THE IMPACT OF FALLIBLE ITEM PARAMETER ESTIMATES ON LATENT TRAIT RECOVERY

In this paper we propose an upward correction to the standard error (SE) estimation of θ̂(ML), the maximum likelihood (ML) estimate of the latent trait in item response theory (IRT). More specifically, the upward correction is provided for the SE of θ̂(ML) when item parameter estimates obtained from an independent pretest sample are used in IRT scoring. When item parameter estimates are employed, the resulting latent trait estimate is called pseudo maximum likelihood (PML) estimate. Traditionally the SE of θ̂(ML) is obtained on the basis of test information only, as if the item parameters are known. The upward correction takes into account the error that is carried over from the estimation of item parameters, in addition to the error in latent trait recovery itself. Our simulation study shows that both types of SE estimates are very good when θ is in the middle range of the latent trait distribution, but the upward-corrected SEs are more accurate than the traditional ones when θ takes more extreme values.