[R-sig-ME] Using mixed-effects modelling to estimate between- and within-Ss variance in an effect

[Mike Lawrence]

Sorry, "Ss" is an old Psych term for "Subjects", the repeated measures unit.

An example can be found in the ANT data set from the "ez" package. In
that data set is the trial-by-trial record of a (fake) experiment
involving 20 Ss (identified by column sid) who are performing a target
identification task. Response time (RT) and accuracy are measured
performance variables. There are two dependent variables (DVs) of
interest: cue (4 levels) and flanker (3 levels). The DVs are
factorially combined within each Ss, and each cell of the 4x3
combination table is repeated 12 times (randomly distributed through
time, which is indexed by the block and trial columns). Ss are
additionally divided into two groups, treatment and control.

In a study like this, I would typically set the "Center Cue" and
"Congruent Flanker" as the first levels of the cue and flanker
factors, respectively, which allows me to do a mixed effects model:

acc_fit = lmer(
    formula = acc ~ group*cue*flank + (1|sid)
    , family = 'binomial'
    , data = ANT
)

One question might be whether the "Center cue versus no cue" effect
has a different between-Ss variance than the "Center cue versus
spatial cue" effect. Or maybe we might be interested in whether those
effects have different within-Ss variance. Or possibly we might be
interested in comparing the between-Ss variance in the "Congruent
Flanker versus Incongruent Flanker" effect between the 2 groups of Ss
(or, similarly comparing the within-Ss variance of those effects
between the groups).

I guess this description suggests that I'm not only interested in
estimating between- and within-Ss variance, but also comparing such
estimates, which raises the question of how such comparison might be
reasonably achieved...

Mike

On Wed, Jul 7, 2010 at 1:09 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> A quick question of clarification, does the notation Ss stand for
> "subject-stimulus"?
>
> Perhaps you could follow up with a few sentences giving a bit more
> background on the type of experiments that you have in mind.
>
> On Wed, Jul 7, 2010 at 10:57 AM, Mike Lawrence <Mike.Lawrence at dal.ca> wrote:
>> Hi folks,
>>
>> In psychology, we're often interested not only in effects, but also
>> their variability. This is mostly from a pragmatic perspective, where
>> we want to know how much time to devote to measuring a certain
>> phenomenon in order to reliably obtain an expected effect.
>> Historically, variability has been quantified with a single measure of
>> "reliability" (typically obtained by correlating subsets of
>> measurements). More recently, it has been suggested that such single
>> measures confound two sources of variability that are of potentially
>> independent interest: between-Ss variability of the effect, and
>> within-Ss variability of the effect. That is, we typically compute
>> effects based on many observations per Ss, so variability of the
>> effect is theoretically computable within each Ss.
>>
>> Prior to my exposure to mixed-effects modelling, I used bootstrap
>> resampling to estimate the between- and within-Ss variabilities of the
>> effect, but now that I have dipped my toes into mixed-effects
>> modelling, I suspect that these values might be already estimated
>> automatically as part of the mixed-effects modelling procedures. Is
>> this the case, and if so, how could I obtain these estimates from,
>> say, the output from lmer?
>>
>> Mike
>>
>> --
>> Mike Lawrence
>> Graduate Student
>> Department of Psychology
>> Dalhousie University
>>
>> Looking to arrange a meeting? Check my public calendar:
>> http://tr.im/mikes_public_calendar
>>
>> ~ Certainty is folly... I think. ~
>>
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>>
>
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-- 
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

Looking to arrange a meeting? Check my public calendar:
http://tr.im/mikes_public_calendar

~ Certainty is folly... I think. ~