Statistics 659
6 Multicategory Logit Models
Logistic regression is a technique for relating a binary response variable Y to one or more
explanatory variables. The explanatory variables may be categorical, continuous, or both.
Here we extend the methods o
STAT 659 Solution to Exam 2
Spring 2016
1. (a) Since the LR statistic G2 = 3.1569 with a P value= 0.2063, we fail to reject H0 : RS = 0 and
conclude that there is insucient evidence to indicate that the interaction term is needed. Thus,
there is no indica
STAT 659 Exam 2
Summer 2016
Name:
INSTRUCTIONS FOR THE STUDENT:
1. You have exactly 70 minutes to complete the exam.
2. There are 12 pages including this cover sheet and 5 pages of SAS output.
3. Each lettered part of a question is worth 8 points unless o
Statistics 659
2 Contingency Tables
In this section we will examine association among two or three categorical variables.
Example:
College students were classified according both to frequency of marijuana use and
parental use of alcohol and psychoactive d
Statistics 659
3
Generalized Linear Models
In the previous chapter we examined association in two-way and three-way contingency tables.
We primarily carried out tests of association and estimated certain measures of association of
categorical variables. I
STAT 659 Exam 1
Spring 2016
Name:
INSTRUCTIONS FOR THE STUDENT:
1. You have exactly 70 minutes to complete the exam.
2. There are 11 pages including this cover sheet and 4 pages of SAS output.
3. Each lettered part of a question is worth 8 points unless o
STAT 659 Exam 1
Summer 2016
Name:
INSTRUCTIONS FOR THE STUDENT:
1. You have exactly 70 minutes to complete the exam.
2. There are 13 pages including this cover sheet and 6 pages of SAS output.
3. Each lettered part of a question is worth 8 points unless o
Statistics 659
6 Multicategory Logit Models
Logistic regression is a technique for relating a binary response variable Y to one or more
explanatory variables. The explanatory variables may be categorical, continuous, or both.
Here we extend the methods o
STAT 659 Exam 1
Spring 2015
Name:
INSTRUCTIONS FOR THE STUDENT:
1. You have exactly 70 minutes to complete the exam.
2. There are 11 pages including this cover sheet and 4 pages of SAS output.
3. Each lettered part of a question is worth 8 points unless o
STAT 659 Spring 2014
Homework 4 Solution
2.29
Let be the odd ratio between the experimental group and the control group. Then the null
hypothesis is = 1 and the alternative is > 1. The potential values for n11 are 7, 8, , 15,
15
so the p-value is
P (n11 =
STAT 659 Spring 2014
Homework 3 Solution
2.16
(a) The response variable is the smoking status and the explanatory variable is the lung
cancer.
(b) It is the case-control study.
(c) No, because the marginal distribution of lung cancer is xed. But we can in
STAT 659 Spring 2014
Homework 6 Solution
4.1
(a) From the output of the software, we know logit = 3.7771 + 0.1449LI. So for LI = 8,
exp(3.7771+0.14498)
= 1+exp(3.7771+0.14498) = 0.068.
(b) Similarly to (a), you can plug in LI = 26 and obtain the correspo
STAT 659 Spring 2014
Homework 7 Solution
5.1
(a) The prediction equation is logit = 9.355 + 0.834weight + 0.307width.
(b) The likelihood ratio test statistic is 32.867 which has a chi-squared distribution with
degree of freedom 2. The P-value is 7.295 108
STAT 659 Spring 2014
Homework 8 Solution
5.13
The Hosmer-Lemeshow test statistic is 12.6818 which has a chi-square distribution with
degree of freedom 8. The P-value is 0.1233 > 0.05 which implies the model is adequate.
5.9
(a) No, the deviance is only su
STAT 659 Spring 2014
Homework 11 Solution
8.2
(a) H0 : 1+ = +1 v.s. Ha : 1+ = +1
McNemars Test
-Statistic (S)
119.1260
DF
1
Asymptotic Pr > S
<.0001
Exact Pr >= S
9.556E-35
Since P-value < 0.0001, we will reject H0 and conclude that the population proport
STAT 659 Spring 2014
Homework 10 Solution
7.1
(a) H0 : Model ts adequately v.s. Ha : Model does not t adequately
(i)2 = 0.8246, df = 1, p-value = 0.3638.
(ii)G2 = 0.8224, df = 1, p-value = 0.364.
So at signicant level = 0.05, we fail to reject H0 , which
Spring 2016 Exam 2
1a. Carry out a test of Equal Odds Ratio
Find the G2 and p value from the Deviance and Pearson Goodness-of-Fit Statistics Chart
Null: (2vars) = 0
p>
o fail to reject null
o there is insufficient evidence to indicate an interaction t
Statistics 659
7 Loglinear Models for Contingency Tables
In Chapter 3, we looked briefly at the Poisson regression model with the log link,
log = + x.
We extended this to a multivariate regression model for Poisson data with the log link:
log = + 1 x1 + +
STAT 659 Spring 2013
Homework 10 Solution
7.1
(a) H0 : Model ts adequately v.s. Ha : Model does not t adequately
(i)2 = 0.8246, df = 1, p-value = 0.3638.
(ii)G2 = 0.8224, df = 1, p-value = 0.364.
So at signicant level = 0.05, we fail to reject H0 , which
STAT 659 Solution to Exam 2
Summer 2015
1. (a) Since the P values of the Wald tests of H0 : k618 = 0 and H0 : hc = 0 equal 0.3424 and
0.5877, respectively, we could consider eliminating these variables. To determine whether this is
appropriate, we should
STAT 659 Solution to Exam 2
Spring 2015
1. (a) Do not reject Ho : SG = 0 since G2 = 0.7713 with a pvalue= 0.3798. There is insucient
evidence to include the interaction term in the model. Hence, there is insucient evidence to
indicate that the ORs dier fo
Test of Equal Odds Ratios
SPRING 2016 Exam 2 1a.
Summer 2015 Exam 2 3a.
Spring 2015 Exam 2 1a.
Homogeneous Association Model , carry out a test of Partial Association
SPRING 2016 Exam 2 1b.
Summer 2015 Exam 2 3b.
Estimate the Odds Ratio using homogenou
STAT 659 Exam 2
Summer 2015
Name:
INSTRUCTIONS FOR THE STUDENT:
1. You have exactly 70 minutes to complete the exam.
2. There are 12 pages including this cover sheet and 5 pages of SAS output.
3. Each lettered part of a question is worth 8 points unless o