A canonical sequential aggregation media model
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Estimating the number of individuals who may see or hear an advertisement and the number of times these individuals will be exposed to the advertisement is a foundation of advertising management. A reach and frequency exposure estimation model is one method that provides this information, which is fundamental to effective media decision making. The main purpose of this study is to explore a new sequential aggregation media exposure model that resolves some inherent limitations and improves accuracy of available non-proprietary media models. Moreover, to reconcile some issues raised in advertising exposure models, this study develops and examines variations of newly developed sequential aggregation models by a range of criteria and ways of aggregation. To accomplish this purpose, first, seven previously developed exposure distribution models—the Binomial Distribution (BIN), the Beta Binomial Distribution (BBD), the Hofmans Beta Binomial Distribution (HBBD), the Dirichlet Multinomial Distribution (DMD), the Canonical Expansion Distribution (CANEX), the Conditional Beta Distribution (CBD), and the Morgensztern Sequential Aggregation Distribution (MSAD)—were compared against the newly developed model, the Canonical Sequential Aggregation (CSD). Then, eighteen CSD variations were developed to find out the effects of aggregation order in the sequential aggregation model utilizing the same canonical expansion reach formula but different aggregation orders by the size of audience variables and ways of aggregation. In total, twenty-six media exposure distribution models (eight main models plus eighteen CSD variations) were evaluated against U.S. Web audience behaviors based on 560 tabulated random schedules from 2003 comScore data. CANEX, CBD, and CSD media models were the most accurate both in reach and exposure distribution estimations. Among them, the CSD model was the most appropriate for using in practice since it accurately estimates reach and exposure distributions without generating negative exposure in a short time. The investigation of order of aggregation resolves the ‘declining reach’ issue, which influences the generation of reach and exposure distribution estimations: the ‘backward’ way of aggregation prevents the declining reach in CSD models. From a practical perspective, however, this study discourages the argument of Chandon (1976) and Lee (1988) that the order of aggregation is an important factor influencing the accuracy in estimation of sequential aggregation models.