Distinguishing constant and dimension-dependent interaction: A simulation study

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 constant order interaction model (COIM) and th e dimension-dependent interaction model (DDIM). Data were simulated accordi ng to the latter model. Three factors were manipulated: sample size, the we ight of the difference between the latent trait value of the examinee and t he interaction parameter, and the value of the interaction parameter. Resul ts 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 poorl y for all levels of the interaction parameter); (2) a larger weight of the difference between the latent trait value and the interaction parameter fac ilitated the rejection of the COIM, although finding the true weight requir ed a large sample size; and (3) the value for the interaction parameter wit h an optimal discrimination between the COIM and DDIM was not 0, as expecte d.