A Markov Mixture Model for Magazine Exposure
作者:
PeterJ. Danaher,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1989)
卷期:
Volume 84,
issue 408
页码: 922-926
ISSN:0162-1459
年代: 1989
DOI:10.1080/01621459.1989.10478856
出版商: Taylor & Francis Group
关键词: Beta-binomial model;Magazine-exposure distribution;Markov chain;Modified beta-binomial model
数据来源: Taylor
摘要:
A magazine-exposure model that mixes Klotz's (1973) dependent Bernoulli-trials model for nonsubscribers with a degenerate distribution for subscribers is proposed. LetXi= 1 if a person reads an issue of a particular magazine and 0 otherwise. Klotz's parameterization is Pr(Xi= 1) =pand Pr(Xi= 1 |Xi–1= 1) = λ fori= 1, …,k.Using the Markov assumption he obtains the joint distribution ofR= Σki=2Xi–1Xi, S= Σki=1Xi, andT = X1+Xk, of which we are interested in the marginal distribution ofS, the total number of issues a person reads. It is expected thatpwill 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 pointS=k.Maximum likelihood estimates ofp, 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.
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