On the Construction of Adjacent Categories Latent Trait Models from Binary Variables, Motivating Processes and the Interpretation of Parameters

Latent trait models have a mathematical representation that provides a link between person and item parameters and the probability of a response in categories. The usefulness of specific models is mainly determined by the motivation of models, the interpretation of parameters and the narratives around models. The focus is on the partial credit model, for which differing and contradicting motivations, interpretations and narratives have been given over time. It is shown that the model can be derived by assuming that binary Rasch models hold for binary variables that are always present in multi-categorical response models. An alternative derivation is based on binary Rasch models for latent variables that compare adjacent categories. It is shown that the PCM can generally be characterized as a model that conditionally compares two categories from the set of response categories. The representation as an adjacent categories model can be seen as just a specific parameterization. It is demonstrated that the confusion of these alternative binary variables in the PCM can be misleading and generate inappropriate interpretation of parameters