The authors examine methods by which the Dirichlet multinominal distribution (DMD) can be parameterized in the modeling of magazine media exposure distributions. The performance of alternative methods of parameter estimation of the DMD is compared with that of three other exposure distribution models. Performance is assessed in terms of accuracy of predicted versus observed distributions on 515 tabulated schedules derived from 1979 SMRB data. Results show the DMD is superior in performance to all other models tested, including the popular beta binomial distribution (BBD).
Get full access to this article
View all access options for this article.
References
1.
AakerDavid A. (1975), “ADMOD: An Advertising Decision Model,”Journal of Marketing Research, (February), 37–45.
2.
Advertising Age (1980), cover of September 11 issue.
3.
AgostiniJ. M. (1962), “Analysis of Magazine Accumulative Audience,”Journal of Advertising Research, 2(December), 24–7.
4.
BrualdiRichard A. (1977), Introduction to Combinatorics.New York: North-Holland Publishing Company.
5.
ChandonJean-Louis Jose (1976), “A Comparative Study of Media Exposure Models,” unpublished Ph.D. dissertation, Northwestern University.
6.
ChatfieldC., and GoodhardtG. (1970), “The Beta-Binomial Model for Consumer Purchasing Behavior,”Applied Statistics, 19, 240–50.
7.
ChatfieldC., and GoodhardtG. (1975), “Results Concerning Brand Choice,”Journal of Marketing Research, 12(February), 110–3.
8.
EhrenbergA. S. C., and GoodhardtG. J. (1982), “The Dirichlet: A Comprehensive Model of Buyer Behavior,”American Statistical Association Meetings, Cincinnati, Ohio.
9.
FellerWilliam (1968), An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed.New York: John Wiley & Sons, Inc.
10.
GreeneJerome D., and StockStevens J. (1967), Advertising Reach and Frequency in Magazines.New York: Market-math Inc. and Reader's Digest Association.
11.
HeadenRobert S., KlompmakerJay E., and TeelJesse E. (1977), “Predicting Audience Exposure to Spot TV Advertising Schedules,”Journal of Marketing Research, 16(February), 1–9.
12.
HofmansPierre (1966), “Measuring the Net Cumulative Coverage of Any Combination of Media,”Journal of Marketing Research, 3(August), 269–78.
13.
JeulandAbel P., BassFrank M., and WrightGordon P. (1980), “A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes,”Operations Research, 28(March-April), 255–77.
14.
JohnsonNorman L., and KotzSamuel (1969), Discrete Distributions.New York: John Wiley & Sons, Inc.
15.
JohnsonNorman L., and KotzSamuel (1972), Continuous Multivariate Distributions.New York: John Wiley & Sons, Inc.
16.
KalwaniManokar U. (1980), “Maximum Likelihood Estimation of the Multinomial-Dirichlet Distribution,” Paper No. 741 (September), Krannert Graduate School of Management, Purdue University.
17.
KishiShizue, and LeckenbyJohn D. (1981), “Error Factors in Exposure Distribution Models,” in Proceedings of the American Academy of Advertising, Gainesville, Florida.
18.
KishiShizue, and LeckenbyJohn D. (1982), “A Test of the Direct/Indirect BBD and Other Exposure Distribution Models,” in Proceedings of the American Academy of Advertising, Lincoln, Nebraska.
19.
KwerelSeymour M. (1964), “Estimating the Unduplicated Audience of a Combination of Media Vehicles: Integrated Theory and Estimation Methods,” unpublished Ph.D. dissertation, Columbia University.
20.
KwerelSeymour M. (1968), “Information Retrieval for Media Planning,”Management Science, 15(December), 137–60.
21.
KwerelSeymour M. (1969), “Estimating Unduplicated Audience and Exposure Distribution,”Journal of Advertising Research, 9(June), 46–53.
22.
KwerelSeymour M. (1975), “Most Stringent Bounds on Aggregated Probabilities of Partially Specified Dependent Probability Systems,”Journal of the American Statistical Association, 70(June), 472–79.
23.
LeckenbyJohn D. (1981), “Exposure Distribution Models: Some Estimation Methods in Application,” paper presented at the Annual Convention of the American Academy of Advertising, Gainesville, Florida.
24.
LeckenbyJohn D., and KishiShizue (1982a), “Performance of Four Exposure Distribution Models,”Journal of Advertising Research, 22(April), 35–46.
25.
LeckenbyJohn D., and KishiShizue (1982b), “How Media Directors View Reach/Frequency Estimation,”Journal of Advertising Research, 22(June), 64–9.
26.
LiebmanLeon, and LeeEdward (1974), “Reach and Frequency Estimation Services,”Journal of Advertising Research, 14(August), 23–5.
27.
LittleJohn D. C. (1969), “A Media Planning Calculus,”Operations Research (January-February), 1–35.
28.
LittleJohn D. C., and LodishLeonard M. (1966), “A Media Selection Model and Its Optimization by Dynamic Programming,”Industrial Management Review (Fall), 15–24.
29.
MauldonJ. M. (1959), “A Generalization of the Beta-Distribution,”The Annals of Mathematical Statistics, 30(June), 509–20.
30.
MetheringhamRichard A. (1964), “Measuring the Net Cumulative Coverage of a Print Campaign,”Journal of Advertising Research, 4(December), 23–8.
31.
MosimannJames E. (1962), “On the Multinomial Distribution, the Multivariate B-Distribution, and Correlations Among Proportions,”Biometrika, 49, 65–82.
32.
RiordenJohn (1958), An Introduction to Combinatorial Analysis.New York: John Wiley & Sons, Inc.
33.
RustRoland T., and KlompmakerJay E. (1981), “Improving the Estimation Procedure for the Beta Binomial TV Exposure Model,”Journal of Marketing Research, 18(November), 442–8.
34.
RustRoland T., and LeoneRobert P. (1982), “Evaluating Mixed-Media Advertising Schedules,”TIMS Marketing Measurement Conference (March).
35.
Simmons Market Research Bureau, Inc. (1979a), 7979 Study of Media and Markets.New York: Simmons Market Research Bureau, Inc.
36.
Simmons Market Research Bureau, Inc. (1979b), Technical Guide: 1979 Study of Media and Markets.New York: Simmons Market Research Bureau, Inc.
37.
TakacsLajos (1967), “On the Method of Inclusion and Exclusion,”Journal of the American Statistical Association, 62(March), 102–13.
38.
WaringE. (1792), “On the Principles of Translating Algebraic Quantities into Probable Relations and Annuities, etc.,”Cambridge University.
39.
ZufrydenFred S. (1975), “Examining the Pattern of Response Behavior in a Media Model,”Management Science (September), 116–24.
