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### Test Information Function

The test information function (TIF), a function of the unknown ability or true score θ, is a measure of the amount of information provided by the item responses on a test about θ. The TIF is defined as the Fisher information for θ contained in the item response vector X, and under the typical item response theory (IRT), assumption of local independence is the sum of the item information functions (IIFs). It is important in the context of ability or true score estimation because the TIF serves as an estimate of the precisions of the maximum likelihood estimator (MLE) $\stackrel{^}{\theta }$ of the ability θ, or equivalently, the inverse of the TIF is an estimate of the variance of the MLE. Test developers often use the ...