Local linear negative binomial nonparametric regression for predicting the number of speed violations on toll road: A theoretical discussion

In this paper, we describe a theoretical discussion about local linear negative binomial regression for predicting the number of speed violations on toll road. Data on the number of speed violations on toll roads is a count data. Count data is a non-negative integer data generated from continuous calculation process. We usually use Poisson regression to analyze count data of a response variable. But, one of infractions on Poisson regression assumption is over-dispersion. To overcome that over-dispersion we should use negative binomial nonparametric regression model approach. The negative binomial nonparametric regression model is a development of the negative binomial parametric regression model. In this research, we theoretically discuss estimation of negative binomial nonparametric regression model based on local linear estimator which is applied to data of the number of speed violations on toll roads. The estimation results of the negative binomial nonparametric regression model that we have obtained then can be used to predict the number of speed violations on toll roads so that the Ministry of Transportation together with the police can use it to take preventive measures.