How can internal consistency reliability of a test and of individual test items be quantified in Item Response Theory models? I know I can resort to Classical Test Theory, Cronbach's alpha, and other measures, but is there a way to characterize reliability within IRT?
Solved – Internal consistency reliability in item response theory models
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Best Answer
You can compute test information curves from your IRT parameter estimates. These curves give you the precision of the test at each $\theta$ of the latent trait. The information $I$ can be transformed into the standard error of estimate $SEE$, which is a direct estimate of the reliability of the test at that $\theta$: $SEE = 1 / \sqrt{I}$.
The metric of the test information can also be converted to a traditional reliability metric expressed by a correlation coefficient (Thissen, 2000): $Rel = 1 - (1/I)$. Here are the conversions from a set of TICs to correlational reliability estimates:
For example, a TIC > 5 corresponds to a reliability > .80.
Thissen, D. (2000). Reliability and measurement precision. In H. Wainer (Ed.), Computerized adaptive testing: A primer (2nd ed., pp. 159–184). Lawrence Erlbaum Associates Publishers.