Generalized Linear Model With Variable Coefficients Application Of Traffic Data

In the classical linear regression model, coefficients of the independent variables are fixed. However, in many practical problems, this assumption is too idealisti. Thus, varying coefficient models were proposed by researchers.Varying coefficient models recently gains many researchers’ attention. The model is assumed to be a linear regression model and regression coefficients are a function of other independent variables in order to increase the flexibility and adaptability of the model. In the data analysis of environmental science, geography and economic fields, the varying coefficient models are widely used.In this paper we proposed a logistic regression model with varying coefficients, where coefficients vary in time and follow an AR(1) model for simplicity. Then we give the corresponding parameter estimation method. To verify the estimation methods, we performed massive simulation studies at different sample number n and different observation period t with statistical software R.Finally, we applied the proposed model to car accident data from Department of Transportation of Michigan in US. Here we converted the injury severity into a dichotomous variable and used a logistic regression model with time varying coefficients to fit the data. The analysis of the data showed that varying coefficient model has better fit than the regular logistic regression model.