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

[Reinhold Kliegl]

There is a bit of evidence for an interaction of COND and PCU:
>> COND1:PCU        48.309     29.850   1.618
If the t-value were larger it would indicate that slopes for the
regression of RRT on PCU differ between the two condition.

There is no statistical support for the the interaction of DIR and PCU
>> PCU:DIR1        -26.835     29.814  -0.900

Now to some of your questions relating to correlations:
(1) The Fixed Effects correlations are probably not what you are
after. For example, in a perfectly balanced design, these correlations
will be zero.

(2) I suspect what you might be after are effect correlations related
to subjects or items. Assuming cond and verb bias are within-subject
effects, you could get an estimate of the parameter for the covariance
component with the following specification.
RRT ~ COND * PCU * DIR + (1 + COND + DIR  | SUBJECT) + (1 | ITEM)

You should check whether adding these variance components to the model
improves the goodness fo fit, for example with an ANOVA..

(3) You used a sum contrast specification for the two factors (COND
and DIR). This is fine. For two-level factors there is no point in
specifying Helmert contrasts. So it is unclear what you referring to
in this context.

Finally, it is generally a bad idea to specify models with
interactions terms leaving out the factors contributing to the
interactions. If you do so, you need to have very good theoretical
reasons.

Reinhold Kliegl


On Thu, Aug 12, 2010 at 10:44 AM, Paul Metzner <paul.metzner at gmail.com> wrote:
> 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/
>
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