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

[Mike Lawrence]

Oops! Sorry, I was brought up to think about "predictor variables" and
"response variables", and while I often try to use the more
conventional "IV/DV" terminology, I often get them confused (the
reason why my original training obviated these terms I gather).

Indeed, group, cue and flanker are IVs (predictor variables). RT &
accuracy are DVs (response variables).

Sorry for the confusion!

On Wed, Jul 7, 2010 at 2:39 PM, Charles E. (Ted) Wright
<cewright at uci.edu> wrote:
> 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
>>
>>
>
> _______________________________________________
> 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. ~