Pairwise Likelihood Estimation of the 2PL Model with Locally Dependent Item Responses

Abstract

The local independence assumption is crucial for the consistent estimation of item parameters in item response theory models. This article explores a pairwise likelihood estimation approach for the two-parameter logistic (2PL) model that treats the local dependence structure as a nuisance in the optimization function. Hence, item parameters can be consistently estimated without explicit modeling assumptions of the dependence structure. Two simulation studies demonstrate that the proposed pairwise likelihood estimation approach allows nearly unbiased and consistent item parameter estimation. Our proposed method performs similarly to the marginal maximum likelihood and pairwise likelihood estimation approaches, which also estimate the parameters for the local dependence structure.

A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items

“…However, these item pairs can be essentially removed from the PML estimation by setting the corresponding weights w 2,ij to zero. This technique has proven successful in estimating the 2PL model [39].…”

“…Sixth, we only considered a normally distributed θ variable and the probit link function in the 2PNO model. PML estimation has the advantage that it can be generalized to other link functions (such as in the 2PL model) or non-normal θ distributions [39]. However, DWLS/ULS and NOHARM rely on the probit link function and the normal distribution and cannot be generalized straightforwardly.…”