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I would like to simulate a 2PL probit model. I want to set up some arbitrary item parameters $a=(a_1,...,a_J)$, $b=(b_1,...,b_J)$ and abilities $\theta=(\theta_1,...,\theta_I)$ ($J$ number of items and $I$ number of individuals), then fit a Bayesian model with flat prior distributions for those parameters. I could do it using the mirt package (function 'simdata'), but I want to do it by hand. So, I would appreciate it if somebody could respond to the questions:

-how does 'simdata' does in order to obtain a dataset of responses?

-assigning flat prior distributions to $a$, $b$ and $\theta$ will necessarily yield posterior estimates close to the values of those parameters arbitrarily chosen?

thanks in advance.

Ludwig
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  • Are you familiar with Bayesian methods? One of the perks that's most relevant here is the incorporation of prior distributions. The posterior is of course your predictions given some data, but the prior distributions represent your beliefs about parameters before seeing said data. It's very common in Bayesian stats to sample from your priors, which is what you're describing. This link gives a good overview of Bayesian IRT implementation via Stan https://mc-stan.org/docs/2_20/stan-users-guide/item-response-models-section.html – jbuddy_13 Sep 23 '21 at 14:33
  • I am familiar with bayesian framework, I can also implement irt in Stan, openbugs, etc.. my questions still stand. – Ludwig Sep 24 '21 at 17:21
  • @Ludwig mirt is open-source code, you can easily look up how it does what it does – philchalmers Sep 25 '21 at 22:14

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