A new Method for Optimization of log Likelihood Function for the purpose of Determining the Coefficients of Accident Prediction Models

In statistical modeling of accidents, exact determination of model coefficients is crucial because it expresses how and how much the dependent variable relates to the independent variables (an incorrect coefficient can result in an incorrect modeling). To determine these coefficients, usually a log likelihood function is optimized using the "gradient vector", "Quasi- Newton" and "Newton-Raphson" numerical methods which all depend on the "Hessian Matrix" and have drawbacks such as slow convergence, high dependency on the initial value and possibility of convergence at a point other than the real highest peak. In this paper, to minimize the above mentioned drawbacks and make a more appropriate model for determination of the coefficients, a new method has been presented in which the "Hessian Matrix" has been eliminated from the "optimized pace length function" of the "vector gradient method" using some mathematical techniques, the results of applying this method on a "road safety performance function", (using the accident and traffic volume data in 160 sections of Iranian urban roads), show that, for the optimization process, the proposed method is independent of the starting moving point and creates convergence of a log likelihood function at the highest possible peak.