[Rasch] [BULK] Use of e in the Rasch model

Mark Moulton markhmoulton at gmail.com
Wed Sep 7 04:36:18 EST 2011


Kenji,

I remember Mike Linacre showing me how using natural logs simplifies the
Rasch standard error formula.  I asked him how Rasch standard errors were
all reported in logits when the formula used to calculate them is based on
probabilities:

SE[i][in logits???] = 1 / sum[across row i](p[i] * (1 - p[i]))

His answer was something along the lines that this is a property of taking
the derivative of the natural log.  Any other base would require using
additional constants of some sort.

Unfortunately I'm foggy on the algebra this morning -- it wasn't hard.
 Maybe someone remembers how it goes.  But the upshot is that any log will
work for the Rasch model -- the only visible difference is that the logit
scale will tend to be more or less dispersed.  However, the natural log does
simplify some of the algebra under the hood.  Plus, it is used by convention
throughout the statistical and scientific world, as was noted.

Mark Moulton


2011/9/5 Kenji Yamazaki <yk0271 at yahoo.co.jp>

> Hi all:****
>
>  ****
>
> I have a question about the formula of the Rasch or IRT model.  Why is e
> (=2.718) used in the formula?  Why is not it 10?  Because e is close to 3,
> why isn’t 3 used for the formula instead of e?  I have been having this
> question for a long time, but all the Rasch and IRT books I have read treat as
> given the use of e (=2.718) in the formula.  If anyone gives me an answer,
> it will be very appreciated.
>
>
> Kenji
>
>
>
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