Distinguishing Constant and Dimension-Dependent Interaction: A Simulation Study

Abstract

A simulation study was conducted to determine how well two models for local item dependency (LID), called interaction models, could be distinguished. The models examined were the constantorder interaction model (COIM) and the dimension dependent interaction model (DDIM). Data were simulated according to the latter model. Three factors were manipulated: sample size, the weight of the difference between the latent trait value of the examinee and the interaction parameter, and the value of the interaction parameter. Results indicated that (1) if the interaction parameter is not too extreme, the COIM will be rejected in favor of the true model (the Rasch model fit poorly for all levels of the interaction parameter); (2) a larger weight of the difference between the latent trait value and the interaction parameter facilitated the rejection of the COIM, although finding the true weight required a large sample size; and (3) the value for the interaction parameter with an optimal discrimination between the COIM and DDIM was not 0, as expected.