Fig. 1

The structural equation model for examining item position effects (Note \(\eta\) = Latent trait; \(\lambda_{1}\) to \(\lambda_{k}\) = factor loadings; \(\tau_{1}\) to \(\tau_{k}\) = item thresholds; \(p_{1}\) = positions of item 1 on the test; \(\beta_{1}\) = linear item position effect for item 1; \(\omega_{1}\) = interaction term between latent trait and positions of item 1)