Visualizing uncertainty of estimated response functions in nonparametric item response theory

Abstract

Visual inspection of estimated response functions (RFs) is an important part of nonparametric item response theory (IRT) analysis. Currently, estimates of RFs are graphically displayed but the uncertainty of the estimated RFs is not. As a result, estimated RFs based on large samples may look exactly the same as estimated RFs based on very small samples. We derive asymptotic standard errors (ASEs) and Wald confidence intervals for the estimated RFs and show how these confidence intervals can be graphically displayed.