[R-sig-ME] Rasch with lme4

[Chuck Cleland]

On 6/9/2009 6:59 AM, Andy Fugard wrote:
> Dear all,
> 
> What happens in practice when you compare the two approaches of item as
> a fixed versus as a random effect?
> 
> Consider:
> 
>   M1 = lmer(Reaction ~ Days + (1|Subject), sleepstudy)
>   M2 = lm(Reaction ~ Days + factor(Subject), sleepstudy)
> 
> The slope estimates for Days for are practically identical, the mean
> intercepts differ:
> 
> For M1:
> 
>   ...
>   Fixed effects:
>               Estimate Std. Error t value
>   (Intercept) 251.4051     9.7459   25.80
>   Days         10.4673     0.8042   13.02
>   ...
> 
> For M2:
> 
>                       Estimate Std. Error t value Pr(>|t|)
>   (Intercept)         295.0310    10.4471  28.240  < 2e-16 ***
>   Days                 10.4673     0.8042  13.015  < 2e-16 ***
>   ...
> 
> I didn't look at the estimators for Subject, e.g., for M2 the predictors:
> 
>   factor(Subject)309 -126.9008    13.8597  -9.156 2.35e-16 ***
>   factor(Subject)310 -111.1326    13.8597  -8.018 2.07e-13 ***
>   factor(Subject)330  -38.9124    13.8597  -2.808 0.005609 **
>   ...
> 
> But it could be done...
> 
> Is there a paper on these sorts of comparisons?  How does the mixed
> effects approach differ from a standard regression model with a heap of
> categorical predictors for representing, e.g., deviations from the mean
> intercept?

Allison, P.D. (2005).  Fixed Effects Regression Methods for Longitudinal
Data Using SAS. Cary, NC: SAS Institute.

  covers some of this territory.  As someone else pointed out, a
limitation is that including "Subject" as a factor precludes inclusion
of specific subject explanatory variables (e.g., gender).

> Presumably this could be done too for estimates for items, e.g., for
> binary logistic models and beyond.
> 
> Cheers,
> 
> Andy
> 
> 
> Ken Beath wrote:
>> On 09/06/2009, at 8:58 AM, Stuart Luppescu wrote:
>>
>>> On 火, 2009-06-09 at 08:04 +1000, Ken Beath wrote:
>>>> The model treats item as a random effect and should be a fixed effect.
>>>
>>> Hmm. In Doran, Bates, Bliese and Dowling (2007), the authors treat the
>>> item as random.
>>>
>>
>> It can be argued that the items are a sample from a population of
>> items which is possibly reasonable for educational testing where there
>> might be a population of questions which can be asked. Even so,
>> assumptions about the distribution are optimistic and most items are
>> used because they test something obvious. Maybe others have a
>> different philosophy. A more pedantic argument is that this isn't the
>> model Rasch used.
>>
>>> [snip]
>>>> Another question to ask is whether the Rasch model is appropriate. If
>>>> an IRT is more sensible it would cause some problems with the second
>>>> model.
>>>
>>> Sorry, but I don't understand this at all.
>>>
>>
>> By an IRT I mean the 2 parameter version where there is a discriminant
>> parameter which varies among items, in contrast to the Rasch where it
>> is constant. It probably gives problems with the other model as well
>> but the second model should have more problems.
>>
>> I don't like the idea of assuming a Rasch model at all, its popularity
>> seems to derive from an era when fitting anything else was difficult.
>> Modern software offers proper solutions, unfortunately at a cost but
>> that shouldn't be a consideration.
>>
>> Ken
>>
>>
>>> -- 
>>> Stuart Luppescu -=- slu .at. ccsr.uchicago.edu
>>> University of Chicago -=- CCSR
>>> 才文と智奈美の父 -=-    Kernel 2.6.28-gentoo-r5
>>> Drusilla: How do you feel about eternal life?
>>> Xander: We couldn't just start with coffee?
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

-- 
Chuck Cleland, Ph.D.
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