A Markov mixture model for magazine exposure

A magazine-exposure model that mixes Klotz’s (1973) dependent Bernoulli-trials model for nonsubscribers with a degenerate distribution for subscribers is proposed. Let X_i = 1 if a person reads an issue of a particular magazine and 0 otherwise. Klotz’s parameterization is Pr(X_i = 1) = p and Pr(X_i = 1 ∣X_i–1 = 1) = λ for i = 1, …, k. Using the Markov assumption he obtains the joint distribution of (Equation presented), and T = X₁ + X_k, of which we are interested in the marginal distribution of S, the total number of issues a person reads. It is expected that p will be low for nonsubscribers but high for subscribers, so this heterogeneity is modeled by mixing Klotz’s Markov model with a point mass of magnitude π at the point S = k. Maximum likelihood estimates of p, λ, and π are used to fit the Markov mixture model to 40 magazines from a large print-media survey. The proposed model is shown to give a much better fit to these data than the beta-binomial model, the most popular nonproprietary magazine model, and a generalization of the beta-binomial model.