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Parameter Invariance

Although parameter invariance may at first glance appear to be an arcane mathematical or statistical concept, in practice, it is far from that. Partly because of parameter invariance, statistical model–based measurement using item response theory (IRT) is one of the most popular current methodological frameworks for modeling data from assessments.

As is widely appreciated in statistics courses, the word parameter indicates that parameter invariance refers to population quantities, whose values are to be estimated with data collected within a random sampling design. Parameters can in this context refer to the set of item parameters (item difficulty, discrimination, and/or guessing) and the set of examinee parameters (the examinee test scores, or theta [θ] scores, implied by the IRT model) that are tied to a particular measurement ...

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