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

[Charles E. (Ted) Wright]

Mike,

I am just kibbitzing this thread since I, liek you, am trying to understand 
better how I can use LMMs in psychological applications. However, in this 
message what you label as dependent variables are, I believe, independent 
variables. Wouldn't the two DVs would be RT and accuracy?

Ted Wright

On Wed, 7 Jul 2010, Mike Lawrence wrote:

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