# [Rasch] complex sampling Rasch

Agustin Tristan ici_kalt at yahoo.com
Tue Feb 16 01:57:45 EST 2010

```Hello! Thank your for the explanation concerng the sample design and the Rasch item's parameters, it is useful because we are also interested to use some ideas from the PISA project . In addition to Randy's question, I wonder if some of the following aspects are considered as important for the item and test calibration for the PISA project:
a) Could it be convenient to get the item calibration for each sub-sample  (schools) and after that to combine the calibrations using the weight for each sample unit to obtain a "general" item calibration?
b) As the Rasch model is sample free (or without a practical implication as Ray did explain), can we use the item calibration of the anchor items independently of the position of the items  in the test?
Regards
Agustin Tristan

Subject: RE: [Rasch] complex sampling Rasch
To: "Randy & Shelley MacIntosh" <srmac at bluebottle.com>, "rasch" <rasch at mailinglist.acer.edu.au>
Date: Sunday, February 14, 2010, 7:31 PM

Randy,

The answer is a bit complicated. Let's put fit aside and assume the
Rasch model and your data are compatible.  Then, it depends upon the
modelling assumptions you make and your estimation method.  If you use
conditional maximum likelihood or a pairwise routine then the item
parameter estimates are sample free and so the sample design does not
influence the estimates.  If you use unconditional or marginal maximum
likelihood then "in theory" there may be some minor effects, but I've
never seen any evidence that it has any practical consequence.

In PISA we do not take the complex sample design into account when
estimating item parameters.

Ray

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
Behalf Of Randy & Shelley MacIntosh
Sent: Monday, 15 February 2010 7:42 AM
To: rasch
Subject: [Rasch] complex sampling Rasch

I am interested in applying the Rasch model to data from a complex
sample design.
I was wondering if this has been done?
For example, is the nature of the PISA sample design explicitly taken
into account when the Rasch estimates are produced?

Thanks,
Randy MacIntosh

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