I'd like to thank Eric, Mark and his colleague Yu-Kang for their advice and suggestions to my problem posted to the list:
I am running a repeated measures ANOVA model with 4 longitudinal measurements for each of the 2 groups. The baseline measurements were found to be quite different. So I include the first measurement as a covariate in order to make adjustment for that while the other 3 measurements as dependent variables.
However, using SPSS I can no longer construct a contrast involving the baseline values because it is now a covariate. How can I get around this problem?
Their responses are as follows.
No need to adjust for the baseline for longitudinal data; just construct contrasts are enough (T0 vs T1, T0 vs T2, TO vs T3 comparing the rate of change from baseline at diff time pts), or assess whether there are any significant difference in trend between the two groups.
Eric
I'm not so sure your approach is sound. I know several people do this from time to time, and I am about to investigate the effects of this directly through simulation. In a related area, take a look at
this article to see why I'm concerned that you might have "indirect" mathematical coupling.
A colleague and I are also concerned that ANCOVA would not work either, as the assumptions are, a priori, that there are no "underlying" differences at baseline. I know the point might be to "control" for baseline differences, but this does not actually mean there may be substantive baseline differences - a common misconception I think. What you would get, if you use ANCOVA is what has been previously described as Lord's paradox - namely your main covariate could (under the null hypothesis) appear significant as a consequence of the baseline differences. I'd be very careful with these data - why do the baselines differ?
For those who are interested in "mathematical coupling" may go to this reference:
Tu, Y.K., Gilthorpe, M.S., and Griffiths, G.S. (2002). Is reduction of pocket probing depth correlated with the baseline value or is it "mathematical coupling"? J Dent Res, 81(10), 722-6.
Peggo Lam
Department of Rehabilitation Sciences
Hong Kong Polytechnic University
Hong Kong
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