An empirical power comparison of directional goodness-of-fit tests for 2-PL IRT model under different intercept patterns

This study investigates the impact of intercept patterns, including symmetric, asymmetric, zeros on the performance of Lagrange Multiplier (LM) tests in two-parameter item-response theory (2-PL IRT) models, comparing it with three other directional goodness-of-fit tests on empirical Type I error rates and power. A series of simulation results show that intercept patterns significantly affect test performance, with zero intercepts yielding the highest power; LM has the best performance that excels in controlling Type I error rates and has higher empirical power. The application to fraction subtraction data confirms LM's efficacy in detecting local dependence under sparsity. The findings offer methodological insights for goodness-of-fit testing under model misspecification.