[R] Computing/Interpreting Odds Ratios for 3-way interactions from lmer

[Owen, Amanda J]

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