Signposts on the Path From Nominal to Ordinal Scales: Moving From a Discrete to a Continuous View.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistics

Background:

• Polytomous item response data are often simplified into nominal or ordinal categories.
• This binary classification may not fully capture the nuanced structure of response data.
• A more flexible approach is needed to assess category ordering.

Purpose of the Study:

• To reframe the nominal-ordinal distinction as a continuum.
• To introduce and evaluate empirical indices for quantifying category ordering in polytomous item response data.
• To provide tools for more accurate measurement and model selection.

Main Methods:

• Development of six empirical indices to quantify category ordering.
• Extensive simulations using various item response theory (IRT) models.
• Application to 245 empirical datasets to assess index performance.

Main Results:

• Two parametric indices, Mean Difference between Slope Parameters (Index 5) and Arctangent of Paired Category Ratios (Index 6), demonstrated robustness and informativeness.
• These indices are effective even with low-frequency categories.
• The proposed indices offer a practical method for assessing ordinal assumptions in item response data.

Conclusions:

• Treating category ordering as a continuum provides deeper insights than a binary nominal-ordinal distinction.
• The developed indices enhance psychometric practice by offering a practical tool for model selection and measurement accuracy.
• This approach strengthens the link between empirical response patterns and theoretical representations in item response theory.