Lecture 2 Introduction: Distributions and
Inference for Categorical Data
1.1 Categorical Response Data
1.2 Distributions for Categorical Data
1.3 Statistical Inference for Binomial Parameters
1.4 Statistical Inference for Multinomial Parameters
1.5 Statis
Estimation problems and alternatives for tting
Binomial regression models
November 8, 2013
1
An example when the Binomial logistic regression
cases model cannot be estimated by maximum likelihood
Suppose that we wish to predict the probability that a part
Binomial regression with multiple explanatory variables
November 5, 2013
1
Example: New teaching method in economics (Spector, L. & Mazzeo, M., 1980)
1.1
Introduction to the data
The dataset consists of measurements on 32 students studying Economics. The
Introduction to Binomial regression
October 17, 2013
1
Review and introduction
Suppose that Y Bern() and (0, 1). Then the probability of success is = E(Y ) =
P (Y = 1) and the odds of success is = /(1 ). Possible values for are in the
interval (0, ). Give
The likelihood ratio test and Pearsons test for
multinomial parameters
September 18, 2013
1
Inference for multinomial parameters
Suppose that we can see a realization of (Y1 , . . . , Yc ) Multinom(n, 1 , . . . , c ) and we wish
to test
H0 : 1 = 10 (), .
The Poisson loglinear model and its application to
contingency tables
November 20, 2013
1
Introduction
In these notes we introduce the Poisson loglinear model (which can be applied generally with
categorical and numerical explanatory variables). Our focus
Ordinal linear association Test in R
October 13, 2013
The R code used in this document is available in the text le ordinalassociation.r
posted on Moodle.
Suppose we observe an I J table:
X=1
X=2
.
.
.
X=I
Total
Y =1 Y =2
n11
n12
n21
n22
.
.
.
.
.
.
nI1
nI
Multinomial logit model
November 17, 2013
1
Introduction
In these notes we extend Binomial logistic regression, for which the response has two categories success and failure, to Multinomial logistic regression, for which the response has
J 2 categories ca
Probability distributions in R
Notes for Stat 5421 Fall 2013
University of Minnesota
1
Binomial distribution
Let Y Binom(n, ). The probability mass function pY (; ) is dened by
pY (y; ) =
n!
y (1 )ny
y!(n y)!
y = 0, 1, . . . n.
To evaluate this function
Proportional odds model
November 20, 2013
1
Introduction
In these notes we extend Binomial logistic regression, for which the response has two categories success and failure, to a model for which the response has J 2 ordinal categories
category 1, categor
Logistic Regression III
(Chapter 5)
Oct 24
Proportion of
successes
in each case
O-ring Example in last lecture
At each of 5 levels of concentration (conc)
of a insecticide, 30 insects were exposed
& death/survival numbers were recorded.
X matrix
Fitted pr
Logistic Regression V
Oct 31
Estimation problems and alternatives for fitting
Binomial regression models
1.#An#example#when#the#Binomial#logistic#regression#cases#model#cannot#
be#estimated#by#maximum#likelihood
Example:
Example:
When#the#temperature#was#
Logistic Regression II (Chapter 5)
Oct 20-22
Case 1.
Case 2.
Case 3 [Code: R_example_logistic_reg.R].
Why the deviances in the three cases are different ?
Binomial logistic regression with a 2 2 2
contingency table
November 5, 2013
1
1.1
Example: Kidney stones data
Introduction to the data
Of 700 patients with kidney stones, 350 were given treatment A and 350 were given treatment
B. The stone size was also
Lecture 2 Introduction: Distributions and
Inference for Categorical Data
1.1 Categorical Response Data
1.2 Distributions for Categorical Data
1.3 Statistical Inference for Binomial Parameters
1.4 Statistical Inference for Multinomial Parameters
1.5 Statis
Exam III, 2:30pm-3:20pm, Wednesday, Dec. 14.
1. Questions in Homework 6-7.
2. Hw 6 question 2
(a) write out the logistic model without interaction. What assumption do we make?
(b) How many parameters in the model of question (a)? Suppose we know the likel
Logistic Regression V
Oct 31
Estimation problems and alternatives for fitting
Binomial regression models
1.#An#example#when#the#Binomial#logistic#regression#cases#model#cannot#
be#estimated#by#maximum#likelihood
Example:
Example:
When#the#temperature#was#
Logistic Regression III
(Chapter 5)
Oct 24
Proportion of
successes
in each case
Text
O-ring Example in last lecture
Confidence interval
At each of 5 levels of concentration (conc)
of a insecticide, 30 insects were exposed
& death/survival numbers were rec
Solution to Homework 5
STAT 5421 Fall 2014
In this homework assignment, you will analyze a dataset concerning the performance of
an insecticide. At each of 5 levels of concentration of this insecticide, 30 insects were
exposed and the number that died and
Logistic Regression II (Chapter 5)
Oct 20-22
Case 1.
Case 2.
Case 3 [Code: R_example_logistic_reg.R].
Why the deviances in the three cases are different ?
Stat 5421 Chapter 2-3
Stat 5421 Lecture 7-12
Sep 17-29
Chapter 2. Describing Contingency Tables
In this chapter we introduce tables that display
relationships between categorical variables.
We also define parameters that summarize their
association.
2.1
3. Textbook 3rd edition problem 1.10 (equivalent to 2nd edition problem 1.9). Perform
Pearsons test and the Likelihood ratio test.
Solution. The first of this problem asks us use the data to estimate the mean of
the un-truncated Poisson distribution. We a
Solution to Homework 6
STAT 5421 Fall 2014
In this homework assignment, you will analyze a dataset concerning breast cancer in Wisconsin. The original dataset consisted of 681 cases of potentially cancerous tumors or which
238 were truly malignant. These
Statistics 5421 Fall 2013 Homework 1 (solutions)
Due Monday, September 23 in lecture. Show all work. For hypothesis tests, state the
required assumptions about the data; state the null and alternative hypotheses; compute
the test statistic realization and