PUBH 7430
Assignment 3 Solutions
October 18, 2011
Due: October 27, 2011 at the beginning of class
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output should be appropriate

PUBH 7430
Assignment 3
October 18, 2011
Due: October 27, 2011 at the beginning of class
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output should be appropriate for inclus

PUBH 7430
Lecture 10
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 6, 2011
Fitting GLMs - applied example
Time trial data
Original data
Outcomes: 5 reaction time trials for 113 individuals
Predictors: Age a

PUBH 7430
Lecture 11
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 11, 2011
Model diagnostics
Plot of residuals vs. tted values
Plot Y vs. , i.e. outcomes versus (estimated) mean
Used to verify reasonablene

PUBH 7430
Lecture 12
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 13, 2011
Estimation, briey
In the GLM, we model the mean
E (Yi | xi ) = i = Xi
To assess covariate eects, we need to:
Estimate the coecie

PUBH 7430
Lecture 13
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 18, 2011
In statistics, as in art, never fall in love with
your model.
Seen on a fortune cookie.
Marginal models for correlated data
Setup
Y

PUBH 7430
Lecture 14
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 20, 2011
Fitting GEE models: Examples
FEV data
Mean model:
E (FEVij | initheighti , ageij ) = 0 + 1 initheighti + 2 ageij
Focus on 1 (inuenc

PUBH 7430
Lecture 15
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 25, 2011
Random/mixed eects/conditional models
Motivating example
Animal Behavior
Lonsdorf et al.(2004) Nature 428: 715-716
Objective: Stud

PUBH 7430
Lecture 16
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 27, 2011
Random/mixed eects models, continued
Example: Wallaby growth
Data
Data on growth (weight, length of ears/head/feet/arms/tail)
of 77

PUBH 7430
Midterm review (Lecture 17)
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
November 1, 2011
Preliminaries: bivariate dependence
The correlation coecient
Know the formula:
(X , Y ) =
Cov (X , Y )
Var (X )
Va

PUBH 7430
Lecture 18
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
November 10, 2011
Linear mixed eects model
Yij = xij + zi bi +
ij
Yij = Observation j from cluster i
xij = Vector of covariates for observation j f

PUBH 7430
Lecture 19
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
November 15, 2011
Random slopes
Random eects model for eect of GART on HIV viral
load
Viral loads within individuals are correlated across time
Sub

PUBH 7430
Lecture 20
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
November 17, 2011
1 / 25
Generalized linear mixed models
2 / 25
Linear mixed models
So far, we have dealt with the linear mixed model (LMM)
Yij = xij

NAME: _SOLUTIONS_
PUBH 7430 Midterm examination
November 3, 2011
This exam runs from 9:45 a.m. until 11:00 a.m.
There are 5 questions, for a total of 80 points.
There is an (optional) BONUS question worth 5 additional
points at the end of Question 1.
Clos

PUBH 7430
Lecture 9
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
October 4, 2011
The Generalized Linear Model
The Generalized Linear Model generalizes the standard
linear model by:
1
Letting a function of the mean b

PUBH 7430
Lecture 8
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 29, 2011
Beyond the linear model
Recall the two key assumptions of the linear model:
1
2
Mean is a linear combination of predictors
Variance

PUBH 7430
Lecture 7
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 27, 2011
Accounting for covariate eects
Sometimes, we want to summarize correlations after
accounting/adjusting for covariate eects.
eg.

PUBH 7430 Assignment 0
September 8, 2011
To be discussed September 13, 2011
Your assignment is to download and explore a dataset which we will be using several times
during the semester. The carot data are extracted from a clinical trial testing the eects

PUBH 7430
Assignment 1
September 15, 2011
Due: September 27, 2011 at the beginning of class
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output should be appropriate for in

PUBH 7430
Assignment 1
Solutions
J. Wolfson
September 29, 2011
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output should be appropriate for inclusion in a scientic report,

Suggestions for Assignment 1 : Common mistakes
Question 1 :
(1) When you are asked about length of Y, it does not make sense to write in wide format, Y is of length
113 and in long format, Y is of length 113*5=565. The format (wide or long) refers to the

PUBH 7430
Assignment 2
September 29, 2011
Due: October 11, 2011 at the beginning of class
UPDATED: October 5, 2011
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output shoul

PUBH 7430
Assignment 2
September 29, 2011
Due: October 11, 2011 at the beginning of class
UPDATED: October 5, 2011
On this assignment, as in all homeworks, UNEDITED COMPUTER OUTPUT IS
NOT ACCEPTABLE. Tables and plots prepared from statistical output shoul

Common mistakes/Suggestions for Assignment 2
Question 1 :
Since the first question is about exploratory analysis, you need to provide plots (and not
just summary statistics) in order to justify the claims that you make. You are not required
to provide an

PUBH 7430
Assignment 4
J. Wolfson
November 10, 2011
Due: November 22, 2011 at the beginning of class
On this (as all homeworks) unedited computer output is NOT acceptable. Tables and plots
prepared from statistical output should be appropriate for inclusi

PUBH 7430
Lecture 1
Julian Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 6, 2011
Course Overview
Preliminaries
Who am I?
Who are you?
Syllabus review
Pre-requisites
Course structure
TAs
Debashree Ray
Ch

PUBH 7430
Lecture 2
Julian Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 8, 2011
Correlation and probability
Independence and lack thereof
Two events A and B are said to be independent if
P (A occurs and B occ

PUBH 7430
Lecture 3
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 13, 2010
Beta-carotene dataset discussion
Note: Code accompanying this lecture will be available on the
course website:
http:/www.biostat.um

PUBH 7430
Lecture 4
J. Wolfson
Division of Biostatistics
University of Minnesota School of Public Health
September 15, 2010
A little bit of notation
Notation - independent data
With independent data on n units, for each unit j we have
(Scalar, one-dimens