Modeling non-linear Behavior of Independent Variables
Yousaf Shad Muhammad, Munawar Iqbal, Ijaz Hussain, Shahid Kamal, Nouman Afgan

Abstract
The modeling non-linear behavior between independent variables and response variable remained a challenging task for the researchers. We consider precipitation data set for two monitoring stations for twenty seven years period during monsoon. Generalized linear models, Generalized additive model and piecewise regression models are used to find appropriate model to describe the characteristics of dependent variable related to independent. The results of these models are compared by means of cross validation and coefficient of determination. It is observed that generalized linear model perform poorly then generalized additive model and piecewise regression model. Since generalized additive model is non-parametric and is more flexible to model non-linear behavior therefore it also explains more variation of dependent variable then piecewise regression models. However,the difference between generalized additive model and piecewise regression model becomes negligible if segmented points are observed from generalized additive model and then those segmented points are used to estimate piecewise regression.

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