A Goodness-of-Fit Measure for the Mokken Double Monotonicity Model that Takes into Account the Size of Deviations

Based on Mokken model and Isotonic Regression, Rivas Moya (2000b) gives a Global Deviation (GD) measure from the Double Monotonicity (DM). This paper illustrates the GD measure and gives the procedure to calculate it. Several examples from responses of 294 subjects to 16 dichotomous items showed (1) the procedure which calculates the GD measure from P00 and P11 matrices obtained by MSP5 (Molenaar et al., 2000) (2) GD is 0 if there are no individual deviations from DM (3) an increase in the number and/or size of individual deviations from DM leads to an increase in GD measure when accumulative scales with different numbers of items are considered. The principal advantage of this measure over other indices which evaluate DM is that the procedure to calculate GD estimates the size of deviations from DM. It also takes into account the number of deviations because it obtains the measure by summing up the deviations in each item pair. This measure provides interesting complementary information to the set of indices which evaluate the DM model. unknown publishedVersion