To link, then to equate
It’s not possible to equate if you didn’t bother to link. In my language, to link means to physically connect; to equate means to do the arithmetic ensuring interchangeable logit scores. Equating is just another version of controlling the model so we could use everything we have just learned about controlling ourselves. But since we are looking for a different kind of answer, it is worth treating as its own topic.
Unleashing the full power of Rasch measurement means identifying, perhaps conceiving an important aspect, defining a useful construct, and calibrating a pool of relevant items that measure it over a meaningful range. So far we have concerned ourselves with processing isolated bunches of items. In this world, linking and equating item sets has been treated as a distinct and unique phase in the process from conception to measurement. With the technology available, this has typically been the most convenient and efficient approach, and may continue to be so.
In the new world, post fixed-form, paper-based instruments, which are more and more passé, building a calibrated pool can be an inherent and natural part of the process and not a separate step. Calibration procedures allow us to combine individual level test data across administrations, perhaps years apart, to check if specific objectivity holds across time or distance. This is just another between-groups comparison, which gives more opportunities for control and investigation of the process.
Continue . . . Linking and Equating