Alternative approaches to updating item parameter estimates in tests with item cloning

Item cloning techniques can greatly reduce the cost of item writing and enhance the flexibility of item presentation. To deal with the possible variability of the item parameters caused by item cloning, Glas and van der Linden (in press, 2006) proposed a multilevel item response model where it is assumed that the item parameters of a 3-parameter logistic (3PL) model or a 3-parameter normal ogive (3PNO) model are sampled from a multivariate normal distribution associated with a parent item. The model is referred to as the item cloning model (ICM). For the situation where each cloned item is presented to a substantial number of respondents, Glas and van der Linden (2006) proposed a Bayesian procedure for parameter estimation using a Markov chain Monte Carlo (MCMC) method (the Gibbs sampler). Two procedures for updating the parameter estimates in the ICM are compared. In the first procedure, the MCMC procedure is run on the combined original and new data set. In the second procedure, the estimates obtained on the original data set are used as priors in an MCMC run using the new data only. Results of simulation studies indicated that the second procedure tended to lead to some loss of precision in the parameter estimates. However, in the simulation studies presented here, this loss was limited. On the other hand, the gain in computation time for the second method was not substantial either.