Lecture 11: Inference, Deviance, Binomial GLMs
(Agresti Section 4.5)
Inference Concerning GLMs
The MLEs of GLMs have the usual asymptotic properties. Assuming the consistency of ,
we will now sketch a proof of the asymptotic normality of this estimator.
T
Lecture 7: Inference for Contingency Tables
(Agresti Sections 3.3-3.5)
Pearson Residuals
We have discussed the Pearson 2 test and LRT for assessing independence of two
variables, X and Y , in a contingency table.
It may be of interest which cells lead t
Lecture 12: More on Binomial GLMs
(Agresti Sections 5.1-5.2)
Setting: Y1 , . . . , YK are K independent Binomial(ni , i ) observations. We model
g(i ) =
p
xij j
j=1
for some link function g.
Binomial Data: More on Deviance
The deviance, D, (which compares
Lecture 19: Gamma GLMs
Recall that for Y Gamma(,), the distribution of Y can be written as
fY (y) = exp
)
(
y 1 log()
+ log + ( 1) log y log () ,
1
where = /. The canonical parameter is 1/, so the canonical link function is
1
g() = .
The dispersion para
Lecture 8: The Exponential Family and Introduction to GLMs
(Agresti Sections 4.1-4.4.3)
We have studied models involving one or two categorical variables. We now move to the
more general case we have one response variable of any type as well as predictor
Lecture 9: Building and Estimating GLMs
(Agresti Sections 4.4.4, 4.6)
We have seen that there are three components to a GLM (the distribution of Yi , the linear
predictor, and the link function).
DEFINITION: There are three necessary and sucient condition
Lecture 10: Estimation and Inference in the GLM Setting
(Agresti Section 4.6)
ASIDE: Sucient statistics. Informally, a sucient statistic is a function of the data
that contains all possible information about the unknown parameters. Formally, if the
distri
Lecture 14: Some Final Notes on Binomial GLMs,
Introduction to Poisson GLMs
(Agresti Sections 5.4, 5.4.1, 6.3.6, 6.2.6, 4.3, 9.7)
Interpretation of Eects when there are Multiple Predictors
Consider the beetle data, but lets assume that we additional infor
Lecture 3: Inference for Binomial Data
(Agresti Sections 1.4-1.5)
EXAMPLE. I once failed 12 out of 51 students in my class. Assuming students earned their
marks independently, lets make inference about the probability, p that I fail students. In
particula
Lecture 2: Inference for Categorical Data
(Agresti Sections 1.3-1.4)
An Important Note about Categorical Data
Consider an outcome consisting of one of d possible (non-numeric) response categories. Often,
such an outcome may be recorded as the random varia
Lecture 21: More on Quasi-Likelihood Estimation
(Agresti Section 4.7)
Recap: Allowing for under- or over-dispersion relative to the Poisson or binomial distributions
In principle, the choice of variance function can be any non-negative function that reaso
Lecture 20: Quasi-Likelihood Estimation
(Agresti Section 4.7)
The quasi-likelihood QL technique is used for estimating regression coecients without fully
specifying the distribution of the observed data. It thus provides a more exible approach
to estimati
Lecture 18: Ordinal Responses, The Dispersion Parameter
(Agresti Section 7.2)
We have been considering log-linear models for cases where the response variable is multinomial. The categories that form the response types are not necessarily ordered (e.g. be
Lecture 22: Asymptotic Properties of Quasi-Likelihood Estimators
(Agresti Section 4.7)
Properties of the Quasi-Score
As in the iid case, the quasi-score shares the three key properties of score functions associated
with GLMs (and hence behaves very simila
Lecture 4: Inference for Multinomial Data, Contingency Tables
(Agresti Sections 1.5-2.1)
EXAMPLE. Globe and Mail poll on Dec. 19, 2011: Where do you see the S&P/TSX index
at the end of 2012? (NOTE: The S&P/TSX Composite Index opened at 11,659.780 that
mor
Lecture 17: More on Multinomial Models
(Agresti Chapter 7)
Example: Fibre/Weight loss study
In a weight loss study, women were randomly assigned to eat one of three types of crackers
before their regular meal. The amount of bloating (a potential side eect
Lecture 5: More on Contingency Tables
(Agresti Sections 2.2-2.3)
Quick note regarding Pearsons 2 test
The original test was presented in the context where, under H0 , there are no unknown
parameters (e.g., H0 : = 0 . However, the test can be extended to t