[R-lang] Contrast coded mixed models: Interactions

[T. Florian Jaeger]

Hi Peter-ling,

can you say a bit more about your data? How many data points each are there
within A-D, A-E, A-F, B-D, B-E, and B-F? If I had to guess I would say you
have either more or less data in D than in E or F (depending on how you
contrast coded)? Is that the way your data is unbalanced? A vs B seems
balanced and I would even guess that the distribution of D vs. E vs. F  is
the same in A and B, but the distribution of D vs. E vs. F overall is
unbalanced?

Anyway, for certain distributions of data, you will find that contrast
coding won't just solve the problem. If you play around with the following
simulation, this becomes quite apparent:

====================================================
# number of subjects
n_s = 20
# number of items within subjects
n_per_s = 16

# let's create an unbalanced data set of the type that I suspect you have
# (see above)
AvB <- as.factor(rep(c(rep("a", 8), rep("b", 8)), n_s))
DvEvF <- as.factor(rep(c("d","d","d", "d", "e", "e", "f", "f"), n_s * 2))
# subjects
s  <- sort(rep(seq(1:20), n_per_s))
# subject effects
rs <- rnorm(n_s,0,0.5)

# clumsy way to encode fixed effects
effect <- function(x) {
    ifelse(x == "a", 2,
     ifelse(x == "b", 1.2,
      ifelse(x == "d", 0.5,
       ifelse(x == "e", -1.5,
        ifelse(x == "f", -0.3, NA)
        )
      )
     )
    )
}
# outcome is specified by effects of AvB and DvEvF (no interaction, but
# feel free to add one) plus noise plus subject effects (also noise).
y <- effect(AvB) + effect(DvEvF) + rnorm(n,0,0.2) + rs[s]

library(lme4)

# treatment coding
contrasts(DvEvF) <- contr.treatment(3)
lmer(y ~ AvB + DvEvF + (1 | s))

# contrast (sum) coding
contrasts(DvEvF) <- contr.sum(3)
lmer(y ~ AvB + DvEvF + (1 | s))

# or with interactions:
contrasts(AvB) <- contr.sum(2)
contrasts(DvEvF) <- contr.sum(3)
lmer(y ~ AvB * DvEvF + (1 | s))

# contrast coding as used by you
# to see that the above contrast coding does the same as
# what you do
DvEvF <- factor(DvEvF, levels=c("e", "d", "f"))
contrasts(DvEvF) <- contr.sum(3)
lmer(y ~ AvB + DvEvF + (1 | s))
====================================================

this gives you something very similar to your pattern of fixed effect
correlations. But play around with other parameters to get a feel.

what can you do now? First, many people would consider a fixed correlation
of < .5 to be reason for caution but not to disregard the results. In the
corpus work I do, I usually try to keep fixed effect correlations much
smaller, but I think folks find .5 acceptable, but maybe people can chime in
and let you know whether I am off on that.

any method that further reduced collinearity will require some decisions
(e.g. what to residualize against what; PCA; or some alternative coding).
For example, helmert coding works quite well for the pseudo data set
mentioned above, if you hypothesis was that e < f < d (and you resort the
factor levels accordingly). Fixed effect correlations would all be <0.26.

HTH,
Florian

On Thu, Oct 1, 2009 at 11:11 AM, Peter Graff <graff at mit.edu> wrote:

>  Dear R-Langs,
>
> I'm currently trying to analyze some experimental data with a contrast
> coded mixed model. I have a 2 (levels:A,B) x 3 (levels:D,E,F) design with
> unbalanced cell sizes. I am coding the following variables:
>
> AvB, DvE, EvF
>
> where sum(AvB)=0, sum(DvE)=0, sum(EvF)=0. Next I fit this model:
>
> lmer(DV~AvB*(DvE+EvF)+(1|Subj)+(1|Item))
>
> And here is the correlation matrix it outputs:
>
> Correlation of Fixed Effects:
>                   (Intr)   AvB    DvE     EvF  AvB:DvE
> AvB         -0.029
> DvE          0.010 -0.006
> EvF         -0.002 -0.001  *0.488  *
> AvB:DvE -0.003  0.015 -0.039 -0.018
> AvB:EvF -0.001 -0.002 -0.018 -0.044  *0.488 *
>
> The question I have is, how to get rid of the collinearity in red and blue
> and whether it's even possible. And if it's not possible, in what way will
> this affect the reliability of my result?
>
> Thanks so much in advance,
>
> Peter
>
> _______________________________________________
> R-lang mailing list
> R-lang at ling.ucsd.edu
> http://pidgin.ucsd.edu/mailman/listinfo/r-lang
>
>
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