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# st: Re: RE: re: RM ANOVA, was SPSS vs. Stata

 From Philip Ender To statalist@hsphsun2.harvard.edu Subject st: Re: RE: re: RM ANOVA, was SPSS vs. Stata Date Tue, 3 Aug 2010 08:23:37 -0700

```<robert.ploutz-snyder-1@nasa.gov> had an example of a repeated
measures anova in which two of the observations were set to missing.
Here are partial results from his Stata output:

Between-subjects error term:  person
Levels:  5         (4 df)
Lowest b.s.e. variable:  person

Repeated variable: drug
Huynh-Feldt epsilon        =  0.5297
Greenhouse-Geisser epsilon =  0.4228
Box's conservative epsilon =  0.3333

------------ Prob > F ------------
Source |     df      F    Regular    H-F      G-G      Box
-----------+----------------------------------------------------
drug |      3    27.71   0.0000   0.0019   0.0047   0.0102
Residual |     10
----------------------------------------------------------------

And here are the partial results from his SPSS:

IN SPSS (same dataset):

Tests of Within-Subjects Effects
Source		Type III Sum of Squares	df	Mean Square	F	Sig.
drug	Sphericity Assumed	478.333	3	159.444	13.932	.004
Greenhouse-Geisser	478.333	1.268	377.157	13.932	.044
Huynh-Feldt			478.333	2.466	193.938	13.932	.008
Lower-bound			478.333	1.000	478.333	13.932	.065
Error(drug)	Sphericity Assume	68.667	6	11.444
Greenhouse-Geisser	68.667	2.537	27.071
Huynh-Feldt			68.667	4.933	13.920
Lower-bound			68.667	2.000	34.333

----------------------

I prefer using -xtmixed- for repeated measures designs with missing
observation.  I think that it is far superior to deleting whole cases
when only one observation is missing.  In this example there are four
observations on each subject.  Two of them are missing only a single
observation.

. xtmixed score i.drug || person:

Performing EM optimization:

Iteration 0:   log restricted-likelihood = -43.456003
Iteration 1:   log restricted-likelihood = -43.456003

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        18
Group variable: person                          Number of groups   =         5

Obs per group: min =         3
avg =       3.6
max =         4

Wald chi2(3)       =     83.43
Log restricted-likelihood = -43.456003          Prob > chi2        =    0.0000

------------------------------------------------------------------------------
score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
drug |
2  |   1.120543   2.136759     0.52   0.600    -3.067427    5.308514
3  |  -10.17271   1.980896    -5.14   0.000    -14.05519   -6.290222
4  |   6.227293   1.980896     3.14   0.002     2.344808    10.10978
|
_cons |   25.77271   3.175225     8.12   0.000     19.54938    31.99603
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
person: Identity             |
sd(_cons) |    6.26194   2.334319      3.015775    13.00226
-----------------------------+------------------------------------------------
sd(Residual) |   2.901958    .646767      1.874915    4.491595
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =    14.32 Prob >= chibar2 = 0.0001

. testparm i.drug

( 1)  [score]2.drug = 0
( 2)  [score]3.drug = 0
( 3)  [score]4.drug = 0

chi2(  3) =   83.43
Prob > chi2 =    0.0000

/* rescale chi2 to F */

. display r(chi2)/r(df)
27.808724

The F-ratio given here is actually closer to the F-ratio for the
complete data (F=24.76) then the F-ratio produced by SPSS (F=13.932).
I this case I have greater trust in -xtmixed- than I do in the SPSS
repeated measures.  In general, I feel that complete case analysis can
lead to greater bias then using a linear mixed model approach.
Further, -xtmixed- allows for more covariance structures than repeated
measure in SPSS which only allows for compound symmetry (echangable)
and unstructured.

Phil
--
Phil Ender
UCLA Statistical Consulting Group
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```