MATH 523: E XAMPLE - P OISSON DATA
An investigation of the incidence of the occurrences of four types of tumor at three different body
locations involved recording counts from 400 randomly sampled can
MATH 523: I TERATIVELY R EWEIGHTED L EAST S QUARES
In the exponential-dispersion family, with weights w1 , . . . , wn and identity dispersion function a() =
, the log-likelihood for independent data y
MATH 523: E XAMPLE - P OISSON DATA WITH O FFSET
A Poisson GLM can also be used in situations where a binomial model might seem more appropriate.
It is well known that if X BinomialFm, G, with m large
MATH 523: S OME KEY ASYMPTOTIC RESULTS
In a probability model with independent data y1 , . . . , yn , maximum likelihood estimation proceeds
by solving the likelihood equations, obtained by setting th
MATH 523: E XAMPLE - B INOMIAL DATA
The following data are counts of the number of failed O-rings (out of six) in twenty three launches
of the space shuttle Challenger at different ground temperatures
MATH 523: D EVIANCE COMPARISON WITH ESTIMATED DISPERSION
When is known, the Analysis of Deviance for nested models M0 M1 containing p0 p1 parameters
respectively, with deviances D0 and D1 , is based o
MATH 523: R ESIDUALS
Three types of residual are used for checking the t of a GLM
Pearson residual
y
p
ai i
p
V p i q
rP i
Anscombe residual
p
Apyiq a Apiq
Api q V pi q
p
p
rAi
'
where function A
MATH 523 - A SSIGNMENT 2: S OLUTIONS
(a) Five basic models can be tted:
M0
M1
M2
M3
M4
Null
age
test
age+test
age+test+age.test
Here model M4 is the saturated model, the most complicated we can t for
MATH 523 - A SSIGNMENT 1: S OLUTIONS
1 By direct calculation
-fY HY I
8
y
y 1
e y
F1 eGy!
F1 e eG
8
y1
Fy 1G!
F1 eG
y 1
Similarly
8
e y
-fY HY FY 1GI
y Fy 1 G
F1 eGy!
y 1
8
2 e y2
F1 eG y2 Fy 2G
MATH 523 - EXERCISES 1
These exercises are not for assessment
1 The birthwt data set included in the MASS library in the package R contains information on the
low birthweight status of 189 babies born
MATH 523 - ASSIGNMENT 2
To be handed in not later than 5pm, Friday 4th March 2011.
Please hand in during lectures, to Burnside 1225, or to the Mathematics Ofce Burnside 1005
The following data reect t