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Which approaches are exist for the estimation of a item difficulty from the statistical data?

Are they measure objective item's complexity?

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    $\begingroup$ Your question is rather sparse. How familiar are you w/ IRT? $\endgroup$ Feb 24, 2017 at 23:55
  • $\begingroup$ I have understood IRT basics (such as multi-parameter logistic curve, probability of giving a correct answer and so on). $\endgroup$ Feb 25, 2017 at 7:12

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There are three main estimation approaches. For Rasch models estimation can be done using the conditional likelihood approach (used by eRm package in R).

For 2PL or 3PL models you can use marginal likelihood approach (used by ltm package in R).

You can also use MCMC for either models. Any decent introductory textbook should have sections that go over these estimation procedures.

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  • $\begingroup$ I think you mean to switch conditional and marginal in your answer. Conditional is generally only possible for Rasch models. $\endgroup$ Feb 27, 2017 at 19:57
  • $\begingroup$ HA, good catch, I was copy pasting and moving some sentences around. $\endgroup$
    – bdeonovic
    Feb 27, 2017 at 20:25

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