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re: st: Specifying a repeated measures analysis in anova and xtmixed


From   David Airey <david.airey@vanderbilt.edu>
To   statalist@hsphsun2.harvard.edu
Subject   re: st: Specifying a repeated measures analysis in anova and xtmixed
Date   Tue, 2 Aug 2005 10:09:16 -0500

.

Briefly, I am conducting research dealing with different ways of presenting medical data to clinicians. One aspect I am interested in is the time it takes for clinicians to reach decisions when using these displays, and whether different ways of presenting the same data take longer or shorter times than others.

My experimental design consists of a series of cases (i.e., data taken from individual patients), each shown in different display formats (i.e., modalities), to a variety of clinician readers, who then decide on what to do with that patient. *Every* case is shown in *every* modality to *every* reader. If I'm using the correct terminology, this is a complete, balanced design, with no nesting, blocking, etc. For each reader, the order of cases/modalities is randomized. Different data are collected from each combination of case, modality, and reader, including the time it takes for decisions to be rendered in each case/modality/reader combination.
If I understand,

Case: fixed within subject effect
Display_format: fixed within subject effect
Reader: random subject effect

See the Stata FAQ for this design:

http://www.stata.com/support/faqs/stat/anova2.html#half713


2) If I wanted to analyze this as a mixed model, what is an appropriate way to use xtmixed? I consider case and reader to be random effects, as both are drawn from larger populations of possible cases and readers. Likewise, I consider modality to be a fixed factor, as there are only N modalities of interest in any particular phase of my study. As such, I came up with the following as a rough guess of how to express it:

There seems a discrepancy between the randomized block factorial design anova solution given at UCLA and that given in the Stata FAQ. Unless the designs are different. I can't tell from the data table.

http://www.stata.com/support/faqs/stat/anova2.html#half713


--------------------------------------------------------------------
| 10 minute time periods and dial
| ------- 1 ------ ------- 2 ------ ------- 3 ------
subject | 1 2 3 1 2 3 1 2 3
---------- +---------------------------------------------------------
1 | 45 53 60 40 52 57 28 37 46
2 | 35 41 50 30 37 47 25 32 41
3 | 60 65 75 58 54 70 40 47 50
--------------------------------------------------------------------


. anova score subject period / subject*period dial / subject*dial period*dial, repeated(period dial)

or

. anova y s a / s*a b / s*b a*b, repeated(a b)

versus

http://www.ats.ucla.edu/stat/stata/faq/xtmixed.htm

----------+---------------------------------------------------------
| a and b
| ------- 1 ------ ------- 2 ------ ------- 3 ------
s | 1 2 3 1 2 3 1 2 3
----------+---------------------------------------------------------
1 | 37 43 48 39 35 46 31 41 64
2 | 42 44 47 30 40 36 21 50 52
3 | 33 36 29 34 31 45 20 39 53
4 | 29 27 38 26 22 27 18 36 42
5 | 24 25 28 21 27 26 10 34 49
----------+---------------------------------------------------------


/ ************************************************************************ ******************/
/ * */
/* randomized block factorial design */
/ * */
/* from kirk -- see http://www.ats.ucla.edu/stat/stata/examples/kirk/ kirkstata10.htm */
/ * */
/ ************************************************************************ ******************/

use http://www.ats.ucla.edu/stat/stata/examples/kirk/rbf33, clear

/* anova code: */ anova y s a b a*b, repeated(a b)

xi3 e.a*e.b

xtmixed y _Ia_2 _Ia_3 _Ib_2 _Ib_3 _Ia2Xb2 _Ia2Xb3 _Ia3Xb2 _Ia3Xb3 || s:

test _Ia_2 _Ia_3

/* scale chi^2 as F-ratio to compare with anova */
display r(chi2)/r(df)

test _Ib_2 _Ib_3

display r(chi2)/r(df)

test _Ia2Xb2 _Ia2Xb3 _Ia3Xb2 _Ia3Xb3

display r(chi2)/r(df)

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