Item Response Theory Models for Carry-Over Effect Across Different Scales.

It is common in educational and psychological tests or social surveys that the same statement is judged on multiple scales. These multiple responses are linked by the same statement, which may cause local dependence. Considering the way a statement is judged on multiple scales, a new class of item response theory (IRT) models is developed to account for the nonrecursive carry-over effect, in which a response can be affected only by its preceding response rather than by a subsequent response. The parameters of the models can be estimated with the freeware WinBUGS. Two simulation studies were conducted to evaluate the parameter recovery of the new models and the consequences of model misspecification. Results showed that the parameters of the new models were recovered fairly well; fitting unnecessarily complicated models to data that did not have the carry-over effect did little harm to parameter estimation; and ignoring the carry-over effect by fitting standard IRT models yielded biased estimates for the item parameters, the correlation between latent traits, and the test reliability. Two empirical examples with parallel design and sequential design are provided to demonstrate the implications and applications of the new models.