[Rasch] Noise in observations ...

Rense renselange at earthlink.net
Sun Nov 4 18:39:49 EST 2007

Hm, the "con" arguments seem to be shifting from raw scores to sufficient
noise in data. This means that Paul must be succeeding in talking us away
from the strengths of the Rasch model. 
It is my understanding that raw scores are meaningful (are sufficient
statistics) only under the Rasch model. Hence, CTT and any other "add'm up"
approaches (weighted or not) derive their strength from this fact. I also
don't see the benefit of repeating or extending Fan's research unless the
preceding is wrong. 
Rasch scaling adds linear measures, straightforward equating, and superior
fit statistics to an otherwise blind system. This is far more important than
the coincidence that raw sums and linear measures correlate highly in the
mid range.
I also don't see any real difference between Rasch and the predictive
approaches - there is nothing wrong with non-Rasch variables correlating
higher with something than do true Rasch variables. All this means that one
has stumbled on a fortuitous combination of indicators that perform better
than a single variable. But, we already know from multiple regression that
using more predictor variables sometimes works better than a single one. By
this argument, the fact that unintelligible mixtures of items outperform
single ones precisely means that one does not know what must be going on.
And, what is wrong with admitting that this may well be the current state of
affairs that simply requires further study. Unless of course, as one might
well interpret Barrett's position, this is not worth doing in the first
Rense Lange


From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Mike Linacre (RMT)
Sent: Sunday, November 04, 2007 12:56 AM
To: rasch at acer.edu.au
Subject: [Rasch] Noise in observations ...

Paul remarks: "... can only be measured if their observations contain
sufficient noise ..."

Of course, as scientists, we endeavor to reduce irrelevant noise in the
observations in the same way as nuclear physicists do in their experiments
in Quantum Mechanics.  But we don't trust only one observation, or
observations that are too close in agreement (recognized as the "attenuation
paradox" in classical test theory or "wood-shedding" in the legal arena). 

We are in the same position as historians:
"When considering an accumulation of evidence, the more randomness in minor
details, the stronger the sense of historical truth."
Gerd Theissen, University of Heidelberg, 1994  (lecture given at the Luther
School of Theology, Chicago).

We are looking for locally-independent sources of information about our
latent variable, in the same way that historians look for
locally-independent accounts of historical events. 

Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org  <http://www.rasch.org/rmt/> www.rasch.org/rmt/ Latest RMT:
21:1 Summer 2007 

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