David Airey wrote:
This might be off topic, but I liked a recent paper by Senn:
Senn S (2006) Change from baseline and analysis of covariance
revisited. Statist. Med. 2006; 25:4334-4344
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Thanks, Dave. I haven't seen the article. I had run across his
corresponding presentation
< www.stochastik.math.uni-goettingen.de/kolloquium/Lord's Paradox
Glasgow.ppt > before, but had forgotten. He summarizes a classic topic, and
the conclusion among experts as it pertains to typical experiments in the
biological and medical fields has been embodied in government guidance
documents ( www.emea.europa.eu/pdfs/human/ewp/286399en.pdf ), and other
locations that you might recognize from proximity, e.g.,
http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/MeasureChange .
He does touch on measurement error in the covariate in his Slide 10.
I guess the fundamental quandary remains about MANCOVA versus SUR
approaches, the equation pairs being
L_after = b10 + b11 * treatment + b12 * L_before + b13 * R_before + e1
R_after = b20 + b21 * treatment + b22 * L_before + b23 * R_before + e2
for MANCOVA, and
L_after = b10 + b11 * treatment + b12 * L_before + e1
R_after = b20 + b21 * treatment + b22 * R_before + e2
for SUR.
The first pair strikes me as overparameterized, but am unable to point to a
defensible reason why it ought to. The second as failing to capture the
bivariate normal relationship between pretreatment responses, although the
correlation between e1 and e2 is what's taken into account in SUR.
Absent theoretical reasons for preferring one, I was wondering whether there
are practical considerations for a choice, and thus the original post.*
It would be nice if one could derive familiar multivariate test statistics
after -sureg-, much as David E. Moore's -mvtest- did after -mvreg- before
the official -manova- came along. But, if I'm not mistaken, constructing
the intermediate matrices requires that the roster of regressors be the
same between equations, which rules out SUR here.
Joseph Coveney
* In the contemplated study, the response variables are representing an
underlying construct; it's not a case of dodging control of Type I error
rate with MANOVA of multiple outcomes. I'm aware that given these
circumstances some would advocate a structural equation model (SEM) over
MANCOVA on a variety of grounds, including statistical power--see, e.g.,
Gregory R. Hancock, Fortune cookies, measurement error, and experimental
design. _Journal of Modern Applied Statistical Methods_ 2:293-305 (2003) at
http://tbf.coe.wayne.edu/jmasm/vol2_no2.pdf . Beyond practical
difficulties, SEM might be a hard sell in this particular environment.
*
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