A multivariate media exposure model consisting of a truncated canonical expansion of the joint exposure probability is developed. The first term of the expansion is the product of the univariate marginal probabilities, resulting in a model that is a generalization of Goodhardt and Ehrenberg's “duplication of viewing law.” The proposed model is compared on the basis of estimation accuracy and computation speed with an accurate and quick “approximate” loglinear model and the popular Metheringham beta-binomial model. For large schedules the canonical expansion is more accurate than the approximate loglinear model but the reverse is true for small schedules. In addition, the proposed model is shown to be six times faster than the approximate loglinear model and much more accurate than Metheringham's model.
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References
1.
AitkenA. C., and GoninH. T. (1935), “On Fourfold Sampling With and Without Replacement,”Proceedings of the Royal Society of Edinburgh, 55, 114–25.
2.
BoydMarsha M. (1985), “The Dirichlet Multivariate Multinomial Distribution as a Magazine Exposure Model,” PhD dissertation, University of Illinois at Urbana.
3.
ChandonJean-Louis J. (1976), “A Comparative Study of Media Exposure Models,” PhD dissertation, Northwestern University.
4.
DanaherPeter J. (1988a), “A Loglinear Model for Predicting Magazine Audiences,”Journal of Marketing Research, 25(November), 356–62.
5.
DanaherPeter J. (1988b), “Parameter Estimation and Applications for a Generalisation of the Beta-Binomial Distribution,”Australian Journal of Statistics, 30(December), 263–75.
6.
DanaherPeter J. (1989a), “An Approximate Loglinear Model for Predicting Magazine Audiences,”Journal of Marketing Research, 26(November), 473–9.
7.
DanaherPeter J. (1989b), “A Markov Mixture Model for Magazine Exposure,”Journal of the American Statistical Association, 84(December), 922–6.
8.
DemingW. Edwards, and StephanFrederick F. (1940), “On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals Are Known,”Annals of Mathematical Statistics, 11, 427–44.
9.
GoodhardtG. J., and EhrenbergA. S. C. (1969), “Duplication of Television Viewing Between and Within Channels,”Journal of Marketing Research, 6(May), 169–78.
10.
HamdanM. A., and JensenD. R. (1976), “A Bivariate Binomial Distribution and Some Applications,”Australian Journal of Statistics, 18(December), 163–9.
11.
HeadenRobert S., KlompmakerJay E., and RustRoland T. (1979), “The Duplication of Viewing Law and Television Media Schedule Evaluation,”Journal of Marketing Research, 26(August), 333–40
12.
HilleEinar, and SalasSaturnino L. (1968), First-Year Calculus.Waltham, MA: Blaisdell.
13.
KishiShizue (1983), “Exposure Distribution Models in Advertising Media,” unpublished PhD dissertation, University of Illinois at Urbana.
14.
LancasterH. O. (1969), The Chi-Squared Distribution.New York: John Wiley & Sons, Inc.
15.
LancasterH. O. (1971), “The Multiplicative Definition of Interaction,”Australian Journal of Statistics, 13(1), 36–44.
16.
LeckenbyJohn D., and BoydMarsha M. (1984), “How Media Directors View Reach/Frequency Model Evaluation Standards,”Journal of Advertising Research, 25(October), 43–52.
17.
LeckenbyJohn D., and KishiShizue (1982a), “Performance of Four Exposure Distribution Models,”Journal of Advertising Research, 22(April), 35–44.
18.
LeckenbyJohn D., and KishiShizue (1982b), “How Media Directors View Reach/Frequency Estimation,”Journal of Advertising Research, 22(June), 64–9.
19.
LeckenbyJohn D., and KishiShizue (1984), “The Dirichlet-Multinomial Distribution as a Magazine Exposure Model,”Journal of Marketing Research, 21(February), 100–6.
20.
LeeA. M., and BurkartA. J. (1960), “Some Optimization Problems in Advertising Media Planning,”Operational Research Quarterly, 11(3), 113–22.
21.
MetheringhamRichard A. (1964), “Measuring the Net Cumulative Coverage of a Print Campaign,”Journal of Advertising Research, 4(December), 23–8.
22.
MorrisonDonald G. (1979), “Purchase Intentions and Purchasing Behavior,”Journal of Marketing, 43(Spring), 65–74.
23.
RoyS. N., and KastenbaumM. A. (1956), “On the Hypothesis of No ‘Interaction’ in Multiway Contingency Tables,”Annals of Mathematical Statistics, 27, 749–57.
24.
RustRoland T. (1986), Advertising Media Models: A Practical Guide.Lexington, MA: Lexington Books.
25.
RustRoland T., and LeoneRobert P. (1984), “The Mixed Media Dirichlet-Multinomial Distribution: A Model for Evaluating Television-Magazine Advertising Schedules,”Journal of Marketing Research, 21(February), 89–99.
26.
RustRoland T., ZimmerMary R., and LeoneRobert P. (1986), “Estimating the Duplicated Audience of Media Vehicles in National Advertising Schedules,”Journal of Advertising, 15(3), 30–7.
27.
SchreiberRobert J. (1969), “The Metheringham Method for Media Mix: An Evaluation,”Journal of Advertising Research, 9(June), 54–6.
