A Class of Probabilistic Unfolding Models for Polytomous Responses

Area of Science:

• Psychometrics
• Item Response Theory
• Statistical Modeling

Background:

• The Rasch model is a foundational tool in psychometrics for analyzing binary and polytomous response data.
• Existing unfolding models for polytomous responses often lack a unified framework and clear interpretation of measurement properties.
• The rating formulation principle provides a basis for developing more general and interpretable models.

Purpose of the Study:

• To construct a general class of unfolding models for ordered polytomous responses.
• To unify previously proposed unfolding models for polytomous data as special cases.
• To enhance the interpretation of analytic and measurement properties within these models.

Main Methods:

• Revisiting and extending the Rasch model for polytomous responses.
• Applying the rating formulation principle to construct unfolding models.
• Defining latent dichotomous unfolding variables and anchoring them at the same location.
• Interpreting probabilistic functions using latitudes of acceptance parameters.

Main Results:

• A general class of unfolding models for ordered polytomous responses has been formulated.
• Previously proposed unfolding models are shown to be special cases of this general class.
• The analytic and measurement properties are well-interpreted via latitudes of acceptance.
• New specific models within this general class are readily specified.

Conclusions:

• The proposed general class of unfolding models offers a unified framework for polytomous response data.
• This formulation enhances the interpretability of measurement properties in psychometric modeling.
• The approach facilitates the development of novel unfolding models for ordered polytomous responses.