[R-sig-ME] Contrasts for interactions in lmer

[Paul Metzner]

Dear all.

I am currently analyzing eye-tracking data and am interested in a main effect of condition (COND) plus its interaction with subjects' operation span (PCU) and the direction of a verb bias (1 or 2). The contrasts are:

> contrasts(COND)
>  [,1]
> a   -1
> b    1

and

> contrasts(DIR)
>  [,1]
> 1   -1
> 2    1

PCU is a continuous predictor which I centered by subtracting the mean (the problem does, however, persist when I split the sample into extreme groups and work with a categorial predictor). With the following model, I don't get a correlation between the fixed effects:

> Linear mixed model fit by REML 
> Formula: RRT ~ COND * PCU * DIR + (1 | SUBJECT) + (1 | ITEM) 
>    Data: fm3 
>    AIC   BIC logLik deviance REMLdev
>  46733 46801 -23355    46768   46711
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  SUBJECT  (Intercept)  8918.29  94.437 
>  ITEM     (Intercept)   404.85  20.121 
>  Residual             34881.69 186.766 
> Number of obs: 3503, groups: SUBJECT, 59; ITEM, 59
> 
> Fixed effects:
>                Estimate Std. Error t value
> (Intercept)     122.900     12.963   9.481
> COND1            15.924      3.165   5.031
> PCU             139.411    120.025   1.162
> DIR1             -7.746      4.107  -1.886
> COND1:PCU        48.309     29.850   1.618
> COND1:DIR1       -3.396      3.164  -1.073
> PCU:DIR1        -26.835     29.814  -0.900
> COND1:PCU:DIR1   -8.069     29.838  -0.270
> 
> Correlation of Fixed Effects:
>             (Intr) COND1  PCU    DIR1   COND1:PCU COND1:D PCU:DI
> COND1        0.002                                              
> PCU          0.004 -0.001                                       
> DIR1         0.002 -0.004  0.004                                
> COND1:PCU   -0.001 -0.001  0.003  0.000                         
> COND1:DIR1  -0.001  0.000  0.000  0.007  0.021                  
> PCU:DIR1     0.005  0.000 -0.003  0.000 -0.009    -0.005        
> COND1:PCU:D  0.000  0.021 -0.002 -0.004 -0.009    -0.001   0.011

But, since I'm mainly interested in the interactions and not so much the main effects of PCU and DIR, I changed the model to the following:

> Linear mixed model fit by REML 
> Formula: RRT ~ COND + COND:PCU + COND:DIR + (1 | SUBJECT) + (1 | ITEM) 
>    Data: fm3 
>    AIC   BIC logLik deviance REMLdev
>  46744 46800 -23363    46769   46726
> Random effects:
>  Groups   Name        Variance Std.Dev.
>  SUBJECT  (Intercept)  8911.15  94.399 
>  ITEM     (Intercept)   406.16  20.153 
>  Residual             34869.91 186.735 
> Number of obs: 3503, groups: SUBJECT, 59; ITEM, 59
> 
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)  122.962     12.959   9.489
> COND1         15.941      3.164   5.039
> CONDa:PCU     91.049    123.553   0.737
> CONDb:PCU    187.055    123.714   1.512
> CONDa:DIR1    -4.340      5.168  -0.840
> CONDb:DIR1   -11.160      5.204  -2.144
> 
> Correlation of Fixed Effects:
>            (Intr) COND1  CONDa:PCU CONDb:PCU CONDa:DIR1
> COND1       0.002                                      
> CONDa:PCU   0.004 -0.001                               
> CONDb:PCU   0.004 -0.001  0.883                        
> CONDa:DIR1  0.002 -0.003  0.006     0.000              
> CONDb:DIR1  0.001 -0.003  0.000     0.006     0.256    

Not I do get a considerable correlation between the interactions. From the output (CONDa:…, CONDb:…), I infer that the model didn't always use helmert coding for condition but applied something else for the interactions. Is that right? When I code COND numerically as -1 and 1, the correlations turn out fine, which supports my conclusion. I would be very grateful for suggestions.

Thanks,
Paul

---
Paul Metzner

Humboldt-Universität zu Berlin
Philosophische Fakultät II
Institut für deutsche Sprache und Linguistik

Post: Unter den Linden 6 | 10099 Berlin | Deutschland
Besuch: Dorotheenstraße 24 | 10117 Berlin | Deutschland

+49-(0)30-2093-9726
paul.metzner at gmail.com
http://amor.rz.hu-berlin.de/~metznerp/