Rasch models assert that items exhibit the model-specified item discrimination. Empirically, however, item discriminations vary. During the estimation phase of Winsteps, all item discriminations are asserted to be equal, of value 1.0, and to fit the Rasch model. But empirical item discriminations never are exactly equal, so Winsteps can also report an estimate of those discriminations post-hoc (as a type of fit statistic). The amount of the departure of a discrimination from 1.0 is an indication of the degree to which that item misfits the Rasch model.

 

DISCRIM=NO Do not report an estimate of the empirical item discrimination.

 

DISCRIM=YES Report an estimate of the empirical item discrimination in the IFILE= and Tables 6.1, 10.1, etc.

 

An estimated discrimination of 1.0 accords with Rasch model expectations for an item of this difficulty. A value greater than 1 means that the item discriminates between high and low performers more than expected for an item of this difficulty. A value less than 1 means that the item discriminates between high and low performers less than expected for an item of this difficulty. In general, the geometric mean of the estimated discriminations approximates 1.0, the Rasch item discrimination.

 

Rasch analysis requires items which provide indication of relative performance along the latent variable. It is this information which is used to construct measures. From a Rasch perspective, over-discriminating items are tending to act like switches, not measuring devices. Under-discriminating items are tending neither to stratify nor to measure.

 

Over-discrimination is thought to be beneficial in many raw-score and IRT item analyses. High discrimination usually corresponds to low MNSQ values, and low discrimination with high MNSQ values. In Classical Test Theory, Guttman Analysis and much of Item Response Theory, the ideal item acts like a switch. High performers pass, low performers fail. This is perfect discrimination, and is ideal for sample stratification, but such an item provides no information about the relative performance of low performers, or the relative performers of high performers.

 

Winsteps reports an approximation to what the discrimination parameter value would have been in a 2-PL IRT program, e.g., BILOG for MCQ, or PARSCALE for partial credit items. IRT programs artificially constrain discrimination values in order to make them estimable, so Winsteps discrimination estimates tend to be wider than 2-PL estimates. For the lower asymptote, see ASYMPTOTE=.

 

The algebraic representation of the discrimination and lower asymptote estimate by Winsteps are similar to 2-PL/3-PL IRT, but the estimation method is different, because Winsteps does not change the difficulties and abilities from their 1-PL values. Consequently, in Winsteps, discrimination and asymptotes are indexes, not parameters as they are in 2-PL/3-PL.

 

A Rasch-Andrich threshold discrimination is also reported, see Table 3.2.

 

With DISCRIM=YES,

+-----------------------------------------------------------------------------------------------+

|ENTRY    RAW                        |   INFIT  |  OUTFIT  |SCORE|ESTIM|                        |

|NUMBER  SCORE  COUNT  MEASURE  ERROR|MNSQ  ZSTD|MNSQ  ZSTD|CORR.|DISCR| ACTS                   |

|------------------------------------+----------+----------+-----+-----+------------------------|

|    23     40     74    2.19     .21|2.42   6.3|4.13   8.9|  .00|  .09| WATCH A RAT            |

|    17     93     74     .16     .19| .65  -2.7| .59  -2.5|  .70| 1.20| WATCH WHAT ANIMALS EAT |