Diagnostic Classification Models for a Mixture of Ordered and Non-ordered Response Options in Rating Scales

Area of Science:

• Psychometrics
• Educational Measurement
• Latent Trait Theory

Background:

• Ordinal rating scales often include unordered response options like "Neutral" or "Don't Know."
• Existing unidimensional item response theory (IRT) models, such as semi-ordered models, address mixed response types.
• Diagnostic Classification Models (DCMs) are used for detailed trait assessment but traditionally assume ordered responses.

Purpose of the Study:

• To extend semi-ordered models to the framework of Diagnostic Classification Models (DCMs).
• To propose a flexible framework for semi-ordered DCMs that can incorporate unordered response options.
• To analyze the relationship between unordered responses and measured latent traits.

Main Methods:

• Developed a flexible framework for semi-ordered Diagnostic Classification Models (DCMs).
• Integrated the handling of both ordered and unordered response options within the DCM framework.
• Utilized an operational study and two simulation studies to validate the proposed models.

Main Results:

• The proposed semi-ordered DCM framework successfully incorporates both ordered and unordered response options.
• The models provide accurate estimation of latent traits when dealing with mixed response types.
• The framework accommodates and extends most earlier DCMs.

Conclusions:

• Semi-ordered DCMs offer a robust approach for analyzing rating scales with mixed response options.
• This framework enhances the analysis of item and respondent characteristics in DCMs.
• The proposed models provide valuable insights into latent trait estimation with complex response structures.