Goodness of Fit Measure Based on Sample Isotone Regression of Mokken Double Monotonicity Model
Based on concepts of Mokken Double Monotonicity model (1971, 1997) and Sample Isotone Regression (Barlow, Bartholomew, Bremmer & Brunk, 1972), a model goodness of fit measure is defined. It permits interpretation of the global deviation from Double Monotonicity in a set of dichotomous response items.
To this end, based on the order induced by the difficulty of the items, the disparity function associated with the proportion of positive and negative responses to pairs of items — given in the matrices P 11 and P 00 — is defined. In each matrix, the global deviation from Double Monotonicity is obtained as the sum of discrepancies between the proportions of responses observed on pairs of items and the disparities associated with these proportions.
Unable to display preview. Download preview PDF.
- BARLOW, R.E., BARTHOLOMEW D.J., BREMNER J.M. and BRUNK H.D. (1972): Statistical Inference under order restrictions. John Wiley and Sons, London.Google Scholar
- MOKKEN, R.J. (1971): A Theory and Procedure of Scale Analysis with Applications in Political Research. Walter de Gruyter, Mouton, Berlin.Google Scholar
- MOKKEN, R.J. (1997): Nonparametric Models for Dichotomous Responses. In: W. J. van der Linden and R. K. Hambleton (Eds.): Handbook of Modern Item Response Theory. Springer, New York. 351–367.Google Scholar
- MOLENAAR, I.W., DEBETS, P., SIJTSMA, K. and HEMKER, B.T. (1994): USER’s Manual MSP4- A program for Mokken Scale Analysis for Polytomous Items. Iec ProGAMMA, Groningen.Google Scholar
- MOLENAAR, I.W. and SIJTSMA, K. (1999): USER’s Manual MSP5 for Windows. A program for Mokken Scale Analysis for Polytomous Items. Iec ProGAMMA, GroningenGoogle Scholar
- RIVAS MOYA, T. (1989): Medida de bondad del ajuste del modelo de Escalamiento Multidimensional Euclideo. Unpublished Ph. D. Thesis. Málaga University.Google Scholar
- RIVAS MOYA, T. (1998): Obtaining disparities as slopes of Greatest Minorant Convex. In: A. Rizzi, M. Vichi and H.-H. Bock (Eds.): Advances in Data Science and Classification Springer, Berlin, 509–516Google Scholar