Sorry, I meant to say: "For the moment I wonder if the solution is not
to use CIs based on the two low SEs produced by the ~ time model, and
to treat them as least-significant difference intervals."
_____________________________
Professor Michael Kubovy
University of Virginia
Department of Psychology
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On Apr 21, 2008, at 9:23 AM, Michael Kubovy wrote:
> Thanks Doug,
>
> You write: "If you want to examine the three means then you should fit
> the model as lmer(rcl ~ time - 1 + (1 | subj), fr)"
>
> I do just that (which is what Dieter just sent). But the CIs are much
> too big compared to the CIs for differences between means (which
> should be bigger than the CIs on the means themselves). If you write
> the model as ~ 1 - time, then the CIs are roughly of the same (large)
> size. But I'm really interested in the CIs on the means that capture
> the variability *within* subjects. I believe that this is what
> experimentalists in psychology need (and have been debating for a long
> time what the correct analysis is that produces these error bars). The
> theory is not about generalizing to people, but generalizing to
> responses to different situations within people. The article by
> Brillouin and Riopelle (2005) is the only one that tries to do this
> within the framework of LMEMs that I know of, and it's couched in
> terms of SAS.
>
> For the moment I wonder if the solution is not to use CIs based on the
> two low SEs produced by the ~ 1 - time model, and to treat them as
> least-significant difference intervals.
>
> On Apr 21, 2008, at 7:56 AM, Douglas Bates wrote:
>
>> On 4/21/08, Michael Kubovy wrote:
>>> To help Kedar a bit:
>>>
>>> Here is one way:
>>>
>>> recall <- c(10, 13, 13, 6, 8, 8, 11, 14, 14, 22, 23, 25, 16, 18, 20,
>>> 15, 17, 17, 1, 1, 4, 12, 15, 17, 9, 12, 12, 8, 9, 12)
>>> fr <- data.frame(rcl = recall, time = factor(rep(c(1, 2, 5), 10)),
>>> subj = factor(rep(1:10, each = 3)))
>>> (fr.lmer <- lmer(rcl ~ time + (1 | subj), fr))
>>> require(gmodels)
>>> ci(fr.lmer)
>>>
>>> Now I have a problem to which I would very much appreciate having a
>>> solution:
>>>
>>> The model fr.lmer gives a SE of 1.8793 for the (Intercept) and
>>> 0.3507
>>> for the other levels. The reason is that the first took account of
>>> the
>>> variability of the effect of subjects. Or using simulation:
>>> Estimate CI lower CI upper Std. Error p-value
>>> (Intercept) 11.107202 6.458765 15.208065 2.1587362 0.004
>>> time2 2.012064 1.301701 2.795128 0.3743050 0.000
>>> time5 3.206834 2.502870 3.939791 0.3694384 0.000
>>>
>>> Now if I need to draw CI bars around the three means, it seems to me
>>> that they should be roughly 11, 13, and 16.2, each \pm 0.75,
>>> because
>>> I'm trying to estimate the variability of patterns within subjects,
>>> and am not interested in the subject to subject variation in the
>>> mean
>>> for the purposes of prediction.
>>
>> If you want to examine the three means then you should fit the model
>> as
>> lmer(rcl ~ time - 1 + (1 | subj), fr)
>>
>>> This what the authors in the paper cited below call on p. 402 a
>>> "narrow [as opposed to a broad] inference space." My question:
>>> ***How
>>> do I extract the three narrow CIs from the lmer?***
>>> @ARTICLE{BlouinRiopelle2005,
>>> author = {Blouin, David C. and Riopelle, Arthur J.},
>>> title = {On confidence intervals for within-subjects designs},
>>> journal = {Psychological Methods},
>>> year = {2005},
>>> volume = {10},
>>> pages = {397--412},
>>> number = {4},
>>> month = dec,
>>> abstract = {Confidence intervals (CIs) for means are frequently
>>> advocated as alternatives
>>> to null hypothesis significance testing (NHST), for which a
>>> common
>>> theme in the debate is that conclusions from CIs and NHST
>>> should
>>> be mutually consistent. The authors examined a class of CIs
>>> for which
>>> the conclusions are said to be inconsistent with NHST in
>>> within-
>>> subjects
>>> designs and a class for which the conclusions are said to be
>>> consistent.
>>> The difference between them is a difference in models. In
>>> particular,
>>> the main issue is that the class for which the conclusions
>>> are said
>>> to be consistent derives from fixed-effects models with
>>> subjects
>>> fixed, not mixed models with subjects random. Offered is
>>> mixed model
>>> methodology that has been popularized in the statistical
>>> literature
>>> and statistical software procedures. Generalizations to
>>> different
>>> classes of within-subjects designs are explored, and
>>> comments on
>>> the future direction of the debate on NHST are offered.},
>>> url = {http://search.epnet.com/login.aspx?direct=true&db=pdh&an=met104397
>>> }
>>> }
>>>
>>> On Apr 21, 2008, at 2:24 AM, Dieter Menne wrote:
>>>
>>>> kedar nadkarni gmail.com> writes:
>>>>
>>>>> I have been trying to obtain confidence intervals for the fit
>>>>> after having
>>>>> used lmer by using intervals(), but this does not work.
>>>>> intervals()
>>>>> is
>>>>> associated with lme but not with lmer(). What is the equivalent
>>>>> for
>>>>> intervals() in lmer()?
>>>>
>>>> ci in Gregory Warnes' package gmodels can do this. However, think
>>>> twice if you
>>>> really need lmer. Why not lme? It is well documented and has many
>>>> features that
>>>> are currently not in lmer.
>>>>
>>>> Dieter
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