[Rasch] thresholds - further to previous email

Stephen Humphry stephen.humphry at uwa.edu.au
Tue Jul 10 12:00:13 EST 2007

Hello again. The papers relevant to previous email are listed below. The
reference is to Andersen (1977) (not Anderson).



Andersen, E.B. (1977). Sufficient statistics and latent trait models.
Psychometrika, 42, 69-81.

Rasch, G. (1966). An item analysis which takes individual differences into
account. British Journal of Mathematical and Statistical Psychology, 19(1),

Andrich, D. (1978). A rating formulation for ordered response categories.
Psychometrika, 43 (4), 561-574.


-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Andrés Burga León
Sent: Saturday, 7 July 2007 10:59 PM
To: rasch at acer.edu.au; rmt at rasch.org
Subject: RE: [Rasch] thresholds

Hello Muy:

Disordered Rash-Andrich thresholds means that the categories define a very
narrow interval on the latent variable. You could check
http://www.rasch.org/rn2.htm for some guidelines about rating scale.

Sometimes when I've collapsed Partial Credit items I get better fit indexes,
and the separation reliability didn’t get worse. If by collapsing I get
worse separation reliability and the fit indexes didn't improve, I prefer
not to do it so.


I know that is harder to use rating / or partial credit items for equating
and that you usually anchor only one o some of he thresholds. Here are a
couple of questions: 
- How do you choose which threshold to use?
- What happens if in Winsteps instead of using the SAFILE to anchor some
thresholds, you use an IAFILE specifying the measure for a partial credit
- If you have disordered thresholds in a sample, is it wise to use them, for
example in anchoring in order to equate different tests?


-----Mensaje original-----
De: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] En nombre
de Mike Linacre (RMT) Enviado el: Sábado, 07 de Julio de 2007 03:12 a.m.
Para: rasch at acer.edu.au
Asunto: Re: [Rasch] thresholds

Dear Muy Ignoto:

Welcome to the Rasch list, and thank you for your questions.

To clarify, Rasch-Thurstone thresholds are always ordered, and are the
intersections of the cumulative probabilities, for example: 0 vs 1+2+3
points,  0+1 vs 2+3 points, 0+1+2 vs 3 points. Rasch-Andrich thresholds can
be disordered, and are the intersections of the category probabilities, for
example: 0 vs 1 point,  1 vs 2 points, 2 vs 3 points.

>Your question: Do we need to collapse the categories if the threshold 
>are disordered?
Reply: This depends on your purpose. For example, are you designing a new
instrument or trying to make sense of an old dataset familiar to your
audience? Also is the threshold disordering an accident of the current
dataset or structural to the instrument? For instance, in survey
instruments, Likert scales are sometimes printed as the response mechanism
to true-false items. This confuses the respondents and such items are
obvious candidates for collapsing categories.

Your objective is to produce Rasch measures that are useful and easy to
communicate. The reason for linear measurement (which Rasch constructs) is
to assist with clear thinking. So if collapsing categories makes the
measures easier to understand, then do it. If collapsing categories makes
the measures more obscure, then consider carefully the advantages and

Mike Linacre
rmt at rasch.org

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