Study of population heterogeneity in innovation diffusion model: Estimation based on simulated annealing

摘要

Parameter variability randomness in diffusion (PVRD) models based on random differential equations have recently been developed to study stochastic evolution of adopters. Analysis of such models is found to generate multimodal life cycle patterns (or intervening slumps) besides the conventional unimodal pattern. Application of these models to real data sets necessitate estimation of parameters of the model. Nonlinear least squares estimation problem is formulated to deal with the minimization of high-dimensional cost function. Using the simulated annealing (SA) framework, effectiveness of the estimation approach and the fitting algorithm is demonstrated in terms of "fit statistics." An important finding from empirical studies reveal that even in unimodal life cycle patterns, parameters of innovation diffusion process are found to possess considerable variability. This finding amply demonstrates the presence of heterogeneity on account of population variability.