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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Re: "Repeated-measures" form of linear regression? |

Date |
Sat, 18 Sep 2010 14:35:57 +0900 |

Pietro Mazzoni wrote: 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? ---------------------------------------------------------------------------- Sounds like a time-varying-covariate repeated-measures ANOVA. You can Google "growth curve model" to find out more. Michael Mitchell has already recommended a couple of SAS references, and I agree that they're both good. You might find their reading a little heavy-going at a few points if you're not into the arithmetic. I would also agree with Michael's implication that -xtmixed- is the way to go with your analysis, except for your mention of "several subjects". SAS's PROC MIXED still has an edge over the competition when it comes to hypothesis testing in small-sample datasets. Until -xtmixed- implements an option corresponding to PROC MIXED's DDFM=KENWARDROGER, it's probably not the best approach in Stata. I think that you can still use least-squares-based methods in Stata to test your hypothesis of interest if your dataset is balanced. One approach is the time-varying-covariate repeated-measures ANOVA approach. I posted a worked example for a simple case from B. J. Winer's _Statistical Principles in Experimental Design_ (the second example in the do-file) at www.stata.com/statalist/archive/2004-01/msg00032.html (full reference in that post). In order to test the hypothesis you mentioned, you'd work with the linear component of the orthogonal contrasts. If you're worried about autocorrelation, then you can use -manova-, again setting up and testing the linear contrast of interest from the regression coefficients. Regarding your colleague's suggestion, you can find out more by Googling "longitudinal data" AND "summary measures" (together). If I had a small-sample dataset that had a small amount of imbalance, I would pursue this approach. Joseph Coveney * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: "Repeated-measures" form of linear regression?***From:*Pietro Mazzoni <pm125@columbia.edu>

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