Modeling correlated effect and random effect of advertising and word-of-mouth on product diffusion

We develop a non-homogeneous Poisson model to study how the relationship between advertising and WOM and the occurrence of unexpected events affect product diffusion. For correlated effect, we generate parameters of advertising and WOM with given correlation by Copula method. For random effect, we use a Markov chain to modulate correlation between two parameters as well as distributions of two parameters. Numerical studies show that correlation between advertising and WOM speeds up diffusion process, but when considering a reasonable level within substitution or complement, managers should balance between scale of diffusion and speed of diffusion. Also, when random effect is neutral, complementary relationship creates more adoptions as unexpected events occur more frequently. Consequently, managers might be able to use correlation wisely to hedge from uncertainties.