Genetic algorithm based technique for defining threshold regression models

TThis study proposes a new technique based on genetic algorithms to define threshold regression models (TR-GA). The threshold regression assumes that the behaviour of the dependent variable changes when it enters in a different regime. The change from one regime to another depends of a specific value (threshold value) of an explanatory variable (threshold variable). In this study, the threshold regression models were composed by two linear equations. The application of genetic algorithms allows evaluating, at the same time: (i) the threshold variable; (ii) the threshold value; and (iii) the statistically significant regression parameters in each regime. The aim of this study was to evaluate the performance of TR-GA models in the prediction of next day hourly average ozone (O3|d+1) concentrations. The considered predictors were hourly average concentrations of carbon monoxide (CO), nitrogen oxide (NO), nitrogen dioxide (NO2) and ozone (O3) and meteorological data (temperature - T, solar radiation - SR, relative humidity - RH and wind speed - WS). The studies were performed in the period from May 2004 to July 2004. Different TR-GA models were obtained, corresponding to different threshold variables and threshold values. Considering both training and test periods and comparing with multiple linear regression (MLR) approach, better performance indexes were achieved in four of these models. The model that presented the best results showed that the O3|d+1 change its behaviour at the temperature of 23 ºC. For temperatures below 23 ºC, O3|d+1 depended on CO, NO, NO2, SR, WS and O3, for higher temperatures, it depended on CO, NO, T, WS and O3, while for MLR, the most important variables were NO, NO2, SR, RH, WS and O3.