An Investigation of Linking Methods Under the Graded Response Model

Abstract

Linking tests from different calibrations under item response theory requires calculation of the slope and intercept of the appropriate linear transformation. Results from five linking methods under the graded response model were investigated using simulated datasets: the characteristic curve method, the minimum x2 method, and three mean and a methods. Examples are presented for horizontal (matched 0) and vertical (unmatched 0) linking situations. Fifty replications of the data were generated for each combination of two underlying ability distributions, two sample sizes, and four lengths of common-item links. Item parameter estimates were placed onto the underlying metric using each of the linking methods. The results indicate that differences in the linking coefficients were small. Root mean square differences and mean Euclidean distances from underlying parameters were very small under most conditions. The results are consistent with previous research on dichotomous models. The five linking methods yielded similar results for longer common-item links with large sample sizes, and when the distribution of item location parameters matched the underlying trait distribution.