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The IRT applications mostly use as link functions the logit and the probit, which are the cumulative distribution function (cdf) of the logistic and normal distributions, the resulting models gives similar inferences. Those are quite difficult to implement computationally (mainly on Bayesian approaches).

I was wondering, why other cdfs are not used, some are much simpler, such as the exponential cdf, etc?

Another question, any cdf with "S" shape would provide similar inferences to the logit/probit?

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