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

Fri Aug 13 10:20:41 CEST 2010

Thank you for the quick answer!

> (1) The Fixed Effects correlations are probably not what you are
> after. For example, in a perfectly balanced design, these correlations
> will be zero.

They are not, but like you suggested, I wanted them to be at least close to zero. When I changed the model like mentioned before, I noticed an increase in fixed effects correlations and a curious change in contrast coding (see below), that I couldn't explain.
My main interest are the fixed effects interactions. My hypothesis is that subjects with a higher PCU will be affected more strongly by the condition manipulation. Also, in some studies only one kind of verbs (DIR) has been shown to evoke the effect, hence the desired interaction of COND and DIR. But, because I really don't want individual differences over and above what is explained by PCU, I implemented the random effect term like you suggested and re-included the factors contributing to the interactions. My model now looks like this:

lmer(log(RRT)~COND + PCU + COND:PCU + DIR + COND:DIR + (1+COND+DIR|SUBJECT) + (1|ITEM), data=fm3)

Although including the covariance component did not improve model fit, I decided to leave it in the model for the reasons mentioned above. I did, however, exclude the three-way interaction COND:DIR:PCU.

> (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.

Being a novice to contrast coding, I thought it was the same. Coincidentally, that seems to be the case for two-level factors. Thanks again for the suggestions!

Paul

On 12 Aug 2010, at 11:24, Reinhold Kliegl wrote:

> 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/
>> 
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>> 

---
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/