[R-sig-ME] main effects in a model with interactions

[Antoine Tremblay]

Dear list member,
I would like to thank you for your past help with the questions I had;
it was well appreciated.

I now have a question regarding main effects in a model with interactions.

We have a model with variables Frequency (High vs. Low), Diagnosis (N
and LI), and Time (continuous from 1 to 1600). The dependent variable
is Reaction Time (logged). Note that the design is unbalanced: there
are more LI than N data points and more High than Low data points.
Roughly put, the model is RT ~ Time*Diagnosis*Frequency + ranefs

The fixed effects portion of the summary would look something like this:

Fixed effects:
                                Estimate    Std. Error  t value
(Intercept)                 6.344e+00  4.598e-02  137.97
Time                       -1.619e-04   1.868e-05   -8.67
DiagN                      -1.103e-01   4.840e-02   -2.28
FreqLow                    3.316e-02   4.005e-02    0.83
Time:DiagN               1.956e-05   2.489e-05    0.79
Time:FreqLow           1.564e-05   1.241e-05    1.26
DiagN:FreqLow         -2.449e-03   4.745e-03   -0.52
Time:DiagN:FreqLow  2.104e-05  1.027e-05     2.05

What we would like to get estimates, standard errors and t values for
the main effects of:
  Time,
  Diagnosis (Diag) and
  Frequency (Freq) and
  a Time slope for N across frequencies,
  a Time slope for LI across frequencies,
  a Time slope for High across groups, and
  a Time slope for Low across groups.

As far as I know, these are not provided in the table (please correct
me if I'm wrong): The (Intercept) row refers to the intercept for the
reference level (here LI-High), the DiagN row refers to the difference
in intercept between N-High and LI-High, the FreqLow row is the
difference in intercept between LI-Low and LI-High, and so forth.

The question is can I do the following to compute the main effect of
Frequency for example:
(1) Get the estimated intercepts for LI-High and N-High (by releveling
and refitting the model), and average them, then get the estimated
intercepts for LI-Low and N-Low and average them?

Note that the design is unbalanced and I think this might affect the
averaging unless this was already taken care of by the LMER modeling
process (please correct me if I'm wrong).

(2) Compute the difference between the mean estimate for High and the
mean estimate for Low and divided it by the pooled (or averaged?)
standard error of the intercepts for LI-High, N-High, LI-Low, and
N-Low.

Would this be an acceptable way to approach the problem?

Your help is always greatly appreciated,
Sincerely,
--
Antoine Tremblay
Department of Neuroscience
Georgetown University
Washington DC