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st: "Repeated-measures" form of linear regression?


From   Pietro Mazzoni <pm125@columbia.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: "Repeated-measures" form of linear regression?
Date   Fri, 17 Sep 2010 16:40:50 -0400

Dear Statalist,

My question is not specific to Stata, but I am hoping that someone can at least point me to the topic of statistical testing on which I can do more reading to answer this question. I appreciate any suggestions.

My hypothesis, in a motor control experiment, is that there is a linear relationship between a perturbation (say, force F) and a response (say, lateral deviation D). I obtained data from several subjects who were tested at various levels of force and whose response was a particular deviation for each force pulse. I feel that it would be incorrect to perform a linear regression of D vs. F on the pooled data, because this would ignore within-subject correlations. I see this data as analogous to repeated-measures ANOVA, because multiple pairs of (F, D) were collected within each subject.  So my intuition tells me I should perform linear regression within each subject, and then somehow combine these results across the group, but I don't know what procedure might be the analog of rm-ANOVA for regression. One suggestion I got was to perform individual regressions within each subject and then average the values of the slopes and intercepts obtained to estimate slope and intercept f!
 or the group. But I am more interested in establishing whether there is a significant relationship at the group level (R square, p value for the group) than in determining the parameters of the regression, and I don't know how to combine the R squares or p values obtained for individual subjects.

Where can I read about repeated-measures approaches for continuous variables/regression?

Thanks in advance for any ideas.

Pietro
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