[R-sig-ME] Plotting means and error bars for fixed effects in a ME model

[Ché Lucero]

Hello, list.

I have a question about error bars on barplotted means of data that has
been analyzed with mixed effects models.

Mixed effects models allow us to simultaneously model variance from
multiple random-effects sources (such as Subjects and Items), a much needed
solution to a problem pointed out (most potently) in my field by Herb Clark
in 1973.

However, to my knowledge, calculating confidence interval/SEM for means has
not advanced to take this modeling approach into account. A series of
papers - Loftus and Masson 94 (Using confidence intervals in within-subject
designs)  Cousineau 05  (Confidence intervals in within-subject designs: a
simpler solution) and Morey 05 (Confidence Intervals from Normalized Data:
A correction to Cousineau)   has specified ways to calculate error bars in
which the within-Subject error has been accounted for.

That approach to calculating error bars for plotting seems to be well
matched for when the statistical procedure is a simple repeated measures
(for Subjects OR Items) ANOVA. But what about the case where I have both
within-Subjects and within-Items (and within-XYZ random factors too)? Is
there a way to construct standard errors of the mean for levels of a fixed
factor (e.g. Condition) taking more than one random-effect into account as
mixed effects models do? It would be really great to have the charts
visually suggest the same inferences that the ME statistics do, but I can't
find any literature about it.

Thanks for your time.

-Ché

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