Homework
Assignment #13
In this assignment you will make use of PROC MIXED to
analyze various data sets. The examples are taken from the
the book SAS
System for Mixed Models
by Ramon C. Littell, Ph.D., George A. Milliken, Ph.D.,
Walter W. Stroup, Ph.D., and Russell D. Wolfinger, Ph.D
Data for the examples, and example programs are given
on-line in Mixed
Model Examples. You should download these examples to
obtain data sets for use in this exercise.
There are other on-line resources for PROC MIXED. Examples
of such resources are given by SAS: Technical
Support. There are documents on the WEB that provide
examples for use of MIXED models accessible from the SAS WEB
site. You should familiarize yourself with the site, and you
may wish to obtain some documents in either PS or PDF format
.
There are potential problems with PROC MIXED in SAS.
You should review the problems given in the Techical notes.
An example of several documented probems are:
DF
appear incorrect if main effect listed after crossed effect
Fixed
Effects Standard Errors Can Be Incorrect With NOPROFILE
Option
Incorrect
results possible with WEIGHT statement and missing values
Incorrect
Likelihood Printed With RANDOM /G and REPEATED Statements
Problems (Data for these problems comes from Mixed
Model Examples , and require reading of background
material in SAS
System for Mixed Models ).
For each problem, prepare a 2 page written summary and
oral presentation (10 min) that includes the following :
- A description of the context and the problems, along
with the data collected.
- A definition of the model and notation used.
- A description of the computing programs used in the
modelling, with a description of the function of the
various statements and possible options.
- A description of the output, interpretations, and
conclusions.
Each pair of students will do one problem. One written
report should be given. Oral reports should be given with
each student participating. The pairings are:
#1. Liping Chen, Hui
Li
#2. Jain Gao, Xingmin Chen
#3. Weining Yang, Zhensheng Li
#4. Lanqing Qui, Shu-Huan Zhang
Due
Dates: The SAS WEB pages should
be reviewed by Thursday, April 23, with the first part of
the problem begun. Questions will be answered in class. The
first two problems will be presented in class on April 28,
with the next two on April 30.
1. a. Randomized complete block model: The ingot
example (p1-13 in Litell et. al.; Data set and programs
1.2.4).
b. Patially balance incomplete block design (15 blocks, 15
treatments with 4 treatments per block): Cochran's cotton
example (p18-29 in Littell et al; Data set and programs
1.5.1 etc).
c. Split-plot example #1: The effect of three bacterial
inoculation treatments applied to two grass cultivars on dry
weight yield (4 blocks divided in half, with 2 cultivars
assigned to each half (a whole plot), whole plots are split
into sub-plots with 3 incoculations applied to each
split-plot): (p31-32, p58-75 in Littell et al; Data set and
programs 2.2a)
2. a. Split-plot example #2: The effect of several modes
of a process condition (ET) on resistance in computer ships
(12 Wafers , 3 wafers assined to 4 modes of ET, with
resistance measured at 4 positions). (p32-58, and 105-108 in
Littell et al; Data set and programs 2.2b etc).
b. Multilocation trials: A multicenter trial with 9 centers,
where at each center, there are 3 blocks with 4 treatments
randomly assigned to plots in a block, with response
corresponding to ADG (p75-86, and p248-251 in Littell et al,
Data set and programs 2.8.1 etc).
c. Repeated measures: A study was conducted to evaluate
exercise therapy in weight lifting. Subjects were randomized
to three treatments, with measures taken on each subject
repeatedly at 7 times. ( p87-105, 108-114 in Littell et al,
Data set 3.2a etc. )
3. a. Repeated measures with missing data: A study was
conducted to evaluate exercise therapy in weight lifting.
Subjects were randomized to three treatments, with measures
taken on each subject repeatedly at 7 times. (p115-125 in
Littell et al, Data set 3.2a used to create 3.2b etc)
b. Unequally space repeated measures: Heart rates are
measured on different subjects over time (24 patients at 5
times): (p126-130 in Littell et al., and Data set 3.5
etc)
c. Random effect models: Nitrogen influent: (6 influent
types by repeated measures) (p135-149 in Littell et al.,
Data set 4.2 etc.)
4. a. Random effects models with Groups: Nitrogen
influent with groups: (6 influent types in 3 groups by
repeated measures) (p149-155 in Littell et al., Data set 4.2
etc.)
b. Continuation of silicon wafer example with nesting: (12
Wafers , 3 wafers assined to 4 modes of ET, with resistance
measured at 4 positions) (p155-164 from Littell et al.,
using data sets 4.4).
c. Analysis of covariance: Data were collected on 32 steers
who were randomly assigned to eight barns, with four diets
randomly assigned to one steer in each barn. The initial
weight and weight gain were reported. (pp171-187 in Littell
et al., and data set 5.2 etc.)
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