Mokken scale

A non-parametric item response theory model

Mokken Scale

The Mokken scale is a type of non-parametric item response theory (IRT) model used in the field of psychometrics for the analysis of questionnaire data. It is named after the Dutch mathematician Rob Mokken, who developed the model in the 1970s. The Mokken scale is particularly useful for constructing and evaluating unidimensional scales, where items are assumed to measure a single latent trait.

Overview

The Mokken scale is based on the principles of monotone homogeneity and double monotonicity. These principles ensure that the items in a scale are ordered by difficulty and that the probability of a positive response increases with the level of the latent trait. Unlike parametric IRT models, such as the Rasch model, the Mokken scale does not assume a specific functional form for the item response functions.

An example of an item response function

Monotone Homogeneity

Monotone homogeneity is a key assumption of the Mokken scale. It implies that the items are ordered by difficulty, and that the probability of a positive response to an item increases with the level of the latent trait. This assumption allows for the construction of a scale where items can be ranked according to their difficulty.

Double Monotonicity

Double monotonicity extends the concept of monotone homogeneity by requiring that the item response functions do not intersect. This means that if one item is more difficult than another, it remains more difficult across all levels of the latent trait. This property ensures that the items can be ordered consistently across different levels of the trait.

Applications

The Mokken scale is widely used in the field of psychometrics for the development and validation of psychological tests and questionnaires. It is particularly useful in situations where the assumptions of parametric IRT models are not met or where a non-parametric approach is preferred.

Item response functions differing in difficulty

Scale Construction

In constructing a Mokken scale, items are selected based on their scalability, which is measured by the Loevinger's H coefficient. Items with higher H values are considered to have better scalability and are more suitable for inclusion in the scale.

Scale Evaluation

The evaluation of a Mokken scale involves assessing the fit of the items to the model's assumptions. This includes checking for violations of monotone homogeneity and double monotonicity, as well as evaluating the overall scalability of the scale.

Advantages and Limitations

The Mokken scale offers several advantages, including its flexibility and the minimal assumptions required for its application. However, it also has limitations, such as the potential for reduced precision compared to parametric models and the challenges associated with interpreting non-parametric item response functions.

Item response functions differing in discrimination

Related Pages

• Item response theory
• Rasch model
• Psychometrics
• Questionnaire