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 (S(i) = 0, 1, ..., k(i), 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) = SIGMA(i=1)m S(i), 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, ..., S(m)). 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.