[R] LME with 2 factors with 3 levels each

[Laura Halderman]

Hello.  I am new to R and new to linear mixed effects modeling.  I am trying to model some data which has two factors.  Each factor has three levels rather than continuous data.  Specifically, we measured speech at Test 1, Test 2 and Test 3.  We also had three groups of subjects: RepTP, RepNTP and NoRepNTP.  

I am having a really hard time interpreting this data since all the examples I have seen in the book I am using (Baayen, 2008) either have continuous variables or factors with only two levels.  What I find particularly confusing are the interaction terms in the output.  The output doesn't present the full interaction (3 X 3) as I would expect with an ANOVA.  Instead, it only presents an interaction term for one Test and one Group, presumably comparing it to the reference Test and reference Group.  Therefore, it is hard to know what to do with the interactions that aren't significant.  In the book, non-significant interactions are dropped from the model.  However, in my model, I'm only ever seeing the 2 X 2 interactions, not the full 3 X 3 interaction, so it's not clear what I should do when only two levels of group and two levels of test interact but the third group doesn't.

If anyone can assist me in interpreting the output, I would really appreciate it.  I may be trying to interpret it too much like an ANOVA where you would be looking for main effects of Test (was there improvement from Test 1 to Test 2), main effects of Group (was one of the Groups better than the other) and the interactions of the two factors (did one Group improve more than another Group from Test 1 to Test 2, for example).  I guess another question to pose here is, is it pointless to do an LME analysis with more than two levels of a factor?  Is it too much like trying to do an ANOVA?  Alternatively, it's possible that what I'm doing is acceptable, I'm just not able to interpret it correctly.

I have provided output from my model to hopefully illustrate my question.  I'm happy to provide additional information/output if someone is interested in helping me with this problem.

Thank you,
 Laura

Linear mixed model fit by REML 
Formula: PTR ~ Test * Group + (1 | student) 
   Data: ptr 
AIC		BIC		logLik 	deviance 	REMLdev
 -625.7 	-559.8  	323.9   	-706.5  	-647.7
Random effects:
 Groups	Name		Variance	Std.Dev.
 student	(Intercept) 	0.0010119 	0.03181 
 Residual              		0.0457782 	0.21396 
Number of obs: 2952, groups: studentID, 20

Fixed effects:
				Estimate	Std. Error	t value
(Intercept)            		0.547962   	0.016476   	33.26
Testtest2             		-0.007263   	0.015889  	-0.46
Testtest1             		-0.050653   	0.016305   	-3.11
GroupNoRepNTP	0.008065   	0.022675    	0.36
GroupRepNTP		-0.018314   	0.025483   	-0.72
Testtest2:GroupNoRepNTP  0.006073   0.021936  	0.28
Testtest1:GroupNoRepNTP  0.013901   0.022613   	0.61
Testtest2:GroupRepNTP	0.046684  	0.024995    	1.87
Testtest1:GroupRepNTP	0.039994  	0.025181    	1.59

Note: The reference level for Test is Test3.  The reference level for Group is RepTP.  The interaction p value (after running pvals.fnc with the MCMC) for Testtest2:GroupRepNTP is p = .062 which I'm willing to accept and interpret since speech data with English Language Learners is particularly variable.