Modelling bivariate exposure distributions for Out of Home advertising

Abstract

Out of Home advertising is traditional outdoor advertising. Over the last decade the digital Out of Home advertising possibilities have grown substantially. These possibilities include hour-based advertisement schedules, rapidly implemented changes to advertisements and obtaining location data from consumers being exposed to advertisements. Investigating these possibilities further for improving customer engagement and optimising target group reach is of great importance in marketing and marketing science. This thesis will focus on exposure data obtained from vehicle locations in central London. Using this data we want to model the frequency with which individuals see advertisements and research the overlap in exposures of individuals to multiple media vehicles where advertisements are displayed. We focus on modelling exposures of individuals to two vehicles, comparing different types of bivariate distributions. In this thesis we present the comparison of two models: an adapted version of the Sarmanov bivariate distribution and copulas. We refer to these models as the Danaher and Copula model respectively.

The fitting and simulations of the models are based on bivariate data of two specified vehicles, to be able to comment on the overlap between these vehicles. To investigate the performance of the models all combinations of vehicles are modelled after which the results are combined. Both models simulate small frequencies of exposures of individuals adequate, but for more extreme values both models fail to represent the observed data. Especially the simulation of overlap is done poorly by the models. Several approaches have been tried to improve the models' performance, without much success. The analysis shows that the data at hand requires more sophisticated methods to handle joint exposure and more research needs to be done.

In addition the variable distance is added to the research problem, which intuitively has great influence on the overlap between media vehicles. This is done by using 3-dimensional copulas. For this research we modify the data: instead of first fitting and simulating a copula model on the data of two vehicles and then combining the results of all vehicle combinations, we first combine the data from all the combinations of vehicles and repeat the fitting procedure thereafter. Several options for the modelling of these copulas are presented. Similar analysis shows, again, that the nature of the data requires more complex models to handle the overlap while also accounting for the vehicle distance. Finally, using the modified data we look back at the 2-dimensional copula model and perceive an excellent resemblance of the data for the Student-t copula.