# Re: st: time-effect in manova (anova with repeated measures )

 From "Maren Kandulla" To Subject Re: st: time-effect in manova (anova with repeated measures ) Date Wed, 16 Nov 2005 10:13:57 +0100

```> Maren Kandulla wrote:
>
> again I am fighting with stata to do the right analysis. My data is a
panel
> design, 6 measuring times, 4 groups to compare, n=75.
> I try to test whether 4 different groups differ in terms of means over
time
> regarding a variable (motivation). In other words wether motivation
differs
> between the 4 groups and wether there is a change over time (motivation is
> decreasing f.e.). First I did a nice graph to see the differences but now
I
> would like to test them using manova.
> I did a manova (for repeated measures)
>     manova motiva_1 motiva_2 motiva_3 motiva_4 motiva_5 motiva_6 = group
> Then I checked, which of the 4 groups differ significantly.
> [omitted]
> This worked out perfectly.
>
> 1.) However, now I would like to see, wether there is a over-all
time-effect
> (wether motivation is decreasing or increasing over time) for all groups
> together and for each group. This is very easy in SPSS but I did not
figure
> it out in Stata even though I read different manuals and books.
> 2.) Secondly I would like to see wether there is a significant difference
> between two groups at a certain time-point (f.e. group 2 and 4 at time 3)
.
> I could do this by using a simple anova but maybe I can integrate it in
the
> manova-model as well?
> 3.) Thirdly I would like to know wether a decrease for one group differ
from
> a certain increase of another group between two time-points (f.e. wether
the
> decrease of group 4 between time 2 and time 3 differes significantly from
> the increase of group 1 at the same time period.
>
> Could you please tell me, how to write the matrix for it. I just did not
> understand it by reading the manual or other books. Question 1 is the most
> important. I know I could do Question 2 and 3 by using a form of
> panelanalysis, but since I am working with psychologist I would rather go
> for anova with repeated measures.
>
> --------------------------------------------------------------------------
------
>
> No one else seems to have taken you up, so I'll give it a try.
>
> 1.) The design matrix in Stata's -manova- is overparameterized like that
in
> SAS's PROC GLM or SPSS's GLM.  To get the mean of the groups at a given
> time, you take _b[_cons] and add the average of the group coefficients.
> (See the -lincom- statement in the do-file below).  So, to test the time
> effect, you need to test this mean across time:  the one-row test matrix
> will have a one in the constant's column (the first column), and (with
equal
> group sizes) one-quarter in each of your four groups' columns.  This is
> illustrated in the do-file below, which uses a dataset from UCLA's
> Technology Services' Statistical Computing Resources website.  The Web
page
> is www.ats.ucla.edu/stat/sas/library/comp_repeated.htm and you can compare
> Stata's results from the do-file below for the main effects for time (and
> the group-by-time interaction) to those in the SAS listing shown on the
Web
> page.  Note that the example dataset from the website has only three
> treatment groups, and not four as in your case, so the illustration below
> divides the sum of the coefficients by three in order to get the average,
> and not four.
>
> 2.) A one-row M matrix with a one for the column for Time 3 and zeroes
> elsewhere, and then a one-row test matrix with a one for the column for
> Group 3 and a minus one for the column for Group 4 and zeroes elsewhere.
> (See do-file below.)
>
> 3.) Analogous to 2.), a one in the column for Time 2 a minus one for Time
3
> and zeroes elsewhere, a one for Group 1 and a minus one for Group 4 and
> zeroes elsewhere.  (See do-file below--the example dataset has only three
> groups, so in the illustration, I substituted Group 3 for your Group 4.)
>
> With 75 people and four groups, you will have unequal representations
among
> groups.  I think that MANOVA does best with equal representation among
> groups, just like factorial ANOVA does.  At the least, you might need to
> adjust the one-quarter to some group-size-weighted fraction in order to
get
> the -lincom- estimate to match that by -summarize-.  I recall B. J. Winer
> recommending harmonic means in the context of unbalanced ANOVA in order to
> get a better estimate of the cell's contribution to the pooled variance.
> This might be worthwhile to look into, depending upon the magnitude of the
> imbalance.  (Probably not if it's 19, 19, 19 and 18.)
>
> For simple main effects testing involving the repeated measurements in the
> context of repeated-measures ANOVA in which the sphericity assumption is
on
> shakey grounds, David Nichols (see the two postings under the subject
> paired Student t-tests.  He mentions that the contrasts can be set up in
> SPSS's MANOVA command (which takes advantage of the pooled between-group
> error), but it is usually easier to do a paired t-test and accept some
loss
> of power.  In the example below, the p-values were similar (essentially
the
> same, actually) whether the test was done in -manova- or by -ttest-.  The
> problem of unbalanced groups goes away with paired Student's t-tests, too.
>
> Joseph Coveney
>
> infile id cond ib1 ib2 ib3 ib4 ib5 ///
>   ms1 ms2 ms3 ms4 ms5 sr1 sr2 sr3 sr4 sr5 ///
>  using ///
> http://www.ats.ucla.edu/stat/mult_pkg/library/repeat/repeat.txt
> compress
> tabulate cond
> // Three treatment groups, balanced
> manova sr1 sr2 sr3 sr4 sr5 = cond
> *
> * Orientation to -manova-'s parameterization
> *
> summarize sr1
> // Compare that mean to:
> lincom [sr1]_b[_cons] + ([sr1]_b[cond[1]] + ///
>   [sr1]_b[cond[2]] + [sr1]_b[cond[3]]) / 3
> // So, in order to track the mean across time,
> // the test matrix is 1 1/3 1/3 1/3
> *
> * Main effects of time
> *
> matrix M = (1, -1, 0, 0, 0 \ 0, 1, -1, 0, 0 \ ///
>             0, 0, 1, -1, 0 \ 0, 0, 0, 1, -1)
> matrix H = (1, `=1/3', `=1/3', `=1/3')
> manovatest , test(H) ytransform(M)
> // Cf. SAS results presented in Web page
> *
> * Group-by-time interaction (lagniappe)
> *
> matrix H = (0, 1, -1, 0 \ 0, 0, 1, -1)
> manovatest , test(H) ytransform(M)
> // Cf. SAS results presented in Web page
> *
> * Group 2 versus Group 3 at Time 3
> *
> matrix M = (0, 0, 1, 0, 0)
> matrix H = (0, 0, 1, -1)
> manovatest , test(H) ytransform(M)
> ttest sr3 if inlist(cond, 2, 3), by(cond)
> *
> * Change from Times 2 to 3 between Groups 1 and 3
> *
> matrix M = (0, 1, -1, 0, 0)
> matrix H = (0, 1, 0, -1)
> manovatest , test(H) ytransform(M)
> generate delta23 = sr2 - sr3
> ttest delta23 if inlist(cond, 1, 3), by(cond)
> exit
>

Dear Joseph,
thanks a lot for this brilliant do-file! I checked it on my data and it
worked out perfectly AND finally I understood the matrix-test-systematic,
what makes me very happy.
However, I do have one request regarding your remark:
> With 75 people and four groups, you will have unequal representations
among
> groups.  I think that MANOVA does best with equal representation among
> groups, just like factorial ANOVA does.  At the least, you might need to
> adjust the one-quarter to some group-size-weighted fraction in order to
get
> the -lincom- estimate to match that by -summarize-.

I have a very unbalanced design. To be more precise than in my previous
email where I "combined information", I have following n-distribution: 1.
Cohort with 4 groups: 21, 14, 35, 17; total 87 and 2. Cohort with 3 groups:
35, 21, 19; total 75; cohorts are analysed seperately.
In the Stata-Manual I found following information:
> manova fits multivariate analysis-of-variance (MANOVA) and multivariate
analysis-of-covariance (MANCOVA) models for balanced and unbalanced
designs...

I therefore decided not to do any adjustment. Please, correct me if this was
wrong!

Maren

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