A reviewer asked my team to calculate residual (change) scores rather than the difference score (task-baseline)? Notworthy: we have a repeated measures design with participants responding to three stimuli. Before each stimulus we have a baseline, and then we have the response to the stimulus. So we have baseline 1 and response 1, baseline 2 and response 2, baseline 3 and response 3. Thus, we would like to use this scores in repeated measures analysis and test their difference using within-subject tests.
Could anyone explain to me how to compute residual change scores? Preferably with SPSS. Thank you!
Hello Lukasz,
Run a simple linear regression, using baseline score as the independent variable and final ("task"?) score as the dependent variable. (Analyze / Regression / Linear). Before running the analysis, click on the "Save..." button, then check the box under "Residuals" for unstandardized.
This will post the residuals (difference between Observed final score and that predicted from the relationship of baseline-final score) to the data worksheet, in the same unit/metric as the scores themselves. Do note that these scores represent the unpredictable portion of the final scores--that which is not linearly related to the baseline scores.
Good luck with your work!
Thank you, David! I updated my question a bit. We use repeated-measures design with three times (T1, T2, T3). Do you think that I should regress all posttests on all pretests for each Time separately or toghether? The problem is that If I calculate residual scores for each T separately, I have a means of 0 for each of them, and it makes within-person analyses pointless. Thank you!
Lukasz,
OK, the question is a moving target! So you have a baseline measure, then either two (e.g., T1 is baseline) or three (baseline preceded T1) follow-up measures (with T3 being the final one). I understand your dilemma (and wonder if your reviewer anticipated that!).
Since it's likely that baseline-T1 (or, if T1 is baseline, T1-T2) correlation is the strongest, you could use that relationship (same equation) to convert the remaining occasion scores to values residualized for the baseline status. Only the first follow-up occasion would have a mean of zero for the residuals; others would not be forced to any specific mean value. That would be adjustment for the relationship present between baseline and the first follow-up.
Hope that helps, and good luck with your project.
Haha, thank you David! It is a moving target, indeed. I am sorry for ma imprecission. Yet, I appreciate each of your resposes as they show solutions to different problems with the residual change score. In fact, we had baseline preceding each stimulus (affective movie clip) - I updated my question again. If we regress for each stimulus (response on baseline) we will have zeros for means. I would not like to discard baseline T2 and T3, because they convey some meaningful information about the most proximal baseline. I tried to convert all the repeated measures data into two variables: Baseline and response - discarding the stimulus number information, and regressing the total response on the total baseline. This in fact generates three times more N than in the original data and ignores the fact that every three Ns are from one person (they are not independent). It troubles me, whether it doe not violate some assumptions. Do you think that there might be some other strategy?
Lukasz,
So, given the third version of your question (lol), I'd suggest using final scores from T1, T2, T3 as your repeated measures (within subjects) factor. Declare the three baseline scores as covariates in the design. That will still permit you to test for change across final scores, having removed the linear association with baselines (though not in a way that forces final values to zero).
Here's spss syntax that would do the job ("F" implies final score; "B" implies baseline measure):
GLM F1 F2 F3 WITH B1 B2 B3
/WSFACTOR=score 3 Polynomial
/METHOD=SSTYPE(3)
/EMMEANS=TABLES(score) WITH(B1=MEAN B2=MEAN B3=MEAN)COMPARE ADJ(SIDAK)
/PRINT=DESCRIPTIVE ETASQ
/CRITERIA=ALPHA(.05)
/WSDESIGN=score
/DESIGN=B1 B2 B3.
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