An example case earlier will be performed using the item characteristic curve model of your choice. The two-parameter model may be a good starting model.

(a) Use the number of items J D 5 and the number of replications R D 10.

(b) Set up the ability parameter to 0:5. Note that you may use a randomly sampled value instead.

(c) Use the item characteristic curve model that you want to employ.

(d) Since you know the value of the examinee’s ability parameter, choose values of the item difficulty parameters randomly from a uniform distribution with a range from 3 to 3. If the two-parameter model is used, choose values of the item discrimination parameters randomly from a uniform distribution with a range from 0:2 to 2:8. For the three-parameter model, try to use values of the guessing parameters randomly selected from a uniform distribution with a range from 0 to 0:35. You may use the following R command lines:

b <- runif(J, -3, 3)

a <- runif(J, 0.2, 2.8)

c <- runif(J, 0, .35)

Almost equivalently, you may use the following command lines, assuming that you want to use only two decimal places for the values of item parameters:

b <- round(runif(J,-3,3), 2)

a <- round(runif(J,0.2,2.8), 2)

c <- round(runif(J,0,.35), 2)

(e) Obtain the ability estimates and standard errors as well as relevant statistics.

When the summary results are obtained on the R console window, try to write down values of the ability estimates on a piece of paper so you can use them in the next exercise.