Dynamic Analysis of Online Review Ratings Using a State-Space Model with Point Process Observations

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yaonan Zhang*+ and Theodoros Lappas and Uri T. Eden and Mark Crovella and Eric Kolaczyk
• Companies: Boston University and Stevens Institute of Technology and Boston University and Boston University and Boston University
• Keywords: online review ratings ; state-space model ; point process ; ordinal logistic regression ; EM

Abstract

Motivated by several articles, in both the popular press and the research community, which publicized that the average rating for top review sites is above 4 out of 5 stars, we are interested in the dynamics of online review ratings. Particularly we want to know what drives the review ratings towards such high scores. Here we look at online restaurant reviews under a state-space model, where the evolution of review intensity and review ratings are driven by a common latent process that characterizes a restaurant's popularity. We represent the latent process as a Gaussian autoregressive model. Given the latent process, review arrival is characterized as a general point process defined by its conditional intensity function, and the review rating is characterized as an ordinal logistic regression. We use an expectation-maximization (EM) algorithm, which combines several efficient signal-processing algorithms, to estimate the unobservable state-space process, its parameters, and parameters of the observation processes. We use a Kolmogorov-Smirnov test based on the time-rescaling theorem to evaluate the agreement between the model and the online restaurant review data.