Augmenting the use of the Rasch model under time constraints

This paper proposes a method for estimating national standardizations of partially speeded tests composed of items from a previously standardized item bank. The model combines two submodels, one for whether the examinee reaches the item, and the second for whether she is successful if she does reach it. The former model is comparable to that for survival analysis using item position in test as a quasi-time parameter (Hutchison 1988). The latter is a straightforward Rasch Model. Combining the two submodels allows for the possibility that ability and drop-out were correlated. The model proposed here is superior that of Bolt et al. (2002), which divides the population into a speeded and a non-speeded group, in that it allows for a range of speededness effects. The model is tested using three UK national standardizations on one outcome and comparing the actual and predicted distributions. It is suggested that the observed discrepancies may be due to differences in the samples drawn, and that in some circumstances the model may actually produce a better estimate than an actual standardization exercise.