When fitting a statistical model and estimating parameters, the variability in parameter estimates due to random sampling is called parameter random error. This is in contrast to systematic bias in parameter estimates, which may arise from model misspecification or convenience sampling. This entry describes parameter random error in the context of educational measurement, specifically as it relates to item response theory (IRT).
In most uses of IRT, item parameters are estimated from a calibration sample prior to operational use. If we denote the population item parameters as Γ, then item parameter estimates Γ that arise from samples 1 to m that are randomly drawn from a population of test takers will be Γ1, Γ2, … , Γm. The variability among these sets of estimates is the ...
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