Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance

Abstract

A maximum likelihood approach is proposed for estimating an innovation diffusion model of new product acceptance originally considered by Bass (Bass, F. M. 1969. A new product growth model for consumer durables. Management Sci. 15 (January) 215–227.). The suggested approach allows: (1) computation of approximate standard errors for the diffusion model parameters, and (2) determination of the required sample size for forecasting the adoption level to any desired degree of accuracy. Using histograms from eight different product innovations, the maximum likelihood estimates are shown to outperform estimates from a model calibrated using ordinary least squares, in terms of both goodness of fit measures and one-step ahead forecasts. However, these advantages are not obtained without cost. The coefficients of innovation and imitation are easily interpreted in terms of the expected adoption pattern, but individual adoption times must be assumed to represent independent draws from this distribution. In addition, instead of using standard linear regression, another (simple) program must be employed to estimate the model. Thus, tradeoffs between the maximum likelihood and least squares approaches are also discussed.