Dear Andrew,

   In looking again at your message of 25/9/98,  titled Re: (Changes in 
binding & mood score) (appended below) 
you give detailed instructions on mean-centering covariates for entry into 
a pre- vs. post- treatment  comparison. 
   To briefly summarize, the steps are:
   a) compute the change score (treatment - baseline),
   b) subtract the mean of the change score from each individual value,
   c) divide the result in half, 
   d) multiply the half score by -1 and enter for the baseline covariate, 
   e) multiply the half score by +1 and enter for the treatment covariate. 

My question regards steps d) and e) :  

Why is the baseline score flagged as negative, and the treatment score as 
positive?   This appears to presuppose that the covariate in question will 
increase after treatment, compared to baseline.  

But supposing it actually is the other way round, i.e. the covariate decreases 
after treatment?  Then shouldn't the positive half score be entered for the 
baseline, and the negative one be used for the treatment covariate?

(Sorry if this question seems obvious, but this point has caused a lot of 
confusion! ) 


Thanks in advance for your clarification,

Ruth Reinsel
Memorial Sloan-Kettering Cancer Center
New York, NY, USA
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______________________________ Reply Separator _________________________________
Subject: Re: (Changes in binding & mood score)
Author:  andrew (<a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind99%26L%3DSPM%26E%3D7bit%26P%3D928835%26B%3D--%26T%3Dtext%252Fplain%3B%2520charset%3DUS-ASCII%3B%2520name%3D%2522Re%3A%2522%26N%3DRe%3A" target="_parent" >[log in to unmask]</a>) at Internet-SHAR
Date:    9/25/98 12:21 PM

     [snip] 

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

Firstly, you have to prepare your covariate: Say your scores for the 
first subject are 1b, 1t for pre & post treatment respectively, 2b & 2r 
for the second subject, 3b & 3r for the third... Then compute the 
change in score for each subject, giving covariate:
        1t-1r, 2t-2r, 3t-3r,...
Now mean correct this covariate (i.e. work out it's mean and subtract 
it from each element), say the mean is m, then you've got
        1t-1r-m, 2t-2r-m, 3t-3r-m,...
Now divide it by two:
        (1t-1r-m)/2, (2t-2r-m)/2, (3t-3r-m)/2,...
...and your covariate (assumming you enter your pre-treatment scans 
first for each subject) is
        -(1t-1r-m)/2, +(1t-1r-m)/2, -(2t-2r-m)/2, +(2t-2r-m)/2, -(3t-3r-m)/2,...

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

The rest of the design is as you suggested above. [0 0 +1] & [0 0 -1] 
look for positive and negative relationships between mood score change 
and binding change.

Since you only have one scan per condition per subject, and only two 
conditions, the inference from this analysis extends to the population 
from which the subjects were drawn.

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

You can sort of see how this works by considering the model: For the 
pre-treatment scans it's:
    pre-binding = pre-treatment mean - (mood change)*slope/2 + subject effect
                                + error
...and for the post-treatment scans it's
    post-binding = post-treatment mean + (mood change)*slope/2 + subject effect
                                + error

...and subtracting the pre from the post model gives:
        binding change = mean binding change + (mood change)*slope + error

...the regression of binding difference on mood score difference! (ta-daa)

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

Hope this helps,

-andrew

+- Dr Andrew Holmes <a href="/cgi-bin/wa-jisc.exe?LOGON=A3%3Dind99%26L%3DSPM%26E%3D7bit%26P%3D928835%26B%3D--%26T%3Dtext%252Fplain%3B%2520charset%3DUS-ASCII%3B%2520name%3D%2522Re%3A%2522%26N%3DRe%3A" target="_parent" >[log in to unmask]</a> 
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