[R-sig-ME] Interpreting lmer() interactions with Helmert contrasts

[Becky Gilbert]

Dear list,

I'm wondering if someone could help me interpret an interaction between two
factors, when one of the factors uses Helmert contrasts?

I ran a linear mixed effects model (lmer) with reaction times as the DV, 2
fixed factors: Time (2 levels) and Word Type (3 levels), and 2 random
factors: Subjects and Items.  I used Helmert contrasts for the Word Type
factor:
- Contrast 1 = level 1 (Untrained) vs levels 2 & 3 (Trained-related and
Trained-unrelated)
- Contrast 2 = level 2 vs. level 3 (Trained-related vs Trained-unrelated)
The data, contrasts, model, summary and model comparisons are listed at the
end of the message.

Model comparisons with anova() showed a significant interaction between
Time and Word Type.  However, I don't know how to get the statistics for
the interactions between Time and each Word Type contrast.

Based on the t-values for coefficients in the model summary, it looks like
the significant Word Type x Time interaction is driven by the interaction
with the 1st contrast for Word Type (t = 2.61).  However I don't think that
the statistics for the fixed effects coefficients are exactly what I'm
looking forward (they are sequential tests, right?).  And if these are the
appropriate statistics, I'm aware of the problems with trying to get
p-values from these  estimates.  So is there a way to do likelihood ratio
tests for each Word Type contrast, or some other way of interpreting the
Word Type x Time interaction?

Data structure:
> str(rtData)
'data.frame': 1244 obs. of  11 variables:
 $ Subject      : Factor w/ 16 levels "AB","AS","AW",..: 1 1 1 1 1 1 1 1 1
1 ...
 $ Item       : Factor w/ 48 levels "ANT","BANDAGE",..: 3 4 6 12 13 14 22
29 30 34 ...
 $ Response     : int  960 1255 651 1043 671 643 743 695 965 589 ...
 $ Time     : Factor w/ 2 levels "-1","1": 1 1 1 1 1 1 1 1 1 1 ...
 $ WordType     : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
 $ logRT        : num  2.98 3.1 2.81 3.02 2.83 ...

> contrasts(rtData$Time)
   [,1]
-1  0.5
1  -0.5

> contrasts(rtData$WordType)
        [,1] [,2]
0  0.6666667  0.0
1 -0.3333333 -0.5
2 -0.3333333  0.5

Model:
lmer(logRT ~ 1 + WordType + Time + WordType:Time +
                      (1 + Time|Subject) +
                      (1|Item),
                    data = rtData)

REML criterion at convergence: -2061.2
Scaled residuals:
    Min      1Q  Median      3Q     Max
-2.7228 -0.6588 -0.0872  0.5712  3.7790
Random effects:
 Groups   Name        Variance Std.Dev. Corr
 Item   (Intercept)     0.000933  0.03054
 Subject  (Intercept)  0.004590  0.06775
          Time1            0.005591  0.07478  0.05
 Residual                 0.009575  0.09785
Number of obs: 1244, groups:  Target, 46; Subject, 16
Fixed effects:
                            Estimate     Std. Error   t value
(Intercept)              2.8765116  0.0177527  162.03
WordType1            0.0111628  0.0110852    1.01
WordType2            0.0007306  0.0071519    0.10
Time1                  -0.0268310  0.0195248   -1.37
WordType1:Time1  0.0301627  0.0115349    2.61
WordType2:Time1 -0.0089123  0.0141624   -0.63

Model comparisons with anova() for main effects and interaction:

-full model vs no Word Type x Time interaction
                               Df     AIC     BIC logLik deviance  Chisq
Chi Df Pr(>Chisq)
rtModelNoInteraction  9 -2077.5 -2031.3 1047.7  -2095.5

rtModelFull               11 -2080.5 -2024.1 1051.2  -2102.5 7.0388      2
   0.02962 *

-full model vs model without Time and interaction
                       Df     AIC     BIC logLik deviance  Chisq Chi Df
Pr(>Chisq)
rtModelNoTime  8 -2077.8 -2036.7 1046.9  -2093.8
rtModelFull      11 -2080.5 -2024.1 1051.2  -2102.5 8.7424      3
 0.03292 *

-full model vs model without Word Type and interaction
                      Df     AIC     BIC logLik deviance  Chisq Chi Df
Pr(>Chisq)
rtModelNoWT  7 -2080.4 -2044.5 1047.2  -2094.4
rtModelFull     11 -2080.5 -2024.1 1051.2  -2102.5 8.0875      4    0.08842
.

Thanks in advance for any advice!
Becky
____________________________________________

Dr Becky Gilbert

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