Person-by-item predictors

In this chapter we consider the inclusion of person-by-item predictors into the model. Unlike person predictors or item predictors, person-by-item predictors vary both within and between persons. The inclusion of person-by-item predictors besides person predictors or item predictors is relevant for modeling various phenomena such as differential item functioning (DIF) and local item dependencies (LID) (see Zwinderman, 1997). To describe models with person-by-item predictors we will distinguish between static and dynamic interaction models. We concentrate here on models for DIF and LID, but the interaction concept is of course more general.