ThinkIR: The University of Louisville\u27s Institutional Repository
Abstract
Item response theory (IRT) is expanding to diverse research settings, without accompanying access to easily implemented model fit methods. One simple model fit approach involves x2/df ratios. However, its utility is not known across several conditions salient to recent applied IRT research. A Monte Carlo simulation was implemented to investigate the effects of several factors (sample size, adjustment condition, type of misfit, and proportion of misfitting items) on x2/df ratios in the context of the Graded Response Model. Results suggested that: (a) adjusted x2/df ratios were appropriate for the largest sample size condition (N=10000), but were extremely inflated for small (N=400) and medium (N=1500) conditions; (b) x2/df ratios were differentially affected across sample sizes by type and amount of misfit; and (c) sensitivity of the x2/df\u3e 3 cut point for identifying misfit in single items was notably low across all study conditions. Implications, limitations, and future directions are discussed