ABSTRACT
This chapter focuses on two measurement theories for ratings within the scaling tradition based on Item Response Theory. It examines the adjacent-category models using Rasch Measurement Theory and cumulative-probability models because they are the most widely used in practice. The chapter focuses on describing and comparing two major measurement models within the scaling tradition that have been proposed for ratings based on the research of G. Rasch and F. Samejima. It describes two approaches for analyzing ratings within the scaling tradition: the Partial Credit Model and the Graded Response Model. The chapter provides some of the key advances related to the conceptualization and modeling of categorical and polytomous data. Psychophysical models can be used to connect unobservable latent variables to probabilities of observing discrete and categorical responses. Adjacent category models focus on directly estimating category response functions, while cumulative category models require two steps that involve first estimating the operating characteristic functions, and estimating the category response functions.
