Estimation of the Dirichlet–Multinomial distribution parameter using Schur Complement based Newton-Raphson method for modeling a road safety measure

Abstract

In this article, we propose to use the Dirichlet–Multinomial distribution to generalize the conditional multinomial model used by N’Guessan et al. (2008, 2015) in the context of modeling road accident data on an experimental site. This distribution allows for an explicit formulation of the data likelihood without relying on a conditional representation. Parameter estimation is performed using the Newton–Raphson algorithm, with the invertibility of the Hessian matrix ensured through a Schur complement-based approach. This approach allows explicit determination of the inverse of the Hessian matrix. The choice of the initial parameter vector a0 which is crucial for the algorithm’s convergence, is related to the overdispersion parameter rho, whose impact is systematically investigated. The results show that for values of rho close to zero, the algorithm is more stable and converges more rapidly.