Maximum likelihood estimation of parameters for double poisson regression: a simulation study

Double Poisson Regression is specifically designed for regression of count variables and allows estimation of the parameters of a regression equation together with a dispersion parameter. Different computational procedures for obtaining maximum likelihood estimates of these parameters are possible. The objective of this contribution is to narrow down which of these computational procedures work best. Four different attributes of the computational procedures are investigated: (1) treatment of the normalisation factor in the Double Poisson with the two specifications: setting this factor equal to 1, and approximating this factor; (2) general estimation strategy with the two specifications: estimating the parameters of the regression equation and the dispersion parameters simultaneously, and estimating them sequentially; (3) starting value for the dispersion parameter with the two specifications: setting this value equal to 1, and computing it from data; and (4) algorithm with three variants of the Newton–Raphson algorithm, two variants of the BHHH algorithm and two variants of the BFGS algorithm as specifications. The four attributes of the computational procedures are investigated using simulation studies. The results of these studies show that the treatment of the normalisation factor very strongly affects parameter estimates and the quality of parameter estimation, whereas the other three attributes have no practically relevant effects. Moreover, the two treatments of the normalisation factor have opposite effects for different evaluation criteria. Therefore, neither treatment can be preferred. In data analyses, both treatments should be applied parallel to each other for sensitivity analysis.