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Re: st: RE: baseline adjustment in mixed models


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: baseline adjustment in mixed models
Date   Mon, 16 Nov 2009 13:54:33 -0500

Clyde et al.--
I haven't read other emails in this thread, but if -group- is an
indicator for a randomly assigned treatment, there is still good
reason for including baseline covariates, which can substantially
increase efficiency in some cases, and will not leave you worse off in
nearly any case.  In these models, you should also have a good
argument as to why the unobserved heterogeneity term is normally
distributed, or the random slopes are normally distributed, if that is
how you specify it. For example, baseline test scores may be normally
distributed by design, but individual-specific growth rates over time
need not be.  Ability is not normally distributed by many common
measures, to be sure.

On Mon, Nov 16, 2009 at 12:48 PM, Clyde Schechter
<clyde.schechter@einstein.yu.edu> wrote:
> Yes, in general.  One could concoct a data generating process in which the
> baseline value y0 exerted some outsize influence over all subsequent
> values (e.g., repeated measures in which the subject was fed back his/her
> response at the baseline measurement shortly prior to each subsequent one
> and asked to try to achieve consistency with that) that would necessitate
> inclusion of y0 as a covariate as well.  But I can't think of any examples
> that aren't really artificial. So, unless there is something about what
> you are studying that specifically suggests y0 is needed as a covariate,
> the standard growth model represented just by
>
> xtmixed y group time groupXtime || id:
>
> (or the corresponding random-slopes version) should do the trick. For most
> situations it adequately accounts for any baseline group difference.
>
> Again, as coded this model assumes that the y-time relationship is linear.
>  If that is not the case, time needs to be transformed or recoded as
> dummies or splines, etc., accordingly.  And again, since the coefficient
> of group represents the mean group difference conditional on the other
> model variables all being zero, life is simplest for this purpose if time
> is coded so that it (or, more generally, all variables representing it) is
> zero at baseline.
>
> I've never really thought about using random slopes as a way of optimally
> regressing extreme values to the mean.  It seems to me that the
> distinction between a random intercept and random slopes model depends on
> what the science says about the evolution of y over time.  If it is
> credible that a single growth rate (coefficient of time) applies within
> each group and that individual deviations from that reflect either
> baseline differences being carried forward or simple random errors (e.g.
> measurement error), then the random intercept model is a complete
> specification.  If, however, it is more reasonable to suppose that, within
> each group, subjects may differ not just in their baseline values but also
> in the rate at which y varies over time, then a random slopes model is a
> better specification.  If the science is not clear, one could test this
> empirically by seeing whether the random slopes model turns up appreciable
> variance for the slope(s) or not.
>
> I don't think I understand your question regarding a model of choice with
> respect to regression to the mean, so I won't say any more about it here.
>
> Clyde Schechter
>
>
>
>> Date: Sun, 15 Nov 2009 10:42:58 -0500
>> From: "Visintainer PhD, Paul" <Paul.Visintainer@baystatehealth.org>
>> Subject: st: RE: baseline adjustment in mixed models
>>
>> Clyde, thanks for the very clear explanation.  You're getting to the root
>> of my question. So, if I understand you correctly, the following model is
>> unnecessary:
>>
>> xtmixed y y0 group time groupXtime || id:
>>
>> or the random slope equivalent, because the group variable accounts for
>> differences at Y0.  Two related questions:
>>
>> 1) You mentioned that coding baseline as Y0 makes life simpler.  Suppose
>> time is coded as baseline plus time1 through time4.  Is there any utility
>> to the model:
>>
>> xtmixed y baseline group time groupXtime || id: , where the time variable
>> does not include baseline Y0.
>>
>> 2)  Controlling for baseline attempts to account for group differences at
>> the start of the trial, and also for control for those observations with
>> extreme values (i.e., regression to the mean).  Am I correct in assuming
>> that the random coefficient model is the model of choice for correcting
>> regression to the mean? My logic (or illogic) here is that the more
>> extreme the baseline values, the greater the effect of regression to the
>> mean (i.e., an individual's slope is a composite of the group assignment
>> plus the effect of regression to the mean depending on his initial value).
>>
>> Thanks, this has been really helpful.
>>
>> - -Paul

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