STA 303/1002: Lecture 10- Case Study III Analysis
Binary Logistic Regression Example
Case Study III: The Donner Party Example
Log Odds, Odds, Odds Ratio
SAS PROC LOGISTIC
Using Additive model
Next class:
Condence interval for Odds Ratio
Testing s Higher-o
STA 303/1002: Lecture 20- Repeated measures
What are repeated measures?
more than one observation per subject or experimental unit
Examples:
1. Measures on all members of a cluster (Eg. a family, a class)
2. Cross-over study- experiment where each subject
STA 303/1002: Lecture 21
Longitudinally repeated measures using (linear) Mixed model (MM)
What are the components of a MM?
How do we estimate the parameters of a MM?
How do we t a MM in SAS?
Case Study VIII example
Model Diagnostics:
What were the model a
STA 303/1002: Lecture 19-Log-linear model checking
What procedures do we use to:
Q: Estimate parameters in log-linear models?
A: Maximum likelihood estimation
Q: Carry out inference (signicance tests and C.I.s)?
A: Wald tests and C.I.s, and LRT
1
What are
STA 303/1002: Lecture 17- Loglinear models for Two-way
Tables
Assume
Dist. of Y
H0
Test Stat.
Analysis I
Row totals xed
Binomial
1 = 2
Z
Analysis II
Overall total xed
Multinomial
ij = i j
2 1)(J1)
(I
Analysis III
Totals are random
Poisson
ij = ni j
2 1)(J
STA 303/1002: Lecture 18
Log-linear models for 3-way tables / Case Study VII Example
Learning Objectives
Write out the models used and the assumptions for inference
Carry out the inference procedures completely
Interpret the respective SAS outputs
1
A Thr
STA 303/1002: Lecture 16- Case Study VI
Three approaches
Ref: https:/www.framinghamheartstudy.org/index.php
Learning Objectives
Use 3 approaches to analyze Case Study VI data
Write out the models used and the assumptions for inference
Carry out the infere
STA 303/1002: Lecture 15- Case Study V
Poisson Regression Example
What did we learn about Poisson Regression?
Underlying probability distribution of response: Poisson
Outcome: Response variable, Y -count variable
Model: log() = X
Model assessment:
Scatter
STA 303/1002: Lecture 14- Binomial to Poisson
Regression
What did we learn about Binomial Logistic Regression?
Underlying probability distribution of response: Binomial
Outcome: Response variable, Y -count variable
Model: log 1 = f (X; ) where f (X; ) is
STA 303/1002: Lecture 22
Case Study VIII Example: Repeated measures / Mixed Model Diagnostics
What procedures do we use to:
Estimate parameters in a general linear mixed model?
Restricted Maximum likelihood estimation for variance and
covariance parameter
STA 303H1/1002H- Winter 2015
Dr. Shivon Sue-Chee
Lecture 1
January 6, 2015
Introduction to Data Analysis II
Use of linear models in which assumptions from STA302/1001
may not apply: 1- and 2- way ANOVA, Logistic and Log-linear
models, Time series and repe
STA 303/1002: Lecture 9-Generalized Linear Models
Case Study III: The Donner Party Example
Generalized Linear Models
What is a Generalized Linear Model?
Common link functions
What is Logistic Regression?
MLE of s
1
Case Study III: The Donner Party Example
STA 303/1002: Lecture 6 Intro
Recall: General Linear Model (GLM)
Response, Y is continuous
Categorical or continuous predictors, X
Y is linear in s
Assumptions: N(0, 2 I)
Recall: One-way ANOVA
Special case of a GLM
One-way classication/ One factor with G
STA 303/1002: Lecture 7-Two-way classication contd
Recall: Case Study II-The Pygmalion eect
Two factors: Company , Treatment
Pygmalion eect- high expectations of a supervisor translate to
improved performance by subordinate
Does mean Treatment eect (the d
STA 303/1002: Lecture 5 Outline
Review- Multiple comparisons
Bonferroni
Tukeys
Diagnostics- checking model assumptions
Normality of errors
Constant variance
Uncorrelated errors
Case Study I Conclusions
Multiple Comparisons: Tukeys Approach
Based on maxa,b
STA 303/1002: Lecture 4 Outline
Recall- Case Study I questions
(Q1) One-way ANOVA with G=2
(Q2) One-way ANOVA with G=6
SAS demonstrations
Multiple comparisons: Bonferroni and Tukeys
Diagnostics- checking model assumptions
Normality of errors
Constant vari
STA 303/1002: Lecture 2 Outline
Spocks Conspiracy Data Example continued
Recall Two-sample t-tests
Linear Model approach
Incorporating SAS
Case Study 1: The Spock Conspiracy Data Example
Recall:
(Q1) Is there evidence that women are underrepresented on
Sp
STA303/1002-Lecture 3 Outline
The General Linear Model
One-Way ANOVA
Case Study I:
QuesDon 1: Comparing 2 groups
QuesDon 2: Comparing >2 groups
The General Linear Model
Response, Y is conDnuous
Explanatory v
Lecture 23-Course Summary
What did we cover in our courseSTA 303: Methods of Data Analysis II?
1
Cases and Methods
Case
I
II
III
IV
V
VI
VII
VIII
Title
Spocks Trial
The Pygmalion Eect
The Donner Party
The Krunnit Islands
Mating Elephants
Heart Study
Three
The humble t-test
And other special cases of the
linear model
1
Spock conspiracy trial
Benjamin Spock
On trial for helping men avoid Vietnam draft
Bestselling American pediatrician, author
Generally well-liked by women due to his books
Boston, 1968
No wom
One-way ANOVA
Linear model approach
1
LM approach
Is there a difference in means for any of the
other six judges?
To answer this second question, well use our
linear model
If Yi is the percent of women in venire i, then
= 0 + 1 , + 2 , + + 5 , +
1
Ig =
ANCOVA
Analysis of Covariance
aka. Saving your experiment
(and other abuses of regression
methods on observational data)
1
Viagra Study
30 men were given a Dose of ViagraTM
Asked to report the number of times they
initiated sexual contact with partner in
999629166
Junyi Liu
2016-02-03
Assignment 1
#1a.
#1b.
According to 2 sample t- test, the p-value is 2.2e-16 and it is smaller than 5%, there is
evidence to reject H0. Therefore, the observed difference is statistically significant. The mean
of thatch_ant
STA303/1002: Assignment 1
Craig Burkett
February 3, 2016
Due in the tutorial on Thursday, Feb 4th . Please hand it in on 8.5 x 11
inch paper, stapled in the upper left, with no other packaging and no title
page. Please try to make this assignment look lik
STA303/1002: Assignment 2
Craig Burkett
March 13, 2016
Due in the tutorial on Thursday, Mar 10th . Please hand it in on 8.5 x 11 inch paper,
stapled in the upper left, with no other packaging and no title page. Please try to make this
assignment look like
STA303/1002 - Methods of Data Analysis II
(Week 09 lecture note)
Wei (Becky) Lin
Mar 07/09, 2017
1/55
Notes
Assignment 3 (last assignment) will be available this week.
Due: April 5. (Roughly, you will have 3 weeks to try)
Midterm
Result will be availabl
STA303/1002 - Methods of Data Analysis II
(Week 11 lecture note)
Wei (Becky) Lin
Mar 21/23, 2017
1/52
Topics learned last week
Poisson regression model
Deivance
D=2
n
X
yi log
i=1
yi
i )
(yi
i
Inference about individual j
Goodness of fit tests: (1) LR
STA303/1002 - Methods of Data Analysis II
(Week 10 lecture note)
Wei (Becky) Lin
Mar 14/16, 2017
1/60
Topics learned last week
Show that the Binomial log-likelihood equals Bernoulli log-likelihood up to a
constant
Deviance for Bernoulli model
`S ()
=2
STA303 - Assignment 1
Last name: Lastname
First name: firstname
Student ID: 0000000
Course section: STA303H1S-L0101
Jan 2nd, 2017
Q1 (a-d: 3+3+2+2) - Data 1: working output
(a: 3pts ) Calculate the means and standard deviations of output for each workman.
STA303/1002 - Methods of Data Analysis II
(Week 06 lecture note - Extra Topics)
Wei (Becky) Lin
Feb 7/9, 2017
1/44
Notes
Assignment 2 is due 22:00, Sunday, Feb 26, 2017.
Midterm is right after the reading week, Mar 2nd.
Midterm will cover lecture note