After doing some more searching of the literature and the web,
let me say that Diana is correct, that is, if one is going to use a
multivariate analysis instead of traditional repeated measures ANOVA,
the approach SPSS calls "doubly-multivariate results" should be
used. But a few more points need to be made:
(1) The question about the two sets of multivariate results was
original asked on the SPSS Usenet group back in 1998 and
David Nichols (Hi David!) gave a response. His post can be
read here:
https://groups.google.com/forum/#!topic/comp.soft-sys.stat.spss/857xHuoXDYwAnd his response is reproduced here:
|I already answered these questions individually, but in
|case others are interested, the tests mentioned are
|indeed the same as those labeled averaged multivariate
|tests in MANOVA.
NOTE to those still using the SPSS MANOVA procedure:
check to see whether only the average multivariate results
are still provided.
|They ignore the parts of the SSCP matrices that involve
|covariation among transformed variables within the same
|measure, but incorporate covariation among transformed
|variables in different measures to produce multivariate tests. I
|'ve seen them referred to as Scheffe's multivariate mixed
|model tests in an article by Robert Boik (I don't have the full
|reference handy). Unfortunately, SPSS does not at the
|current time have a test for the condition of multisample
|sphericity that is required for them to be valid. To get corrected
|averaged univariate tests printed in Release 7.5, double
|click on the table with the averaged tests, then choose
|Pivot->Move Layers to Rows, or activate the pivoting trays
|and move the Epsilon corrections icons from the Layers
|area to the Rows area. In Release 8.0, the table is presented
|with these tests displayed.
(2) I don't know which Boik article David is referring to but
one that explicitly refers to the second method is covered in
the following reference:
Boik, R. J. (1991). Scheffés mixed model for multivariate
repeated measures: a relative efficiency evaluation. Communications
in Statistics-Theory and Methods, 20(4), 1233-1255.
At the end of the article's abstract Boik writes:
|Based on relative efficiency evaluations, the adjusted MMM
|[NOTE: MMM = Scheffe's multivatiate mixed model] analyses
|described in this paper can be recommended only when sample
|sizes are very small or there is reason to believe that multivariate
|sphericity is nearly satisfied. Neither the €-adjusted analysis
|suggested in the SPSS MANOVA output (release 4.0) nor the
|adjusted analysis suggested by Boik (1988) can be recommended
|at all.
NOTE: Yes, Boik refers to good old version 4.0 of SPSS.
I Don't think SPSS has changed MANOVA or the multivariate
analysis much since back then (except GLM came after
version 4.0).
(3) An old reference that argues strongly for the Multivariate
approach to repeated measures analysis is the following
reference:
O'Brien, R. G., & Kaiser, M. K. (1985). MANOVA method for
analyzing repeated measures designs: an extensive primer.
Psychological bulletin, 97(2), 316.
The authors use the term MANOVA to refer to both the statistical
procedure and the SPSSX (what it was called back then) procedure.
(4) Given the issues above, one wonders why SPSS has not
provided the multivariate sphericity test that would show whether
the second set of multivariate (Scheffe) results are valid. Without
it, one has to try to work it out on one's own or see if some other
package provides it (or do the analysis in a SEM package).
And does the MANOVA procedure (still available via syntax)
still only give the Scheffe results? If so, warnings about whether
to use it or not should be more widely communicated.
If anyone has more up-to-date knowledge about this situation,
either in SPSS or in other programs (e.g., SAS, Stata, etc.),
I think it would be of benefit to the user community if it were
provided here.
-Mike Palij
New York University
[hidden email]
----- Original Message -----
From: Kornbrot, Diana
To:
[hidden email]
Sent: Tuesday, September 06, 2016 11:27 AM
Subject: Re: Question about SPSS MANOVA output
1st output table is the one to use
it makes full use of the correlation matrix between repeated measures,
i.e different correlation between t1, t2 and t2,t3
2nd table ASSUMES all pairwise correlation same and estimates a mean
correlation and then makes various corrections for correlation
differences
it was rocket science when SPSS launched some decades ago when the truly
multivariate method was computationally expensive
why it is still there I have no idea, but spss does not like to drop
anything
the Maunchley test is testing whether all the pairwise correlations ARE
the same. In my view it is better to use full correlation matrix even if
Maunchley is ns [power is low anyway]
best
Diana
On 5 Sep 2016, at 03:12, Jeff Miller <
[hidden email]> wrote:
My question concerns two separate tables of "Multivariate" tests
produced by
the GLM command. As an example, I will use a design with two groups
(e.g.,
males/females). Each individual was measured at each of three time
points
(time1/time2/time3) on each of four dependent variables
(dv1/dv2/dv3/dv4).
(At the end of this question is a syntax file that will generate sample
data
and run the analysis, allowing me to ask the question with reference to
specific values.)
The first "Multivariate Tests^a" output table appears early in the
output,
and it includes one section for "Between Subjects" effects (i.e.,
intercept
& group, in this design) and another section for "Within Subjects"
effects
(i.e., Time and Time*group).
The second "Multivariate^a,b" table appears later in the output (after
Mauchley's test) under the major heading "Tests of Within-Subjects
Effects".
Each of these two tables displays the results of multivariate tests (eg
Pillai's Trace, Wilks' lambda) for the two Within-Subjects sources
(i.e.,
Time and Time*group), but the two tables give different values.
My question is simply, "what is the difference between these two
tables?"
For example, what are the models and null hypotheses in each case? Why
are
the error df's different? What would it mean if the first table's test
of
Time was significant and the second table's was not, or vice versa?
Any insight would be greatly appreciated. Thanks for your time.
----- Syntax file follows: Just copy, paste, and run all to see a
specific
data set and analysis illustrating my question.
* Here is a syntax file to generate and analyze an example data set,
* so that the question can be posed in terms of specific values.
* For this example, there are 2 groups of randomly-selected individuals
(cases).
* Each case is measured at 3 time points on 4 different DVs.
* Set the RNG seed so that the results are reproduced exactly.
set RNG=MT MTINDEX=121314.15.
new file.
input program.
compute #SampleSize = 50.
loop #i = 1 to #SampleSize.
compute group = 1.
compute dv1time1 = rv.normal(0,1).
compute dv1time2 = rv.normal(0,1).
compute dv1time3 = rv.normal(0,1).
compute dv2time1 = rv.normal(0,1).
compute dv2time2 = rv.normal(0,1).
compute dv2time3 = rv.normal(0,1).
compute dv3time1 = rv.normal(0,1).
compute dv3time2 = rv.normal(0,1).
compute dv3time3 = rv.normal(0,1).
compute dv4time1 = rv.normal(0,1).
compute dv4time2 = rv.normal(0,1).
compute dv4time3 = rv.normal(0,1).
end case.
end loop.
loop #i = 1 to #SampleSize.
compute group = 2.
compute dv1time1 = rv.normal(0,1).
compute dv1time2 = rv.normal(0,1).
compute dv1time3 = rv.normal(0,1).
compute dv2time1 = rv.normal(0,1).
compute dv2time2 = rv.normal(0,1).
compute dv2time3 = rv.normal(0,1).
compute dv3time1 = rv.normal(0,1).
compute dv3time2 = rv.normal(0,1).
compute dv3time3 = rv.normal(0,1).
compute dv4time1 = rv.normal(0,1).
compute dv4time2 = rv.normal(0,1).
compute dv4time3 = rv.normal(0,1).
end case.
end loop.
end file.
end input program.
execute.
GLM
dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY group
/WSFACTOR = Time 3 Polynomial
/MEASURE = DV1 DV2 DV3 DV4
/METHOD = SSTYPE(3)
/EMMEANS = TABLES(group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(group*Time)
/PRINT = DESCRIPTIVE HOMOGENEITY
/CRITERIA = ALPHA(.05)
/WSDESIGN = Time
/DESIGN = group .
* Here is a more specific version of my question.
*
* An earlier "Multivariate Tests^a" output table includes the line:
* Within Subjects Time Pillai's Trace 0.145
1.935^b 8.000 91.000 0.064
*
* Two tables farther along is a "Multivariate^a,b" table that includes
the
line:
* Within Subjects Time Pillai's Trace 0.068
1.712 8.000 388.000 0.094
*
* These two tables include the same sources (i.e., Time and Time*group),
* but they give different values and different error df's.
*
* What is the difference between these two tables?
* (My question pertains to both of the sources, Time and Time*group).
--
View this message in context:
http://spssx-discussion.1045642.n5.nabble.com/Question-about-SPSS-MANOVA-output-tp5733053.htmlSent from the SPSSX Discussion mailing list archive at Nabble.com.
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________________________________________
Professor Diana Kornbrot
Work
University of Hertfordshire
College Lane, Hatfield, Hertfordshire AL10 9AB, UK
+44 (0) 170 728 4626
[hidden email]
http://dianakornbrot.wordpress.com/http://go.herts.ac.uk/Diana_Kornbrotskype: kornbrotme
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[hidden email] (not to SPSSX-L), with no body text
except the command. To leave the list, send the command SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command INFO
REFCARD
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