[R-sig-ME] 3-level fixed factor in lme4

[Obermeier Andrew]

Hello Mixed Modelers,

I came to this list with a question a couple months ago, and will admit it was a very humbling experience. There were a few kind responses, but my question was mostly ignored or I was told I needed to read basic statistics books. I take full blame for this, and know that I was not asking my question in the right way. Now, 2 months later, I am trying again.

I am not a statistician but want to learn. Especially, I like learning statistics with R because it helps me to see the nuts and bolts of statistics much more than the big commercial user interface packages do, and I get a much better feel for how to look at data.

I am writing a dissertation in second language acquisition, analyzing my data using lme4 for a mixed model with subjects and items set as random effects. My dependent variable is reaction time (RT). My independent variable is Target Condition (TarCond). TarCond is a three-level factor: nonword, related, unrelated.

When I run the model, lmer provides the summary below. The Fixed effects section tells me that for the three factors of my independent variable I get the following mean reaction times (RT), and all of these have big t values:
nonword (Intercept): 1239.64
TarCondrelated: 1239.64 - 370.72 = 868.92
TarCondunrelated: 1239.64 + 318.34 = 1557.98

(lmer summary)
-----------------------------------------------------------------
Linear mixed model fit by REML 
Formula: RT ~ TarCond + (1 | Subject) + (1 | Item) 
   Data: postest 
   AIC   BIC logLik deviance REMLdev
 30949 30982 -15468    30966   30937
Random effects:
 Groups   Name        Variance Std.Dev.
 Item     (Intercept)  22371   149.57  
 Subject  (Intercept)  65149   255.24  
 Residual             560665   748.78  
Number of obs: 1920, groups: Item, 96; Subject, 20

Fixed effects:
                 Estimate Std. Error t value
(Intercept)       1239.64      65.61  18.894
TarCondrelated    -370.72      56.13  -6.605
TarCondunrelated   318.34      56.13   5.672

Correlation of Fixed Effects:
            (Intr) TrCndr
TarCondrltd -0.285       
TarCndnrltd -0.285  0.333
----------------------------------------------------------------------


Since the t values in the above model were all well above 2 or below -2, I read that this might mean I have a significant effect. 

I followed the analysis in Baayen, Davidson, and Bates' (2007) article titled "Mixed-effects modeling with crossed random effects for subjects and items." Though this article informs me that p-values calculated with the degrees of freedom used by pvals.fnc will be "anti-conservative", I proceeded to analyze the fixed effects in this model with Markov chain Monte Carlo sampling.
 
-------------------------------------------------------------------------------------------------
> mcmcpostest <- pvals.fnc(postest.lmer, nsim = 10000)
> mcmcpostest$fixed
                 Estimate MCMCmean HPD95lower HPD95upper  pMCMC Pr(>|t|)
(Intercept)        1239.6   1239.5     1108.9     1365.0 0.0001        0
TarCondrelated     -370.7   -371.2     -474.6     -263.8 0.0001        0
TarCondunrelated    318.3    317.8      214.3      428.8 0.0001        0
-------------------------------------------------------------------------------------------------

My apologies for this long preamble, but my questions are as follows. 
(1) Is this analytical procedure appropriate? 
(2) Specifically, is it OK for me to test the significance of a 3-level factor in this way? (My advising professor tells me that the t value can only be used to compare 2 means.)
(3) How does lme4 calculate t values for a factor that is greater than 2 levels.

Below I have attached my dataset in CSV format. If there is any other information I need to provide, please let me know and I will very gladly do so. 

My apologies if my questions are misguided or inappropriate. I am way out of my league here.

I would be very grateful for any attention that anyone can offer to my questions.

Sincerely,

Andrew Obermeier
Associate Professor, Kyoto University of Education
PhD Candidate, Temple University Japan

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