R help - Jan 2009 - Computing/Interpreting Odds Ratios for 3-way interactions from lmer

Hello, 
  I am a relative novice at both using regression analysis and at using R in
general  (and at object oriented programing). A colleague convinced me that
binary logistic regression is the most appropriate analysis for the data that I
have though, so I've been trying to muddle through.

I'm currently stumped on how to interpret/compute odds ratios for two and
three way interactions when a variable has more than 2 factors.
The study design is an examination of the use of past tense by 3 subject
populations in 3 different sentence types and 2 locations within each sentence.
I have been treating subject and main/subordinate verbs as random factors and
group (age, sli, mlu) and condition (and, that, when) and clause order
(first/second) as fixed factors.  In each case it is worth noting that the first
factor is the reference group. I would like to be able to clearly interpret the
interactions because specific hypotheses hinge on the results.

Two other points that may be relevant: 1) The original design was balanced, but
the current results are  unbalanced because of data loss (e.g. children failing
to respond) and this is not randomly distributed across groups.  2) There is
some colinearity between the conditions (corr between subord/when = .44)  and
between the groups (corr between SLI/MLU =.48).  This is somewhat logical given
the targets, but is not easily reduced.

The syntax I'm using for the analysis is: 
clauseOPCyesI <- lmer(OPCorrect == "past" ~ group*Cond*
Clause.Order + (1|SUBJ) + (1|sub.V) + (1|main.V), subset(a),
family="binomial")

And the results I obtain are: 

Generalized linear mixed model fit by the Laplace approximation 
Formula: OPCorrect == "past" ~ group * Cond * Clause.Order + (1 |
SUBJ) +    (1 | sub.V) + (1 | main.V)
   Data: subset(a) 
  AIC  BIC logLik deviance
 5673 5817  -2816     5631
Random effects:
 Groups Name        Variance Std.Dev.
 main.V (Intercept) 0.056843 0.23842 
 SUBJ   (Intercept) 1.248441 1.11734 
 sub.V  (Intercept) 0.085521 0.29244 
Number of obs: 6827, groups: main.V, 47; SUBJ, 38; sub.V, 36

Fixed effects:
                                     Estimate Std. Error z value Pr(>|z|)    
(Intercept)                           2.19570    0.35057   6.263 3.77e-10 ***
groupm                                0.67645    0.52638   1.285   0.1988    
groups                               -0.59218    0.47534  -1.246   0.2128    
Condsubord                            0.27588    0.23297   1.184   0.2363    
Condwhen                             -0.17839    0.20278  -0.880   0.3790    
Clause.Ordersecond                   -0.10066    0.19965  -0.504   0.6141    
groupm:Condsubord                     0.38856    0.52295   0.743   0.4575    
groups:Condsubord                    -0.07662    0.29406  -0.261   0.7944    
groupm:Condwhen                      -1.82957    0.31892  -5.737 9.65e-09 ***
groups:Condwhen                      -1.42286    0.26601  -5.349 8.85e-08 ***
groupm:Clause.Ordersecond            -0.29247    0.33645  -0.869   0.3847    
groups:Clause.Ordersecond            -0.53254    0.26494  -2.010   0.0444 *  
Condsubord:Clause.Ordersecond        -0.60703    0.28965  -2.096   0.0361 *  
Condwhen:Clause.Ordersecond           1.64044    0.34265   4.788 1.69e-06 ***
groupm:Condsubord:Clause.Ordersecond -2.95511    0.60007  -4.925 8.45e-07 ***
groups:Condsubord:Clause.Ordersecond -0.04796    0.38893  -0.123   0.9019    
groupm:Condwhen:Clause.Ordersecond   -0.36423    0.48229  -0.755   0.4501    
groups:Condwhen:Clause.Ordersecond    0.05882    0.41775   0.141   0.8880    


While I know to talk about odds ratios I need to raise e to the estimate of the
coefficient for main effects, I am less clear about interactions terms.
So for instance, if I would like to say that the SLI group was X% less likely to
produce a correct past tense for in the second clause than in the first clause
do I add the estimates (groups+Clause.Ordersecond+groups:ClauseOrdersecond =
-1.22538) and then compute the OR 0.293646094?  "The odds of the SLI group
producing a past tense form in the second clause was approximately 29% as
compared to their productions in the first clause"   Or since the reference
group is their age matched peers would I need to say "The odds of the SLI
group producing a past tense form in the second clause was approximately 29% as
compared to the age-matched groups productions in the first clause of the target
sentences".  (Note that the second sentence is much less useful to me than
the first).

Similarly if I would like to talk about the fact that Condwhen is relatively
poorer for the MLU/SLI groups than the age matched-coordinate but I get muddled
by the fact that there is  improvement in the Cond when, second clause  (as
compared to condwhen-first clause-age-matched, right?).  Again, my trouble is
with what to use as the reference group and how to separate that out in terms of
computing percentages.

Thanks so much for any assistance you can lend. 

Amanda 

Amanda J. Owen PhD CCC-SLP
Assistant Professor
Dept of Communication Sciences and Disorders
University of Iowa
319-335-6951 (office)
amanda-owen at uiowa.edu