I am developing an online assessment system and I need to calibrate the bank of questions but I do not have enough people to implement a pilot test. That is why I decided to simulate the responses of the question bank. I will use the Rasch model for the development of a computer adaptive test (CAT); I have only questions from the bank and the number of options for each. How I can do a simulation using only this data?
I had thought to make it generate a random number $X$, if $X < 1 / N$, where $N$ is the number of options in a particular question, then the person has gotten the answer correct, otherwise it is incorrect.
Is this a correct approach for calibrating the item bank to a Rasch model via simulation?
PS: What I want to do is to calculate the level of difficulty of each question. It is my understanding that to calibrate a question bank, that bank must be applied to a sample of subjects, but I do not have enough people to do this, so I decided to try a simulation approach. I tested the function
sim.rasch in the
psych package, and I see that I need to take into account the number of options for each question, as this may influence their difficulty.