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 Mokken's nonparametric item response theory approach.
Grayson, D.A. (1988). Two-group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383-392.
5.
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: Princeton University Press.
6.
Holland, P.W. (1981). When are item response models consistent with observed data? Psychometrika, 46, 79-92.
7.
Holland, P.W., & Rosenbaum, P.R. (1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 14, 1523-1543.
Kingma, J., & TenVergert, E.M. (1985). A nonparametric scale analysis of the development of conservation. Applied Psychological Measurement, 9, 375-387.
10.
Lewis, C. (1983). Bayesian inference for latent abilities. In S. B. Anderson & J. S. Helmick (Eds.), On Educational Testing (pp. 224-251). San Francisco: Jossey-Bass.
11.
Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin,45, 507-530.
12.
Lord, F.M. (1980). Applications of item response theory to practical testing problems. Hillsdale NJ: Erlbaum.
13.
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
14.
Lumsden, J. (1978). Tests are perfectly reliable. British Journal of Mathematical and Statistical Psychology, 31, 19-26.
15.
Meijer, R.R., Sijtsma, K., & Smid, N.G. (1990). Theoretical and empirical comparison of the Mokken and the Rasch approach to IRT. Applied Psychological Measurement , 14, 283-298.
16.
Mokken, R.J. (1971). A theory and procedure of scale analysis. New York/Berlin: De Gruyter .
17.
Mokken, R.J., & Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417-430.
18.
Mokken, R.J., Lewis, C., & Sijtsma, K. (1986). Rejoinder to "The Mokken scale: A critical discussion ." Applied Psychological Measurement, 10, 279-285.
19.
Molenaar, I.W. (1982). Een tweede weging van de Mokken-schaal [A second weighing of the Mokken scaling procedure]. Tijdschrift voor Onderwijsresearch, 7, 172-181.
20.
Molenaar, I.W. (1983). Rasch, Mokken en schoolbeleving [Rasch, Mokken, and school experience]. In S. Lindenberg & F. N. Stokman (Eds.), Modellen in de Sociologie (pp. 195-213). Deventer: Van Loghum Slaterus.
21.
Rosenbaum, P.R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425-435.
