[R] LME with 2 factors with 3 levels each

[Ista Zahn]

Hi Laura,

If you want ANOVA output, ask for it! A general strategy that almost
always works in R is to fit 2 models, one without the term(s) you want
to test, and one with. Then use the anova() function to test them.
(models must be nested, and in the lmer() case you need to use REML =
FALSE).

So, try something like this:

m1 <- lmer(PTR ~ Test  +  Group + (1 | student), data=ptr)
m2 <- lmer(PTR ~ Test * Group + (1 | student), data=ptr)
anova(m1, m2)

Best,
Ista

On Tue, Oct 12, 2010 at 11:59 PM, Laura Halderman <lkh11 at pitt.edu> wrote:
> 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.
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>



-- 
Ista Zahn
Graduate student
University of Rochester
Department of Clinical and Social Psychology
http://yourpsyche.org