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Table 1 Summary table of key terms

From: Mokken scale analysis of mental health and well-being questionnaire item responses: a non-parametric IRT method in empirical research for applied health researchers

Key term Explanation
Mokken models Two probabilistic models (MHM and DMM, see below) which relax strict assumptions on the shape of the ICCs imposed by traditional parametric models such as Rasch or two-parameter logistic model.
Latent trait (θ) Latent construct intended to be assessed with a scale
Item A question in a measure (linked to response category options)
Item characteristic curve (ICC) Probability of endorsement of specific response category as a function of latent trait
Unidimensionality Scale under consideration measures a single latent trait
Monotonicity ICC is a monotonically increasing function, i.e the higher the value of latent trait, the higher is the ICC; actually it may be the same, but not lower.
Non-intersection ICCs that do not intersect with each other
Monotone homogeneity model (MHM) Mokken model assuming unidimensionality, monotonicity, and local independence of items within a scale. After these assumptions are checked, respondents can be ordered according to the simple sum score of items (at least for scales that consist of binary responses)
Double monotonicity model (DMM) Mokken model assuming unidimensionality, monotonicity, local independence and non-intersection of items within a scale. If these assumptions are met then (additionally to MHM features) items have IIO property.
Scalability coefficient Index of homogeneity of item pairs (H ij ), items (H i ) and scale (H) used in assessment of unidimensionality.
Invariant item ordering (IIO) Items have the same “difficulty” ordering irrespective of value of latent trait. Consequences resulting from IIO are described in the introduction section.