The aim is to show that it is possible to parameterize discrimination for sets of items, rather than individual items, without destroying conditions for sufficiency in a form of the Rasch model. The form of the model is obtained by formalizing the relationship between discrimination and the unit of a metric. The raw score vector across item sets is the sufficient statistic for the person parameter. Simulation studies are used to show the implementation of conditional estimation solution equations based on the relevant form of the Rasch model. The model also applied to two numeracy tests attempted by a group of common persons in a large-scale testing program. The results show improved fit compared with the Rasch model in its standard form. They also show the units of the scales were more accurately equated. The paper discusses implications for applied measurement using Rasch models and contrasts the approach with the application of the two parameter logistic (2PL) model.