An automated item selection procedure for selecting unidimensional scales of polytomous items from multi dimensional datasets is developed for use in the context of the Mokken item response theory model of monotone homogeneity (Mokken & Lewis, 1982). The selection procedure is directly based on the selection procedure proposed by Mokken (1971, p. 187) and relies heavily on the scalability coefficient H (Loevinger, 1948; Molenaar, 1991). New theoretical results relating the latent model structure to H are provided. The item selec tion procedure requires selection of a lower bound for H. A simulation study determined ranges of H for which the unidimensional item sets were retrieved from multidimensional datasets. If multidimensionality is suspected in an empirical dataset, well-chosen lower bound values can be used effectively to detect the unidi mensional scales.
Batley, R.M., & Boss, M.W. (1993). The effects on parameter estimation of correlated dimensions and a distribution-restricted trait in a multidimensional item response model. Applied Psychological Measurement, 17, 131-141.
2.
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick, Statistical theories of mental test scores (pp. 396-479). Reading MA: Addison-Wesley.
3.
Cavalini, P.M. (1992). It's an ill wind that brings no good. Studies on odour annoyance and the dispersion of odor-ant concentrations from industries . Unpublished doctoral dissertation, University of Groningen , The Netherlands.
4.
de Gruijter, D.N.M. (1993). Comparison of the nonparametric Mokken model and parametric IRT models using latent class analysis. Applied Psychological Measurement, 18, 27-34.
5.
Ellis, J.L., & van den Wollenberg, A.L. (1993). Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model . Psychometrika, 58, 417-429.
6.
Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9, 255-282.
7.
Guttman, L. (1950). The basis for scalogram analysis. In S. A. Stouffer, L. Guttman , E. A. Suchman, P. F. Lazarsfeld, S. A. Star, & J. A. Clausen (Eds.), Measurement and prediction (pp. 60-90). Princeton NJ: Princeton University Press.
8.
Hemker, B.T., & Sijtsma, K. (1993). A practical comparison between the weighted and the unweighted scalability coefficient of the Mokken model. Kwantitatieve Methoden, 14(44), 59-73.
9.
Junker, B.W. (1993). Conditional association, essential independence and monotone unidimensional item response models. The Annals of Statistics, 21, 1359-1378.
10.
Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin, 45, 507-530.
11.
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
12.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
13.
Meijer, R.R., Sijtsma, K., & Molenaar, I.W. (1995). Reliability estimation for single dichotomous items based on Mokken's IRT model. Applied Psychological Measurement, 19, 323-335.
14.
Meijer, R.R., Sijtsma, K., & Smid, N. (1990). Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT. Applied Psychological Measurement , 14, 283-298.
15.
Mokken, R.J. (1971). A theory and procedure of scale analysis. New York/Berlin: De Gruyter .
16.
Mokken, R.J., & Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417-430.
17.
Mokken, R.J., Lewis, C., & Sijtsma, K. (1986). Rejoinder to "The Mokken scale: A critical discussion ." Applied Psychological Measurement, 10, 279-285.
Molenaar, I.W. (1986). Een vingeroefening in item response theorie voor drie geordende antwoordcategorieen [An exercise in item response theory for three ordered response categories]. In G. F. Pikkemaat & J. J. A. Moors (Eds.), Liber amicorum Jaap Muilwijk (pp. 39-57). Groningen : Econometrisch Instituut.
20.
Molenaar, I.W. (1991). A weighted Loevinger H-coefficient extending Mokken scaling to multicategory items. Kwantitatieve Methoden, 12(37), 97-117.
21.
Molenaar, I.W. (in press). Nonparametric models for polytomous responses. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern psychometrics (pp. 361-373). New York: Springer .
22.
Molenaar, I.W., Debets, P., Sijtsma, K., & Hemker, B.T. (1994). User's manual for the computer program MSP (Ver. 3.0. Groningen: iec ProGAMMA, Rijksuniversiteit Groningen.
23.
Reckase, M.D., & McKinley, R.L. (1991). The discriminating power of items that measure more than one dimension. Applied Psychological Measurement, 15, 361-373.
Samejima, F. (1969). Estimation of latent trait ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.
26.
Sijtsma, K., & Prins, P.M. (1986). Itemselectie in het Mokken model [Item selection in the Mokken model]. Tijdschrift voor Onderwijsresearch, 11, 121-129.
27.
Stout, W. (1990). A new item response theory modelling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 49, 293-325.
28.
Wood, R. (1978). Fitting the Rasch model-A heady tale. British Journal of Mathematical and Statistical Psychology, 31, 27-32.
