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. 

Keywords

• system R-square
• adjusted system R-square
• goodness–of–fit
• a system-of-equations model
• contemporaneous correlation.