Jason A. Duan

Path to Purchase: A Mutually Exciting Point Process Model for Online Advertising and Conversion

This paper studies the effects of various types of online advertisements on purchase conversion by capturing the dynamic interactions among advertisement clicks themselves. It is motivated by the observation that certain advertisement clicks may not result in immediate purchases, but they stimulate subsequent clicks on other advertisements, which then lead to purchases. We develop a novel model based on mutually exciting point processes, which consider advertisement clicks and purchases as dependent random events in continuous time. We incorporate individual random effects to account for consumer heterogeneity and cast the model in the Bayesian hierarchical framework. We construct conversion probability to properly evaluate the conversion effects of online advertisements. We develop simulation algorithms for mutually exciting point processes to compute the conversion probability and for out-of-sample prediction. Model comparison results show the proposed model outperforms the benchmark models that ignore exciting effects among advertisement clicks. Using a proprietary data set, we find that display advertisements have relatively low direct effect on purchase conversion, but they are more likely to stimulate subsequent visits through other advertisement formats. We show that the commonly used measure of conversion rate is biased in favor of search advertisements and underestimates the conversion effect of display advertisements the most. Our model also furnishes a useful tool to predict future purchases and advertisement clicks for the purpose of targeted marketing and customer relationship management. This paper was accepted by Eric Bradlow, special issue on business analytics.

The Role of Spatial Demand on Outlet Location and Pricing

In this paper we consider the problem of outlet pricing and location in the context of unobserved spatial demand. Our analysis constitutes a scenario wherein capacity-constrained firms set prices conditioned on their location, demand and costs. This enables firms to develop maps of latent demand patterns across the market in which they compete. The analysis further suggests locations for additional outlets and the resulting equilibrium effect on profits and prices. Using Bayesian spatial statistics, we apply our model to seven years of data regarding apartment location and prices in Roanoke, Virginia. We find spatial covariation in demand to be material in outlet choice; the 95% spatial decay in demand extends 7.5 miles in a region measuring slightly over 9.5 miles. We further find that capacity constraints can cost complexes upwards of

Modeling space-time data using stochastic differential equations

193 per apartment. As predicted, price elasticities and costs are biased downward when spatial covariance in demand is ignored. Using our analysis to suggest locations for entry, we find that a proper accounting of spatial effects and capacity constraints leads to an entry recommendation that improves profitability by 66% over a model that ignores these effects.

Managing User-Generated Content: A Dynamic Rational Expectations Equilibrium Approach

This paper demonstrates the use and value of stochastic difierential equations for modeling space-time data in two common settings. The flrst consists of point-referenced or geostatistical data where observations are collected at flxed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochas- tic difierential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that afiords mean- ingful interpretation for the results of statistical inference. Other applications of stochastic logistic difierential equations with space-time varying parameters in- clude modeling population growth and product difiusion, which motivate our flrst, point-referenced data application. We propose a method to discretize both time and space in order to flt the model. We demonstrate the inference for the geosta- tistical model through a simulated dataset. Then, we flt the Cox process model to a real dataset taken from the greater Dallas metropolitan area.

Commentary---Reexamining Bayesian Model-Comparison Evidence of Cross-Brand Pass-Through

This paper considers the creation and consumption of content on user-generated content platforms, e.g., reviews, articles, chat, videos, etc. On these platforms, users’ expectations regarding the amount and timing of participation by others becomes germane to their own involvement levels. Accordingly, we develop a dynamic rational expectations equilibrium model of joint consumption and generation of information. We estimate the model on a novel data set from a large Internet forum site and offer recommendations regarding strategies of managing sponsored content and content quality.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mksc.2015.0937 .

Generalized Spatial Dirichlet Process Models

Using the Bayes factor estimated by harmonic mean [Newton, M. A., A. E. Raftery. 1994. Approximate Bayesian inference by the weighted likelihood bootstrap. J. Roy. Statist. Soc. Ser. B.56(1) 3--48] to compare models with and without cross-brand pass-through, Dube and Gupta [Dube, J.-P., S. Gupta. 2008. Cross-brand pass-through in supermarket pricing. Marketing Sci.27(3) 324--333] found that, in the refrigerated orange juice category, a model with cross-brand pass-through was selected 68% of the time. However, Lenk [Lenk, P. J. 2009. Simulation pseudo-bias correction to the harmonic mean estimator of integrated likelihoods. J. Comput. Graph. Statist.18(1) 941--960] has demonstrated that the infinite variance harmonic mean estimator often exhibits simulation pseudo-bias in favor of more complex models. We replicate the results of Dube and Gupta in the refrigerated orange juice category and then show that any of three more stable finite variance estimators select the model with cross-brand pass-through less than 1% of the time. Relaxing the assumption that model errors are distributed normally eliminates all instances in which the cross-brand pass-through model is selected. In 10 additional categories, the harmonic-mean-estimated Bayes factor selects the model with cross-brand pass-through 69% of the time, whereas a finite variance estimator of the Bayes factor selects the model with cross-brand pass-through only 5% of the time. Applying arguments in McAlister [McAlister, L. 2007. Cross-brand pass-through: Fact or artifact? Marketing Sci.26(6) 876--898], these 5% of cases can be attributed to capitalization on chance. We conclude that Dube and Gupta should not be interpreted as providing evidence of cross-brand pass-through.