Nonlinear Poisson regression using neural networks: a simulation study

We describe a novel extension of the Poisson regression model to be based on a multi-layer perceptron, a type of neural network. This relaxes the assumptions of the traditional Poisson regression model, while including it as a special case. In this paper, we describe neural network regression models with six different schemes and compare their performances in three simulated data sets, namely one linear and two nonlinear cases. From the simulation study it is found that the Poisson regression models work well when the linearity assumption is correct, but the neural network models can largely improve the prediction in nonlinear situations.