A Markov-Chain Model for Multivariate Magazine-Exposure Distributions

A multivariate magazine-exposure model that generalizes Danaher's univariate model is developed. Let S i be the number of issues of magazine i a person reads (Si = 0, 1, …, ki , i = 1, …, m). My Markov-chain model considers both within- and between-magazine correlation with the result that S1,…., S m are conditionally independent given the reading outcome for the first issue of each magazine. I am ultimately interested in modeling S T = σ m i=1 Si , the total number of exposures a person has to a set of magazines, and I derive this from the model for the joint distribution of (S1 ,…, Sm ). The proposed model is shown to give a significantly better fit to observed exposure distributions than the best currently known models. Finally, I obtain the asymptotic distribution of S T , which can be used for advertising schedules with many magazines and has the benefit of being computationally much faster than my exact model.