A FORTRAN 77 program for a nonparametric item response model: The Mokken scale analysis

Abstract

A nonparametric item response theory model-the Mokken scale analysis (a stochastic elaboration of the deterministic Guttman scale}-and a computer program that performs this analysis are described. Three procedures of scaling are distinguished: a search procedure, an evaluation of the whole set of items, and an extension of an existing scale. All procedures provide a coefficient of scalability for all items that meet the criteria of the Mokken model and an item coefficient of scalability for every item. Four different types of reliability coefficient are computed both for the entire set of items and for the scalable items. A test of robustness of the found scale can be performed to analyze whether the scale is invariant across different subgroups or samples. This robustness test serves as a goodness offit test for the established scale. The program is written in FORTRAN 77. Two versions are available, an SPSS-X procedure program (which can be used with the SPSS-X mainframe package) and a stand-alone program suitable for both mainframe and microcomputers.The Mokken scale model is a stochastic elaboration of the well-known deterministic Guttman scale (Mokken, 1971; Mokken & Lewis, 1982;Mokken, Lewis, & Sytsma, 1986). The Mokken model is applied to dichotomous items for which one alternative is designated as positive with respect to the latent variable of interest (attitude, ability, etc.). This model belongs to the general family of the popular item response theory models (Mokken & Lewis, 1982). The Mokken model has been shown to be very useful for scaling social attitudes, political knowledge, political participation, and political efficacy (Gillespie, Ten Vergert, & Kingma, 1987a, 1987bLippert, Schneider, & Wakenhut, 1978; Mokken, 1969a Mokken, , 1969bStokman, 1977;Stokman & Van Schuur, 1980). In psychological research, the Mokken model has been applied successfully to the construction of developmental scales of Piagetian concepts (Kingma, 1984; Kingma & Loth, 1985;Kingma & Reuvekamp, 1984;Kingma & Ten Vergert, 1985; Kingma & Van den Bos, in press), as well as to cumulative scaling of problem solving tasks (Henning, 1976) and sleep quality (Mokken & Lewis, 1982). The purpose of this paper is to describe a user procedure FORTRAN 77 program (which can be used with SPSS-X) and a stand-alone Fortran 77 program of which both mainframe and MS-DOS versions are available. These programs, both named Mokscal, perform the Mokken scale analysis. Before presenting a review of the program and the various statistics, we describe in shorthand the underlying assumptions of the Mokken model, which are crucial for the appreciation of this rather unknown model. THE MOKKEN MODELThe Mokken model treats the attitude, the ability, or any other variable of interest as a single latent trait on which the person's location is represented by the parameter (J and the item's location is represented by the parameter o. Given a reasonably unidimensional set of items-that is, one dominated by the latent variable measured-the person's parame...