A Canonical Expansion Model for Multivariate Media Exposure Distributions: A Generalization of the “Duplication of Viewing Law”

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.

[1]  Jean-Louis Chandon,et al.  A comparative study of media exposure models , 1976 .

[2]  Marvin A. Kastenbaum,et al.  On the Hypothesis of No "Interaction" In a Multi-way Contingency Table , 1956 .

[3]  D. G. Morrison.  Purchase Intentions and Purchase Behavior , 1979 .

[4]  Roland T. Rust,et al.  The Duplication of Viewing Law and Television Media Schedule Evaluation , 1979 .

[5]  Robert P. Leone,et al.  Estimating the Duplicated Audience of Media Vehicles in National Advertising Schedules , 1986 .

[6]  A. M. Lee,et al.  Some Optimization Problems in Advertising Media Planning , 1960 .

[7]  A. C. Aitken,et al.  XI.—On Fourfold Sampling with and without Replacement , 1936 .

[8]  Peter J. Danaher,et al.  PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION , 1988 .

[9]  H. O. Lancaster.  The chi-squared distribution , 1971 .

[10]  Andrew Ehrenberg,et al.  Duplication of Television Viewing between and within Channels , 1969 .

[11]  D. R. Jensen,et al.  A BIVARIATE BINOMIAL DISTRIBUTION AND SOME APPLICATIONS1 , 1976 .

[12]  Peter J. Danaher,et al.  A Log-Linear Model for Predicting Magazine Audiences , 1988 .

[13]  Peter J. Danaher,et al.  An Approximate Log-Linear Model for Predicting Magazine Audiences , 1989 .

[14]  Roland T. Rust,et al.  The Mixed-Media Dirichlet Multinomial Distribution: A Model for Evaluating Television-Magazine Advertising Schedules , 1984 .

[15]  H. O. Lancaster.  The Multiplicative Definition of Interaction , 1971 .

[16]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[17]  Makoto Abe,et al.  A Moving Ellipsoid Method for Nonparametric Regression and its Application to Logit Diagnostics with Scanner Data , 1991 .

[18]  Charlotte H. Mason,et al.  Collinearity, power, and interpretation of multiple regression analysis. , 1991 .

[19]  Roland T. Rust,et al.  Advertising Media Models: A Practical Guide , 1986 .

[20]  John D. Leckenby,et al.  The Dirichlet Multinomial Distribution as a Magazine Exposure Model , 1984 .

[21]  Peter J. Danaher.  A Markov mixture model for magazine exposure , 1989 .