A Fast Method for Agent-Based Model Fitting of Aggregate-Level Diffusion Data

Abstract

This paper provides theoretical arguments and simulation evidence regarding how a differential equation-based diffusion model (DE) can be used to improve the efficiency of an agent-based model (ABM) fitting market-level diffusion data. Using computational experiments, we observe that the DE fits ABM diffusion processes very well and that the linear correlativity between the ABM parameters and their corresponding DE estimates is very well in a wide range of settings. However, as significantly systematic biased forecasts of the DE for ABM diffusion processes exist, the ABM cannot be replaced by the DE to forecast real-world diffusion. Based on these findings, we design a fast parameter estimation method for the ABM by integrating the DE into a component to locate an initial point near the optimal solution.The empirical study demonstrates that the proposed procedure can search out the optimal solution by evaluating only a small number of points. Furthermore, the empirical study also demonstrates that certain ABMs and the simple averaging method have better explanatory and forecasting performance than the DE. This method prepares the ABM to forecast innovation diffusion and also makes a contribution to the literature on the validation of ABM.

Keywords: Forecasting, Agent-based model, Bass model, Networks, New product diffusion