NATIONAL CHIAO TUNG UNIVERSITY

INSTITUTE OF STATISTICS

 

GENERALIZED LINEAR (AND ADDITIVE) MODELS

FALL 2009

 

 

 


Instructor:

Guan-Hua Huang, Ph.D.

 

Office: 423 Joint Education Hall

 

Phone: 03-513-1334

 

Email: ghuang@stat.nctu.edu.tw

Class meetings:

Thursday 9:00-12:00 at 407 Joint Education Hall

Office hours:

By appointment

Class website:

http://140.113.114.4/course/glm09/

Credit:

Three (3) credits

 

COURSE SUMMARY

 

The objects of his course are

 

Ÿ   To present regression methodologies for categorical and count responses unified under the framework of generalized linear models and generalized additive models.

Ÿ   To familiarize the usage of statistical software implementing these regression methodologies.

Ÿ   To provide references for your future research.

 

Topics include review of likelihood inference and large sample test statistics, generalized linear models framework, analysis of binary, polytomous and count data, smoothing, additive models and generalized additive models.

 

HANDOUTS AND TEXTBOOKS

 

Handouts corresponding to each lecture will be available on the class website before each class. Reading assignments are from the following two books:

 

Ÿ   McCullagh P. and Nelder J.A. (1989). Generalized Linear Models, 2nd edition. Chapman and Hall.

Ÿ   Hastie T.J. and Tibshirani R.J. (1990). Generalized Additive Models. Chapman and Hall.

 

PREREQUISITES

 

Students are expected to have background on undergraduate probability, mathematical statistics, and linear regression.

 

METHOD OF STUDENT EVALUATION

 

The course grade will be based on four homework assignments (50%), one midterm exam (20%), and one final exam (30%).

 

COURSE OUTLINE

 

Readings refer to:

McCullagh P. and Nelder J.A. (1989): Generalized Linear Models, 2nd edition. (McCullagh & Nelder)

Hastie T.J. and Tibshirani R.J. (1990). Generalized Additive Models. (Hastie & Tibshirani)

 

Module

Topic

Reading

1

Review

Ÿ  Likelihood function and some basic properties

Ÿ  Exponential family

Ÿ  Three large sample test

Ÿ  Conditional likelihood inference

 

2

Generalized linear models (GLM)

Ÿ  The origins of GLM

Ÿ  Systematic and random components of GLM

Ÿ  Some statistical properties of GLM

Ÿ  Maximum likelihood estimation versus weighted least squares

Ÿ  Deviance - a measure of goodness-of-fit

Ÿ  Iterative reweighted least squares algorithm

McCullagh & Nelder

Chapter 2

3

Analysis of binary data

Ÿ  Binomial distribution

Ÿ  Link functions

Ÿ  Case-control applications

McCullagh & Nelder

Chapter 4

4

Analysis of polytomous data

Ÿ  Multinomial distribution

Ÿ  Model for nominal scales

Ÿ  Model for ordinal scales

Ÿ  Nested or hierarchical response scales

McCullagh & Nelder

Chapter 5

5

Analysis of count data

Ÿ  Poisson distribution

Ÿ  Log-linear model for contingency tables

Ÿ  Connection with multinomial model

Ÿ  Poisson regression – application to cohort studies

McCullagh & Nelder

Chapter 6

6

Smoothing

Ÿ  Bin smoothers

Ÿ  Kernel smoothers

Ÿ  Splines

Hastie & Tibshirani

Chapter 2

7

Additive models

Ÿ  Fitting additive models

Ÿ  Estimating equations for additive models

Ÿ  Solutions to the estimating equations

Hastie & Tibshirani

Chapters 4, 5

8

Generalized additive models (GAM)

Ÿ  Local scoring for GAM

Ÿ  Semi-parametric GAM

Ÿ  Inferences

Ÿ  Smoothing parameter selection

Hastie & Tibshirani

Chapter 6