Klaas Sijtsma

Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT

The Mokken model of monotone homogeneity, the Mokken model of double monotonicity, and the Rasch model are theoretically and empirically compared. These models are compared with respect to restrictiveness to empirical test data, properties of the scale, and accuracy of measurement. Appli cation of goodness-of-fit procedures to empirical data largely confirmed the expected order of the models according to restrictiveness: Almost all items were in concordance with the model of mono tone homogeneity, and fewer items complied with the model of double monotonicity and the Rasch model. The model of monotone homogeneity was found to be a suitable alternative to more restric tive models for basic testing applications; more sophisticated applications, such as equating and adaptive testing, appear to require the use of para metric models.

Mokken scale analysis for polychotomous items: theory, a computer program and an empirical application

This paper contains three subjects. First, an extension of Mokkens nonparametric item response models from dichotomous items to items with two or more ordered answer categories is proposed. Second, a computer program to analyze multicategory item scores is presented. This program is called MSP. The analyses by means of MSP are based on the multicategory extension of Mokkens theory. Finally, an application of MSP to empirical multicategory test data is presented in order to illuminate its possibilities.

A method for investigating the intersection of item response functions in Mokken's nonparametric IRT model

For a set of k items having nonintersecting item response functions (IRFS), the H coefficient (Loevinger, 1948; Mokken, 1971) applied to a transposed persons by items binary matrix HT has a non-negative value. Based on this result, a method is proposed for using HT to investigate whether a set of IRFS intersect. Results from a monte carlo study support the proposed use of HT. These results support the use of HT as an exten sion to Mokkens nonparametric item response theory approach.

Rejoinder to "The Mokken scale: a critical discussion

The nonparametric approach to constructing and evaluating tests based on binary items proposed by Mokken has been criticized by Roskam, van den Wol lenberg, and Jansen. It is contended that their argu ments misrepresent the objectives of this approach, that their criticisms of the role of the H coefficient in the procedures are irrelevant or erroneous, and that they fail to distinguish the inherent requirements (and limitations) of general nonparametric models and pro cedures from those of parametric ones. It is concluded that Mokkens procedures provide a useful tool for re searchers in the social sciences who wish to construct and evaluate tests for measuring theoretically mean ingful latent traits while avoiding the strong parametric assumptions of traditional item response theory.

The Linear Logistic Test Model and heterogeneity of cognitive strategies

Some properties of the Linear Logistic Test Model (LLTM) are discussed. Two prerequisites should be met in order to test a cognitive model by means of the LLTM. First, the items used in testing the cognitive model should make up a Rasch homogeneous scale. Second, the population under consideration should be homogeneous with regard to the cognitive strategy employed in solving items representing the task at hand. For a task consisting of solving balance problems it is demonstrated that the second prerequisite is not fulfilled As a consequence the LLTM does not fit for the whole population. By dividing the population into four strategy homogeneous subpopulations a fitting LLTM could be found within one of these subpopulations. Consequently, it is recommended that in using the LLTM for testing cognitive models the population under consideration should be investigated with respect to different cognitive strategies.

MSP: A Computer Program for Item Analysis According to a Nonparametric IRT Approach

A computer program is presented for item analysis according to the nonparametric approach to item response theory as proposed by Mokken. Item scores may be either polychotomous or dichotomous.