The Rasch Model Explained

Abstract

This Chapter explains the Rasch model for ordered response categories by demonstrating the latent response structure and process compatible with the model. This is necessary because there is some confusion in the interpretation of the parameters and the possible response process characterized by the model. The confusion arises from two main sources. First, the model has the initially counterintuitive properties that (i) the values of the estimates of the thresholds defining the boundaries between the categories on the latent continuum can be reversed relative to their natural order, and (ii) that adjacent categories cannot be combined in the sense that their probabilities can be summed to form a new category. Second, two identical models at the level of a single person responding to a single item, the so called rating and partial credit models, have been portrayed as being different in the response structure and response process compatible with the model. This Chapter studies the structure and process compatible with the Rasch model, in which subtle and unusual distinctions need to be made between the values and structure of response probabilities and between compatible and determined relationships. The Chapter demonstrates that the response process compatible with the model is one of classification in which a response in any category implies a latent response at every threshold. The Chapter concludes with an example of a response process that is compatible with the model and one that is incompatible.