# [Rasch] Estimating Rasch Measures for Extreme Scores

Rense Lange rense.lange at gmail.com
Sat Apr 30 02:47:05 EST 2011

```First, the committee doesn't understand that this applies to "raw" scores
equally? (there is theorem that says that (a) if you want to use raw scores
as ordinal versions of interval level number), then items must be Rasch
scalable, and (b) only if items are Rasch scalable then (transformed) raw
scores will define an interval scale. In other words, you should do Rasch
even if you were going to use raw scores for some reason.

Second, what about additionally using non-parametric statistics on the
sacred raw scores, these should reach the same conclusions about means etc.
(if x is the perfect score, they do agree that x > x-1, right?). Also, there
are estimation methods for which there IS a direct value for perfectly
low/high scores - but I forgot off the top of my head which ones.

Third, let's for the sake of argument say that perfect raw scores are
problematic. But, typically you are not interested in individuals. Rather,
individuals are grouped, male vs. female, rural vs urban, ... Now, by using
Facets you can sidestep the whole issue by measuring gender rather than
individuals, residence rather than individuals etc - this is so because it
is highly unlikely that either all men, all women, or both have perfect
scores, etc. So, measure only at the person-category level!

Rense

On Fri, Apr 29, 2011 at 11:11 AM, <liasonas at cytanet.com.cy> wrote:

> Thank you for the response but I am not sure if I understood well. Each
> student has 12 "items". Basically they are three assessments for each
> subject (scores from 1-5). If somebody has perfect score, it means that he
> has 12x5=60 points. Do you mean I could remove the students with perfect
> scores and rerun the analysis and compare the results? This does not solve
> the problem of estimating the perfect scores... My fault for not making this
> clear in the previous post. I hope now the problem is clearer -
> Thank you all for your time
> Jason
>
> Sent from my BlackBerry® smartphone
> ------------------------------
> *From: * Rense Lange <rense.lange at gmail.com>
> *Date: *Fri, 29 Apr 2011 09:46:38 -0500
> *To: *Iasonas Lamprianou<liasonas at cytanet.com.cy>
> *Cc: *rasch list<rasch at acer.edu.au>
> *Subject: *Re: [Rasch] Estimating Rasch Measures for Extreme Scores
>
> Since getting better faculty seems out of the question, would this solve
> it? Re-run twice using Facets.
>
>    - Once use all items, including those giving "perfect" scores,
>    - Once with the perfect items removed for each student/teacher getting
>    perfect ratings.
>
>
> Then plot the two sets of students/teachers? estimated parameters - they
> should be very similar (Y = X). While you are at it, you could show the
> probably non-trivial effects of differences in rater leniency/ severity on
> the student/teacher evaluations.
>
> Rense Lange
>
>
>
> 2011/4/29 Iasonas Lamprianou <liasonas at cytanet.com.cy>
>
>>
>> Dear colleagues,
>> I rarely submit requests in this list unless it is urgent and important
>> because I respect the time of the people who tend to reply most often. I
>> would like to thank them. This time, it is important and that is why I
>> politely request you to help me. The post is long, but it has to do with the
>> problems Rasch-users face in the harsh world of academia. I think that the
>> post concerns most of us.
>>
>> I am trying to help a student with her PhD thesis (so I am writing on her
>> behalf). She submitted her thesis and her examiners spotted some problems
>> and she has to address them.
>>
>> The problem: The PhD thesis is about the performance of students.  For
>> each student participating in the study (N>1000), the researcher has his/her
>> score on four subjects: language, science, maths and history. For each
>> subject, each student has three teacher assessments which were awarded in
>> January, March and June. Each score runs from E (Failure) to A (Excellent).
>> So, overall, each student has three ordinal teacher assessment measures for
>> each of four subjects. It is a typical repeated measures case for four
>> variables/subjects with three measures per variable/subject.
>>
>> Design: Since the data are ordinal (E=1=Failure to A=5=Excellent) the
>> researcher used a Partial Credit Rasch model with three  items  to build
>> four Ability scales, one for each subject (the Rating Scale did not have
>> good fit). Also, the student used all 12 scores (4 subjects X 3 measures) to
>> produce one overall Ability  Academic Performance  measure. Then, the
>> researcher used these Rasch ability measures as dependent variables to run
>> OLS regressions.
>>
>> Issue 1:
>> A serious problem spotted by the examiners is that a large proportion of
>> students (around 20%) has perfect scores (three  A s) on some of the four
>> subjects. The researcher used a Winsteps routine to find measures of ability
>> for those students with extreme scores. The examiner has major reservations
>> about the validity of this decision and asks whether these data (extreme
>> scores) should be dropped. The examiner says:  If a Rasch analysis is to be
>> used to derive attainment scores, the final distribution must provide a
>> realistic representation of attainment. This means that the large group of
>> candidates who achieve perfect scores (on the extreme right of the
>> histograms) need to be properly represented. These scores need to be
>> appropriately dealt with by Rash (if this is possible), or they need to be
>> removed from the analysis (with an
>> assessment made about the impact of the resulting loss of data).
>> To the defense of the researcher, the distance between the  perfect score
>>  and the  perfect-1  estimate is neither huge nor unreasonable: it is around
>> 1.4 logits on a scale which extends from around -11 to 11 logits. When the
>> researcher draws the scatterplot between raw scores and logits, the
>> sigma-curve looks beautifully smooth and the estimates of the extreme scores
>> look neither  too extreme  nor out of tune with the rest data points on the
>> scatterplot. The distance between the  perfect score  and the  perfect-1
>>  estimate is not grossly out of line compared to the other distances between
>> raw scores estimates (for example, the distance between the  perfect-1  and
>> the  perfect-2  scores is only around 0.3 logits smaller).
>> (a) The researcher needs strong references to defend her decision NOT to
>> drop the extreme data estimates. Can anyone please provide strong
>> peer-reviewed papers to support the decision to keep the extreme score
>> estimates as valid representations of the ability of the participants?
>>
>>
>> Issue 2:
>> Stemming from the previous comment, one of the suggestions of the
>> examiners is that the researcher could ditch the Rasch model and instead sum
>> the three measures in one subject (e.g. A+B+B=5+4+4=13) and then use this
>> sum for an OLS regression. The examiner says  A serious discussion needs to
>> be held about the benefits, if any, the Rasch analysis provides over a more
>> direct analytical path (e.g.   a linear regression of results averaged over
>> three   [teacher assessments] . We all know that this is simply wrong to do
>> because we cannof average ordinal measures and the student already explains
>> this in her Methodology section, but she probably needs more references.
>> (b) Can anyone please provide a list of (recent, if possible) papers in
>> good peer-reviewed journals which explain that this is not the right thing
>> to do?
>>
>>
>> Issue 3:
>> Another suggestion of the examiners is that the researcher could ditch the
>> Rasch model and just use the ordinal measure (E=1=Failure to A=5=Excellent)
>> as a dependent variable in a proportional odds models. This means that the
>> researcher should run three different models for each subject (for the
>> Teacher Assessment awarded in January, March and June).
>> (c) Can anyone pleased provide a list of (recent, if possible) papers in
>> good peer-reviewed journals which explain that this is NOT better than using
>> the Rasch model to get one linear measure instead of three ordinal?
>>
>>
>> I feel that the examiners did a very good job overall and were very fair
>> and consistent. They spent too much time to read every little detail in a
>> long thesis, they spotted some important issues and we need to credit them
>> for this. I feel that we may want to help the student address these
>> interesting issues to the full satisfaction of the examiners.
>>
>> Thank you for your time
>>
>> In anticipation of your help
>> Jason Lamprianou
>> University of Cyprus
>>
>>
>>
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>
>
>
>
> --
> Rense Lange, Ph.D.
> via gmail
>

--
Rense Lange, Ph.D.
via gmail
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