While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
With the number of item characteristic curve model parameters mdl
the item parameters are randomly sampled from the uniform distributions; for
example, under the three-parameter logistic model, b
from the -3 to
3 range, a
from the 0.2 to 2.8 range, and c
from the 0 to
.35 range.
Each of the 33 ability levels from the -3 to +3 range with .1875 interval,
the observed proportion of correct response is generated from the binomial
distribution for sample size of 21.
The chi-square goodness-of-fit index is obtained and reported with the
set of item parameters.