Papers, Statistics, University of Otago

STAT412 Generalised Linear Models

Second Semester

20 points

In 1972, Nelder and Wedderburn published a paper entitled Generalized linear models in which they presented a unified approach to linear models that does not require an assumption of normal errors. This paper produced a dramatic change in the type of data that could be analyzed within a linear modeling framework.

Paper details

We consider the theory and use of generalized linear models. This paper will include theory, but primarily emphasize application with a focus on parameter interpretation and hypothesis testing in real data analysis using R.

Potential students

For any student who wishes to know more about this important framework for analyzing many types of data. A working knowledge of these models is extremely valuable for any practicing statistician.

Main topics

Introduction to generalized linear models
Nominal and ordinal logistic models
Poisson models
Overdispersion
Zero-inflated models
Modelling rates using an offset
Log-linear models
Gamma and lognormal models
Quasi-likelihood
Generalised additive models
Survival models

Prerequisites

STAT 341

STAT 362

Required text

None

Useful references

Collett (1991) Modelling binary data, Chapman and Hall

Dobson and Barnett (2008) An Introduction to generalized linear models, Chapman and Hall

Faraway (2006) Extending the linear model with R, Chapman and Hall

Krzanowski (1998) An introduction to statistical modelling, Arnold

McCullagh and Nelder (1989) Generalized linear models, Chapman and Hall

Lecturer

Dr Ting Wang, Room 518, Extension 7773

Dr Graham Wood, Room 516

Lectures

Two hours of lecture per week. Time and location to be arranged.

Tutorial

One per week at a time to be arranged

Internal Assessment

The final internal assessment is based on 4 assignments and a project. The assignments are worth 75% in total and the project 25%. The project will involve a presentation to the rest of the class.

Exam format

The final exam is three hours long.

Final mark

Your final mark F in the paper will be calculated according to this formula:

F = max(E, 0.6E + 0.3A + 0.1P)

where:

E is the Exam mark
A is the Assignments mark
P is the Project mark

and all quantities are expressed as percentages.

Students must abide by the University’s Academic Integrity Policy

Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.

The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.

Academic misconduct: Plagiarism

Plagiarism is defined as:

Copying or paraphrasing another person’s work and presenting it as your own.
Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.

All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.

Academic misconduct: Unauthorised Collaboration

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.

Further information

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.

Adrien-Marie Legendre 1752-1833.
In 1805 Legendre presented the method of least squares and applied it to the determination of the ellipticity of the earth, and hence the length of the metre (a metre was defined to be 1/10,000,000 of a meridian quadrant — the distance from the equator to the North Pole). Gauss published the method of least squares in 1809 but claimed that he had been using the technique since 1795. Even now — two centuries later — researchers are still trying to establish who was the first to discover the method of least squares. Even though Legendre derived the least squares estimator based on the minimization of the sum of squares error, he only treated the special case that there is a perfect fit. However, Gauss developed the method by using the method of maximum likelihood and showed that the least squares estimator was the solution when the random errors are normally distributed. Furthermore, Gauss also considered the case of unequal variances that leads to the weighted least squares.