Multivariate beta binomial distribution model as a web media exposure model
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This study develops and tests a new multivariate distribution model for the estimation of advertising vehicle exposure. The new multivariate distribution model is developed as three versions (i.e., one which doesn't adjust negative probabilities, and the others which adjust negative probabilities in unvariate distributions). In addition, eight other media exposure models are evaluated against a database of 440 tabulated schedules constructed from 2003 comScore network data. The types of models tested include: three univariate models -- the Binomial Distribution Model (BIN), the Beta Binomial Distribution Model (BBD), and the Hofmans Beta Binomial Distribution Model (HBBD); three multivariate models -- the Dirichlet Multinomial Distribution Model (DMD), the Canonical Expansion Model (CANEX), and the Conditional Beta Distribution Model (CBD); and one aggregation model -- the Morgensztern Sequential Aggregation Model (MSAD). All of the models tested are based on probability distributions. Some models are a combination of probability distributions and ad hoc methods. In addition, the approximation model of the MBD called the Hyper Beta Distribution Model (HBD), is described and tested. The accuracy of the eleven models is assessed via two evaluation criteria of model performance -- the Average Percentage Error in Reach (AER) and the Average Percentage Error in Exposure Distribution (APE). All models are compared according to their relative overall accuracy as assessed by the two error measures. The proposed new multivariate model -- the Multivariate Beta Binomial Distribution Model (MBD) -- was generally more accurate than the other models for the estimation of reach. For the estimation of the exposure distribution, the model proved more accurate than the Binomial Distribution Model (BIN), the Beta Binomial Distribution Model (BBD), the Hofmans Beta Binomial Distribution Model (HBBD), and the Dirichlet Multinomial Distribution Model (DMD), but less accurate than the Canonical Expansion Model (CANEX), the Conditional Beta Distribution Model (CBD), the Morgensztern Sequential Aggregation Model (MSAD), and Hyper Beta Distribution Model (HBD). This study provides the foundation for further improvement of the model, along with recommendations for further investigation, since the theoretical potential for the performance of the model is high.