical computing, distributed free of charge, available for unix, Windows, Macintosh, and Linux. You want the "Precompiled binary distribution", not the "source code". For Windows installation, go to the link for "Windows (95 and later)", open folder base, and click on R-2.2.1-win32.exe to download the installer. Run R-2.2.1-win32.exe to install R on your computer.
• An Online Splus Tutorial from Dalhousie University

Exercises - to hand in

• Exercise #1 - Answer all questions on the STATS 3N03/3J04 Final Examination from December 2007, three times: by hand (with a calculator), in Splus or R, and in SAS.

Assignments

• Assignment #1 - Due 2007-02-13 08:30
  • Exercise 1.5 from Dobson (2002). Add: (d) Find the Wald, score and likelihood ratio confidence intervals for beta. (e) Find the MLE, LSE and all three 95% confidence intervals for the following two samples: 1 2 2 4 0 0 3 2 5 3 and 43 54 52 72 59 60 52 52 59 55.
  • Do Exercises 3.1 to 3.10 from Dobson (2002).
• Assignment #2 - Due 2007-03-20 08:30
  • If f₀(y) is a probability density function and M(x) its moment generating function, show that f(y; q) = exp(yq) f₀(y) / M(q) is a probability density function and belongs to the exponential family. This is called "exponential tilting". Show that the non-central hypergeometric distribution is an exponentially-tilted hypergeometric and hence find expressions for its mean and variance. Show that q is the canonical parameter. For the case N = 4, m = 2, n = 2, find the canonical link. What other link functions might be used with this distribution? [Note: q is supposed to be "theta" but may not display correctly in your browser.]
  • Do Exercises 4.1, 4.2, 4.3 from Dobson (2002).

Tests

Test #1	Mon Feb 12	17:30-19:30	BSB-241 Student Technology Centre*
Test #2	Mon Mar 19	17:30-19:30	BSB-241 Student Technology Centre*

Aids permitted: Open book.

*You must have a valid userid, password and laser printing account for the Student Technology Centre. Tests MUST be submitted on paper; electronic submission is NOT permitted.

If you are unable to write a test at the scheduled time, please e-mail me at least 3 days before to make special arrangements.

Some Other Links

• My work on mixture distributions
• Statistical Society of Canada / Société statistique du Canada

Need more help?

• If you have concerns about preparing for tests and examinations, improving your study habits, giving class presentations, or mastering English as a second language, the Centre for Student Development can help.