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

Polytomous item response data are typically classified as either nominal or ordinal, but this binary distinction may oversimplify their true structure. In this paper, we reframe the nominal-ordinal distinction as a continuum and introduce six empirical indices to quantify the degree of category ordering in item response data. Through extensive simulations with various item response theory (IRT) models and applications to 245 empirical datasets, we evaluate the indices' sensitivity, computational efficiency, and interpretability across diverse measurement contexts. Our findings show that two parametric indices-Mean Difference between Slope Parameters (Index 5) and Arctangent of Paired Category Ratios (Index 6)-are particularly robust and informative, even with low-frequency categories. These indices offer a practical tool for assessing whether and how item categories align with ordinal assumptions, supporting more accurate measurement and model selection. We conclude that treating ordering as a continuum, rather than a binary property, provides deeper insights for psychometric practice and strengthens the connection between empirical response patterns and their theoretical representations.