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. |