[Rasch] CTT vs Rasch

Mike Linacre (RMT) rmt at rasch.org
Tue Jun 10 08:01:32 EST 2008

Anthony asks "Is there any source available to show how and why Rasch 
accommodate missing data? What property of the Rasch modelling takes care 
of missing data?"

The exact details depend on the estimation method, but in general, the 
properties are
1.) Rasch models are formulated at the individual observation level, and
2.) the accumulation of the observations for any parameter are its 
sufficient statistic.

Accordingly, in principle, only the observations which relate to a 
parameter are required in order to estimate that parameter.

Consequently, the Rasch model does not know that any data are "missing", it 
only knows about the data that are present.

If the data are rectangularly complete, then short-cuts can be taken in the 
estimation process, such as the non-iterative PROX method, or using a 
scoring table to assign measures to all the persons. Conditional Maximum 
Likelihood Estimation (CMLE) becomes computationally overwhelming if there 
are more than a few missing data patterns.


Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:4 Spring 2008
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