Section 13.2: Generalized Linear Mixed Models
Observations often occur in related clusters. Phrases like repeated
measures and longitudinal data get at the same thing: theres
correlation among observations in a cluster.
Chapter 12 dealt with an estimati
Random vectors
X
1
X2
Recall that a random vector X = . is made up of, say, k
.
.
Xk
random variables.
A random vector has a joint distribution, e.g. a density f (x), that
gives probabilities
P (X A) =
f (x)dx.
A
Just as a random variable X has a mean E
Matrices and vectors
A matrix is a rectangular array of numbers. Heres an example:
2.3
1.4 17
A=
.
22.5
0
2
This matrix has dimensions 2 3. The number of rows is rst, then
the number of columns.
We can write the n p matrix X
x11 x12
x21 x22
X = x31 x32
Chapter 12: Population-averaged models for Bernoulli
repeated measurements
Example of repeated measures:
Data are comprised of several repeated measurements on the
same individual over time, e.g. Yij = 1 indicates acne outbreak
for patient i in month j ;
Stat 771 Homework 5, due Monday, April 25
We will consider data from a longitudinal study at Harvard of eects of air pollution on
respiratory illness in children. The children were examined annually at ages 7 through 10
and classied according to the prese
Stat 771 Homework 4, due Monday, April 18
We will consider data from an AIDS trial comparing two drugs, ddI and ddC (Abrams
et al., 1995). This was a multicenter, randomized, open label trial to compare ddI to ddC in
HIV-infected patients who were intoler
Stat 771, Fall 2011: Homework 3
Due Wednesday, March 23
The le insulin.dat contains longitudinal data from a study on m = 36 rabbits; 12 rabbits were
randomly assigned to each of 3 groups: group 1 rabbits received the standard insulin mixture, group 2
rab
Stat 771, Fall 2011: Homework 2
Due Wednesday, February 23
1. The le insulin.dat contains longitudinal data from a study on m = 36 rabbits; 12 rabbits were
randomly assigned to each of 3 groups: group 1 rabbits received the standard insulin mixture, group
Stat 771, Fall 2011: Homework 1
Due Wednesday, February 6
1. Let
A=
2
1
1
2
,B =
2
1
1
2
, and c =
1
3
.
(a) Find 3B.
(b) Find A B.
(c) Find AB.
(d) Find |A|.
(e) Find A1 .
(f) Is A full rank? Why or why not?
(g) Let x =
x1
x2
. Show
x Ax = 2(x2 + x1 x2 +
Longitudinal Data Analysis
Spring 2011
Monday/Wednesday 2:303:45 in LeConte College 210A
Instructor: Prof. Tim Hanson
Oce: LeConte 219C (777-3859)
email: [email protected]
Website: http:/www.stat.sc.edu/hansont/stat771/
Oce hours: Monday & Wednesday 1: