[Rasch] Average Threshold Measure in PCM

Mike Linacre rmt at rasch.org
Thu Mar 31 10:44:20 EST 2011


Matthew:

Yes: * the "Rasch-Thurstone thresholds" (50%PRB) indicate the points on the 
latent scale where where an examinee has equal probability of being below 
the current category or *at/above* the current category. These parameters 
are never disordered.

Amended: * the "Rasch-Andrich thresholds" (MEASURE) indicate the points on 
the latent scale where an examinee has equal probability of being in the 
category *immediately below* the current category or *in* the current 
category. These parameters may be disordered.

You asked: Now, if the categories are, in fact, disordered,does the 
interpretation of the Rasch item difficulty (from the IFILE) still hold?

Reply:
The item difficulties in IFILE= are the points on the latent variable where 
the numerically top and bottom categories are equally probable. Category 
disordering or Andrich threshold disordering do not change this computation.

If the categories are substantively disordered, e.g., "1=Yes, 2=No, 3= 
Maybe", then the Rasch measures (abilities and difficulties) may be 
meaningless. This category disordering is usually detected through Rasch 
fit statistics and disordered average measures for the categories: see 
www.rasch.org/rmt/rmt131a.htm

If the categories are ordered, e.g., "1=No, 2=Maybe, 3= Yes", but the 
Rasch-Andrich thresholds are disordered, e.g., Andrich threshold 1-2 is +2, 
Andrich threshold 2-3 is -2, then this indicates that category 2 has a low 
probability of being observed. The observed category frequencies may be 100 
observations in category 1; 5 observations in category 2; 100 observations 
in category 3. This threshold disordering indicates does not change the 
interpretation of the overall item difficulty.

OK?

Mike L.


Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  24:4 Spring 2011
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