lme() direction

I'm most interested in the interaction between color and type, but I
know that there is likely an effect of word. Yet since word is not
completely crossed with type, simply adding it to an aov() won't work.
A colleague recommended I look into lme() but so far I can't figure
out the proper call.

Another issue is whether to collapse across repetition before running
the stats, particularly since errors will leave unequal numbers of
observations per cell if it's left in.

Mike Lawrence <mike <at> thatmike.com> writes:

Thanks for the excellent reproducible sample set!

I'm most interested in the interaction between color and type, but I
know that there is likely an effect of word. Yet since word is not
completely crossed with type, simply adding it to an aov() won't work.
A colleague recommended I look into lme() but so far I can't figure
out the proper call.

Without word, it would be

summary(lme(rt~type*color, data=a,random=~1|id))

With the interaction, the extreme would be
summary(lme(rt~type*color*word, data=a,random=~1|id))

or, less extreme

summary(lme(rt~type*color+color:word, data=a,random=~1|id))

but all these fail because of the rather degenerate structure
of you data set. While lmer in package lme4 allows for a wider
set of solutions, I currently do not see how it could help,
but I might be wrong with p=0.5.


              word happy joy sad grumpy
type     color
positive white         93  90   0      0
        red           90  88   0      0
        green         88  87   0      0
negative white          0   0  88     95
        red            0   0  91     85
        green          0   0  88     88

Another issue is whether to collapse across repetition before running
the stats, particularly since errors will leave unequal numbers of
observations per cell if it's left in.

That's one of the points where you have little to bother with the lme
approach. Collapsing would give equal weights to unequal numbers of
repeat, and might of minor importance when not too extreme, though.

Dieter


set.seed(1)
a=rbind(
       cbind(
               type='positive'
               ,expand.grid(
                       id=1:10
                       ,color=c('white','red','green')
                       ,word=c('happy','joy')
                       ,repetition = 1:10
               )
       )
       ,cbind(
               type='negative'
               ,expand.grid(
                       id=1:10
                       ,color=c('white','red','green')
                       ,word=c('sad','grumpy')
                       ,repetition = 1:10
               )
       )
)

#add some fake rt data
a$rt=rnorm(length(a[,1]))

#And because people make errors sometimes:
a$error = rbinom(length(a[,1]),1,.1)

#remove error trials because they're not psychologically interesting:
a=a[a$error==0,]

library(nlme)
ftable(a[,c(1,3,4)])
summary(lme(rt~type*color, data=a,random=~1|id))

Would it improve things if "type" were a continuous variable rather
than categorical? I chose words at the extreme ends of a valence
rating scale but I still have the raw valence ratings for each word.

With the interaction, the extreme would be
summary(lme(rt~type*color*word, data=a,random=~1|id))

or, less extreme

summary(lme(rt~type*color+color:word, data=a,random=~1|id))

Mike Lawrence <mike <at> thatmike.com> writes:

Would it improve things if "type" were a continuous variable rather
than categorical? I chose words at the extreme ends of a valence
rating scale but I still have the raw valence ratings for each word.

With the interaction, the extreme would be
summary(lme(rt~type*color*word, data=a,random=~1|id))

or, less extreme

summary(lme(rt~type*color+color:word, data=a,random=~1|id))

..
Something like

summary(lme(rt~type*color+color:as.numeric(word), data=a,random=~1|id))

(please replace as.numeric() by the raw valence, the example above it
simply wrong)

could gain you a few degrees of freedom if you are willing to accept the
linear hypothesis. And as there is something like raw valence, one should
not throw away details about a-priori ordering in favor of a categorical
hypothesis.

Dieter

And if I decided to ignore the "type" variable altogether and simply
use the continuous "valence" variable, this is what I'd use?

summary(lme(
	fixed = rt~valence*color
	, data = a
	,random = ~1|id
))

I also have continuous luminance measurements of each color that vary
from participant to participant (we used different monitors). If I
were interested in luminance *instead* of color, would the following
be appropriate, or do I need to do something special to account for
the fact that each participant has different values of luminance?

summary(lme(
	fixed = rt~valence*luminance
	, data = a
	,random = ~1|id
))