[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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