A rasch model for carry-over effect in longitudinal data

In many longitudinal studies, tests are administered repeatedly to measure growth across time. Such tests often consist of a set of common items to link all items on the same scale so that growth can be quantified. These common items are responded by the same persons more than once, which may result in carry-over effect. If so, the usual assumption of local independence is violated. If the carry-over effect exists but is ignored by fitting standard item response theory models, the parameter estimates will be biased and the conclusions will be misleading. To resolve this problem, we develop a new Rasch model that specifically account for the carry-over effect in common items in longitudinal data. Results of a series of simulations demonstrated that the parameters of the new model were recovered fairly well by using WinBUGS. An empirical example of growth in mathematical proficiency was provided to illustrate the implications and applications of the new Rasch model.