using lmer instead of 2-way repeated measure ANOVA for categorical response data

Stefano,

In my opinion, a bar chart with error bars is not a good way to summarize the inferences.
Even when all of the required conditions are met (normality, proper standard error, uncontroversial
degrees of freedom calculation, ...) this display invites misuse.  First of all, the usual practice
is to use an inappropriate individual 95% confidence level instead of simultaneous CIs with an
overall 95% level of confidence.  Even when this is corrected (which is relatively easy to do),
the display is still invariably misinterpreted by readers who "test" for differences by comparing
the endpoints of the error bars to see if they overlap, which is not a proper way to make these
inferences.  In general I recommend using the "multcomp" package to obtain CIs and/or p-values
for a set of meaningful comparisons (e.g. two main effects and an interaction contrast, or "simple
effects" for each factor holding the other fixed).  Unfortunately there are several issues when
trying to do this for a mixed effects glm, so this is not an ideal solution in your case.

My second suggestion is that you try some models with separate random effects for the factors rather
than allowing them all to be correlated.  I'm not sure what "(1 t|subject)" means, but I suggest
you try some or all of the following:

     (1|subject) + (0+phase|subject)
     (1|subject) + (0+contrast|subject)
     (1|subject) + (0+phase|subject) + (0+contrast|subject)

There are several other options that allow some subset of the random effects to be correlated.  All
of them are less complex than your "full" model, and some of them may work better for your data.

Regards,   Rob Kushler

using lmer instead of 2-way repeated measure ANOVA for categorical response data

Thread (4 messages)