Uncovering Audience Preferences for Concert Features from Single-Ticket Sales with a Factor-Analytic Random-Coefficients Model

Abstract

To better plan their programs, producers of performing arts events need forecasting models that relate ticket sales to the multiple features of a program. The framework we develop, test and implement uncovers audience preferences for the features of an event program from single-ticket sales, while accounting for interactions among program features and for preference heterogeneity across markets. We develop a factor-analytic random-coefficients model that overcomes four major methodological challenges. First, the historical data available from each market is limited, preventing the estimation of models at the market level, and requiring some form of shrinkage estimator that also takes into account the diversity in preferences across markets, as well as the fact that preferences for the many (26 in our application) program features are correlated across markets, requiring the estimation of a large covariance matrix for these preferences across markets. Our proposed factor-analytic regression formulation parsimoniously captures the principal components of the correlated preferences and provides shrinkage estimates at the individual market level. The second challenge we face is the fact that orchestras differ on how they sell season subscriptions, leading to substantial unobserved effects on ticket sales across orchestras; an added benefit of our random-coefficients approach is that it incorporates a random effect that captures any shift in the dependent variable caused by unobservable factors across all events in each individual market, such as the unobservable effect of season subscriptions on single-ticket sales.

The third methodological challenge is that program features are likely to interact requiring the estimation of a large set of pair-wise interactions. We solve this problem by mapping the interactions on a reduced space, arriving at a more parsimonious model formulation. The fourth methodological challenge relates to implementation of the model results beyond the relatively small sample of markets for which historical data was available. To overcome this limitation, we demonstrate how our model can be applied to markets not included in our sample, first using only managerial insight regarding the similarity between the focal market and the ones in our sample and by updating this subjective prior as ticket sales data become available.

Keywords: factor-analytic regression, forecasting, response modeling