GENERALIZED LINEAR MODELS
SPRING
2007
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Instructor: |
Guan-Hua Huang, Ph.D. |
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Office: 423 Joint Education Hall |
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Phone: 03-513-1334 |
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Email: ghuang@stat.nctu.edu.tw |
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Class meetings: |
Wednesday 9:00 am -12:00 pm at 407 Joint Education Hall |
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Office hours: |
By appointment |
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Class website: |
http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/course/glm07/ |
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Credit: |
Three (3) credits |
COURSE SUMMARY
The objects of his course are
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To present regression
methodologies for categorical and count responses unified under the framework
of generalized linear models.
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To familiarize the usage of
statistical software implementing these regression methodologies.
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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; and estimating functions.
HANDOUTS AND
TEXTBOOKS
Handouts corresponding to each lecture will be
available on the class website before each class. There is one required textbook for this course and reading assignments will be made
primary in this book:
McCullagh P. and Nelder
J.A. (1989). Generalized
Linear Models, 2nd edition. 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 five homework assignments (50%), one midterm exam (20%), and one final exam (30%).
COURSE OUTLINE
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Module |
Topic |
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1 |
Review Ÿ
Likelihood function and some
basic properties Ÿ
Exponential family Ÿ
Three large sample test Ÿ
Conditional likelihood
inference |
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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 |
Chapter 2 |
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3 |
Analysis of binary data Ÿ
Binomial
distribution Ÿ
Link
functions Ÿ
Case-control
applications Ÿ
Over-dispersion |
Chapter 4 |
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4 |
Analysis of polytomous
data Ÿ
Multinomial
distribution Ÿ
Model
for nominal scales Ÿ
Model
for ordinal scales Ÿ
Nested
or hierarchical response scales |
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 |
Chapter 6 |
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6 |
Quasi-likelihood
function and estimating functions Ÿ
Construction
of quasi-likelihood function Ÿ
Optimal
estimating functions Ÿ
Some
applications of estimating functions |
Chapter 9 |