Fwd: RE: [Rasch] Re: Rasch Digest, Vol 35, Issue 12

Thomas Salzberger Thomas.Salzberger at wu-wien.ac.at
Wed Jul 2 19:57:17 EST 2008


-> forwarded from Andrew Stephanou:

>Hi Thomas,
>
>Please forward this email to the list.  We do need to make a point here.
>
>"By tau, I referred to the uncentralised thresholds (scaled
>'absolutely', i.e. with reference to the scale origin)."
>
>This statement may add to the confusion.
>
>Here is the relationship between the ACER deltas and taus and the RUMM
>centralised and uncentralised thresholds.  In this email I am also
>including our off-the-list correspondence.
>
>Delta =  Uncentralised threshold
>Tau = Centralised threshold
>Deltas and taus are coordinates of the same points on the scale.  They
>differ in the selected origin.
>Mean delta is called "delta dot".
>
>I find the RUMM use of the word uncentralised confusing because
>centralised implies a common central point for all items, but this is
>not the intention.  The uncentralised thresholds have a central point
>which is the origin of the scale.  Centralised in the RUMM usage of the
>word means that the coordinates are centralised on each item.  Each item
>has its own origin for the coordinates of the points of equal
>probability between its adjacent categories.
>
>In the literature there is so much confusion in the labels used for
>indicating points of equal probability between adjacent categories that
>the controversy in substantial issues of the polytomous Rasch model is
>not surprising.  And we are supposed to be the promoters of correct
>usage of units of measurement!
>
>This situation is not healthy for Rasch Measurement.
>
>Cheers,
>Andrew
>
>Andrew Stephanou
>ACER
>
>
>
>------------------------------------------------------------------------
>--------
>From: Thomas Salzberger [mailto:Thomas.Salzberger at wu-wien.ac.at]
>Sent: Wednesday, 2 July 2008 6:54 AM
>To: Stephanou, Andrew
>Subject: RE: [Rasch] Re: Rasch Digest, Vol 35, Issue 12
>
>Hi Andrew,
>
>I think this is just due to different notation.
>By tau I meant the uncentralised thresholds. Delta is the mean of the
>uncentralised thresholds. The centralised thresholds (say tau') are the
>uncentralised thresholds minus delta.
>Of course, it is exactly as you have put it.
>
>At 22:28 01.07.2008, you wrote:
>
>Hi Thomas,
>
>"Yes, the mean of the thresholds (the tau
>parameters) is the (overall) item location
>(delta)."
>I find this a bit confusing.
>
>The coordinates of the points of equal probability between adjacent
>categories can be expressed in deltas (uncentralised thresholds) or taus
>(centralised thresholds).  The origin of the scale is used for deltas
>and the mean delta is used as the origin of the taus.  The item
>difficulty is the mean delta.
>
>How do you then call the mean of the deltas? Just mean delta?
>
>Regards,
>Thomas
>
>The mean of the taus of an item is always zero.  The mean delta and the
>mean tau is the same point on the scale.
>
>Regards,
>Andrew
>-----Original Message-----
>From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
>Behalf Of Thomas Salzberger
>Sent: Wednesday, 2 July 2008 7:00 AM
>To: talilij at yahoo.com; rasch
>Subject: Re: [Rasch] Re: Rasch Digest, Vol 35, Issue 12
>
>Juanito,
>
>Andrew Stephanou pointed out that we should be careful to distinguish
>between centralised and uncentralised thresholds.
>By tau, I referred to the uncentralised thresholds (scaled 'absolutely',
>i.e. with reference to the scale origin). The centralised thresholds are
>deviations from the item overall location.
>Centralised thresholds therefore add up to zero.
>
>Thomas
>
> >1. For each item (or person), Rasch provides m-1 thresholds for the m
> >response categories.  The arithmetic mean of the m-1 thresholds for
> >each item(person) is then the item (or person) location or commonly
> >called item (or person) measure.  Am I right?
>
>Yes, the mean of the thresholds (the tau parameters) is the (overall)
>item location (delta). However, for persons there is just one parameter,
>so no need to calculate a mean.
>
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>Rasch at acer.edu.au
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