Modeling and Multivariate Methods - SAS

528 Scoring Tests Using Item Response Theory Chapter 22
Launching the Platform
the trait level increases, there is always a theoretical chance of 100% probability of correctly answering the
item.
Figure 22.6 Three item characteristic curves
Note, however, that the 3PL model may by unnecessarily complex for many situations. If, for example, the c
parameter is restricted to be zero (in practice, a reasonable restriction), there are fewer parameters to predict.
This model, where only a and b parameters are estimated, is called the 2PL model.
Another advantage of the 2PL model (aside from its greater stability than the 3PL) is that b can be
interpreted as the point where an examinee has a 50 percent chance of getting an item correct. This
interpretation is not true for 3PL models.
A further restriction can be imposed on the general model when a researcher can assume that test items have
equal discriminating power. In these cases, the parameter a is set equal to 1, leaving a single parameter to be
estimated, the b parameter. This 1PL model is frequently called the Rasch model, named after Danish
mathematician Georg Rasch, the developer of the model. The Rasch model is quite elegant, and is the least
expensive to use computationally.
Caution: You must have a lot of data to produce stable parameter estimates using a 3PL model. 2PL
models are frequently sufficient for tests that intuitively deserve a guessing parameter. Therefore, the 2PL
model is the default and recommended model.
Launching the Platform
As an example, open the sample data file MathScienceTest.jmp. These data are a subset of the data from the
Third International Mathematics and Science Study (TIMMS) conducted in 1996.
To launch the Item Analysis platform, select Analyze > Multivariate Methods > Item Analysis. This shows
the dialog in Figure 22.7.