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Okay this is my problem:

  • I have 12 participants.
  • Each participant spent 3 nights in my lab doing a reaction time task at four timepoints during the night(12, 1, 2 and 3 oclock), with one week between each of those nights.
  • Each night, each participants was exposed to one of three experimental conditions, such that each participant completed each condition at the end of the three weeks, but with the order of conditions fully balanced over subjects.

So in the end I have for each participant, for each condition, four mean reaction times.

I wanted to use a linear mixed model with condition and timepoint during the night, and the interaction of condition*timepoint as fixed effects(since I expect reaction time to decrease less in one of the three conditions during the night). As a random effect I wanted to include subject, but I'm not confident of how I would be doing this in SPSS and whether a mixed model is the right way to go.

Can someone give me a few hints on how to proceed? I'd really appreciate it!

Thanks in advance

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You don't need to specify a covariance structure and it is highly discouraged: If you choose the wrong structure, you might miss the targeted type-I-error. Instead, use the procedure described here. It is a generalization of ANOVA for unknown covariance matrices and even applicable if there are more repeated measures than independent subjects.

Unfortunately, it is not (yet) implemented in SPSS. But there are SAS macros. See how hld-f2.sas is used.

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  • $\begingroup$ Are you aware of an R implementation of this idea? $\endgroup$ – Henrik May 12 '15 at 13:09
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If you want to model the covariance structure simply as compound symmetric, the results from-mixed effect modeling and repeated-measures ANOVA should match if the data are balanced and not missing. If you want to model the covariance structure as something else (e.g., unstructured or autoregressive), then you need to use mixed-effects modeling.

How do you know which covariance structure to use? First, plot the data and see is the variance/correlation noticeably changes over nights. Second, compute a covariance matrix to see whether the (co)variance remains constant over nights. Third, check the journal you are thinking of submitting your article to. Does it prefer advanced or conventional techniques? If the journal publishes only articles using ANOVAs, then you may want to stick with ANOVA as well (unless you feel comfortable justifying the use of an alternative covariance structure based on mixed-effects modeling).

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