Hello,

For some of my models, my summary output is missing various beta values for
my three-way interactions.

I am using lme (though the same happens with lmer) to do growth curve
analysis (a type of mixed effects model, just with orthogonalized
non-linear time predictors in addition to condition effects). I am modeling
the effect of two categorical variables A and B, each of which have two
factors 0 and 1. The general question is whether manipulations A and B
(different manipulations of task difficulty) alter the fit of a curve that
traces the participants' pupil size response functions (continuous DV)
across time.

I have found that the best fitting model for my data includes a three-way
interaction of condition A, B, and the third order polynomial (time3) and a
three-way interaction of conditions A, B and the fourth order polynomial
(time4), as well as main effects of each of these variables and some
two-way interactions.

Here is part of the output table I get using summary():

                             value    stderr    df    t-val    p-val
......
time1:A1        353.1338  85.49229 9294   4.13059  0.0000
time2:A1       -68.5389  16.57307 9294  -4.13556  0.0000
time3:A1       -154.4407  23.43786 9294  -6.58937  0.0000
time5:A1        123.8607  16.57307 9294   7.47361  0.0000
time3:B1        100.1996  23.43786 9294   4.27512  0.0000
time4:B1        201.6411  23.43786 9294   8.60322  0.0000
time3:A1:B1   -68.6999  33.14614 9294  -2.07264  0.0382
time4:A1:B0   132.5765  23.43786 9294   5.65651  0.0000
time4:A1:B1  -124.2845  23.43786 9294  -5.30272  0.0000

I don't understand why the output only includes a breakdown of the
conditions into two components for time4 but not for time3. If I analyze a
smaller subset of the data (only trials on which participants respond
correctly, about half the data), I get this output:

time1:A1        346.3393  116.5548 9295   2.97147  0.0030
time2:A1       -60.7709   23.1383 9295  -2.62642  0.0086
time3:A1      -195.9600   32.7224 9295  -5.98855  0.0000
time5:A1       125.5764   23.1383 9295   5.42722  0.0000
time3:B        -77.7772   32.7224 9295  -2.37688  0.017
time4:B        160.3758   28.3385 9295   5.65930  0.0000
time3:A1:B     135.0679   46.2765 9295   2.91871  0.003
time4:A1:B    -108.9340   32.7224 9295  -3.32903  0.0009

The output no longer breaks down either interaction, NOR does it even put a
number (0 or 1) next to the interaction term. I am unclear on how to
interpret or report the three way interaction-- should it be broken down or
should there only be one beta value associated with it?

All the F tests [anova()] of the individual predictors are significant and
do not break down the interactions in this way,  HOWEVER, there is a
different number of degrees of freedom that occur with the F value for the
model that breaks down the interaction (2 for the numerator) versus the
model that does not (1 for the numerator) which I assumes it's estimating
these values differently.

Any input or references for this output would be greatly appreciated.
Thanks so much in advance!
-Stefanie

---------------------------------------------

Stefanie E. Kuchinsky, Ph.D.

Postdoctoral Scholar

Hearing Research Program

Medical University of South Carolina

Charleston, SC

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