Estimates and Estimators: connecting model to data
The essential attributes of a Rasch model are sufficient statistics and separable parameters, which allow, but don’t guarantee, specific objectivity. Well, actually sufficient statistics come pretty close if they really are sufficient to capture all the relevant information in the data. We will come back to this in the discussion of what Rasch called control of the model and most of us call goodness of fit. The current topic is a demonstration, more intuitive than mathematical, of how to manipulate the model to estimate item difficulties.
The process begins with the basic Rasch model for how likely the person wins when one person takes one dichotomous item: . . . The Disappearing Beta Trick