Original Article |
2010, Vol.32, No.5, pp. 519-525
A goodness-of-fit measure for a system-of-equations model
Jirawan Jitthavech
pp. 519 - 525
Abstract
Two statistics, SR2 and adjusted SR2 , are developed to measure the goodness–of–fit for a system-of-equations model based on a new definition of the norm of a square matrix with positive diagonal elements, and by this overcome the shortcomings of the McElroy R2 and the system weighted R2 . The proposed measures are tested with the simulation data and the simulation results show that the proposed measures outperform the McElroy R2 and give similar results as the AIC and BIC criteria. The proposed measures are fairly constant when the irrelevant variables are eliminated but the sharp change in the measure is obviously visible when one relevant variable is eliminated from the model. The movement of the McElroy R2 statistic is very slow comparing with the other four statistics and the sharp change in the measure is not visible when one of relevant variables is eliminated.