Sample 30584: Analyzing Repeated Measures in JMP Software
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Analyzing Repeated Measures Data in JMP®
Software
Often in an experiment, more than one measure is taken on the same
subject or experimental unit. This means that a repeated measures analysis of
the data may be necessary to make valid inferences and to draw meaningful
conclusions.
JMP
offers two methods to analyze repeated measures: a univariate split-plot
approach and a multivariate repeated-measures approach. These two types of
analyses are compared in the following discussion. The example uses the
DOGS
(dogs.jmp)
sample data table, which is the result of a study with repeated measures.
Figure
A
shows
selected columns from the DOGS
table.
This data table contains information on sixteen dogs assigned to groups defined
by the independent variable drug
with
values "morphine" and "trimeth." The blood concentration of histamine is
recorded before drug injection and again at one and three minutes after
injection. Also, there is an additional ID
column,
declared Nominal, which will be used to account for the within-subject
variability in a univariate analysis of repeated-measures data.
Figure
A: Arrangement of Data Table, Multivariate
Approach.
Figure
B
shows selected columns from the restructured DOGS table where the
LogHist
columns have been stacked into a single response
column.
Figure
B: Arrangement of Data Table, Univariate
Split-Plot Approach.
A Multivariate Approach
The
original DOGS
table
with multiple response columns is in the form needed for a multivariate analysis
that tests the same effects–nothing needs to be changed.
With this data table active, again choose Fit Model from the Analyze Menu.
Specify LogHist0, LogHist1
and
LogHist3
as
Y
variables. Change the Fitting Personality to Manova.
Assign drug
as
the model effect and run the model.
When
there are multiple Y variables, JMP automatically performs a multivariate
analysis. When you first run the model, the multivariate control panel appears.
To test the effect of drug
over
time, select "Repeated Measures" as the response design from the popup menu on
the control panel. In the
repeated-measures dialog that appears, use the default effect name
Time
but check "Univariate Tests Also" to obtain univariate and adjusted
univariate tests. This option includes a test of sphericity (not shown here),
which checks whether the unadjusted univariate F tests are appropriate. If the
sphericity chi-square test is not significant, you can use the unadjusted
univariate F tests. However, if the sphericity test chi-square is significant,
then the criterion is rejected and the multivariate F tests or the adjusted
univariate F tests should be used. JMP gives both the Greenhouse-Geisser (G-G),
and the Huynh-Feldt (H-F) adjusted F tests.
A Univariate Approach
A univariate model has a single response. Each source of variation
(between-subjects and within-subjects) is included as an effect in the
model.
The univariate analysis requires that the response measurements be in
a single column. Using the Stack command in the Tables menu,
you can stack the LogHist0,
LogHist1,
and
LogHist3
columns
to create a new response column, as shown in Figure
B.
The new response, LogHist,
and also the new classification variable, Time,
were created by the Stack command.
With the data table correctly set up, choose Fit Model from the Analyze Menu.
Select LogHist
as
Y, and add the Effects in Model as
shown in Figure
C.
Figure
C: Univariate Repeated Measures
Specification.
To create the model shown to the left, which has a random effect for
testing the between-subjects effect in the model, click the following variables
and buttons:
·
drug
in
the variable selection list, then Add
·
ID
in
the variable selection list, then Add
·
drug
in
the variable selection list, and
·
ID
in
the Effects in Model
list,
then Nest
·
ID[drug]
in
the Effects in Model
list,
then select Random
from
the Effect Attributes
pop-up
menu giving ID[drug]&
Random
in
the Effects in Model
list
·
Time
in
the variable selection list, then Add
·
drug
in
the variable selection list and
·
Time
in
the variable selection list, then Cross
The
between-subject effect, drug
is
the whole plot effect of a split-plot design. The Subject
effect
is nested within drug. This
Subject(drug)
effect
is the appropriate error term for the between-subject effect. Therefore, it is
specified as a random effect using the Random selection from the Effect Attributes pop-up menu. JMP uses a random effect as the error term to test
appropriate terms in the Effects in Model list.
The
within-subject effects, Time
and
drug*Time
will
be tested with the residual error term.
After
running this model you can examine the significance of the model effects seen in
the "Tests wrt Random Effects" table shown in Figure
D.
Figure D: Comparison of
Univariate and Multivariate Results.
Comparing the Two Methods
A
comparison of analysis results is shown in Figure
C.
By examining each analysis, you can see the relationship between the univariate
and multivariate effects tests:
1.
For
between-subject effects (drug),
the multivariate approach gives the same results as the univariate approach when
there are no missing values. If there are missing values, a univariate analysis
uses all nonmissing data values but the multivariate analysis excludes any
subject with any missing values.
2.
If
there are no missing values, the within-subjects Time
variable
in the univariate model is the same as the unadjusted Time effect in a multivariate model having a "Repeated Measures" response
design. However, these tests are appropriate only if the sphericity test
criterion (mentioned previously) is met. Otherwise, the multivariate tests or
the adjusted univariate tests should be used.
3.
Often
in a repeated-measures study the most important effect is the within-subject by
between-subject interaction– the hypothesis of interest is whether the study
treatment has an effect over time. In the univariate analysis, the
drug*Time
interaction
appears insignificant.
4.
In
this example the more powerful multivariate approach shows the drug*Time
interaction
effect to have marginal significance.
In summary, if you have repeated-measures data, JMP can analyze the
data as either a univariate split-plot model or a multivariate model. Each type
of analysis has its advantages and disadvantages:
·
The multivariate analysis is easy and intuitive to specify in JMP.
Its tests are usually more powerful. From a computing standpoint, this method
is most efficient. However, if a subject is missing a value, all information for
that subject is lost to the analysis.
·
The univariate analysis can use all the data–only a subject's missing
measurement is lost to the analysis. However, the univariate analysis can be
very computationally intensive, particularly if there are many subjects.
Also,
the univariate tests for within-subject effects and interactions involving these
effects require assumptions about the covariance matrix in order for the
probabilities provided by the ordinary F tests to be correct. If these
assumptions are not met (if the sphericity test is rejected), then probabilities
for adjusted Figure
C: Comparison of Univariate and Multivariate Results univariate
F tests (given in the multivariate report) or the multivariate F tests should be
used. Because of these assumptions, the univariate approach should be
considered only when the Sphericity condition is met. For more information see the discussion
on this test in the JMP
Statistics and Graphics Guide,
in the Multivariate Model Fitting chapter.
Cole and Grizzle, J.E. (1966), "Sixteen Dogs," Biometrics,
22:810
These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.
These sample files and code examples are provided by SAS Institute Inc. "as is" without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability and fitness for a particular purpose. Recipients acknowledge and agree that SAS Institute shall not be liable for any damages whatsoever arising out of their use of this material. In addition, SAS Institute will provide no support for the materials contained herein.
| Type: | Sample |
| Date Modified: | 2008-04-22 09:46:10 |
| Date Created: | 2007-11-16 13:48:35 |
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