In general, estimating the latent trait in item response theory (IRT) models was based on the item parameters known. But, in practice, only the estimates of item parameters can be obtained. Thus, the estimate of latent trait and the corresponding standard error will adversely influenced by the ignored calibration error, especially when the calibration sample was small. It will lead the standard error for the latent trait underestimated, which is because the standard errors for the latent trait are obtained on the basis of test information only, as if the item parameters are known. And obtaining good estimates of the standard errors for the latent trait estimates is important in adaptive testing.
This paper proposed an algorithm to upward correct the standard error of the latent trait. The simulation study shows that the traditional standard error and the upward-corrected standard error are very good when θ is in the middle range of the latent trait distribution, but the upward-corrected standard errors are more accurate than tradition ones when θ located in the extreme values.