Published research and working papers

Bumbaca, Misra, and Rossi (2020) propose a parallelizable algorithm for estimating a large number of customer-level parameters in a Bayesian hierarchical model. However, the algorithm follows from a mathematical error in the derivation of the target posterior density, which calls into question the theoretical support for the algorithm sampling from the specified model. Adapting the algorithm to be consistent with the corrected math nullifies the claimed benefits in scalability and efficiency. Notwithstanding that error, unbiasedness requires the number of customers to be asymptotic per computational node, which is more restrictive than being asymptotic in the size of the dataset as a whole. The more the algorithm is parallelized, the greater the bias. Potential adopters should be aware that the algorithm does not sample from the exact posterior distribution, and that its ability to take advantage of distributed computing infrastructure is limited.

Making sense of massive, individual-level data is challenging: marketing researchers and analysts need flexible models that can accommodate rich patterns of heterogeneity and dynamics, work with and link diverse data types, and scale to modern data sizes. Practitioners also need tools that can quantify uncertainty in models and predictions of consumer behavior to inform optimal decision-making. In this paper, we demonstrate the promise of probabilistic machine learning (PML), which refers to the pairing of probabilistic modeling and machine learning methods, in pushing the frontier of combining flexibility, scalability, interpretability, and un- certainty quantification for building better models of consumers and their choices. Specifically, we overview both PML models and inference methods, and highlight their utility for addressing four common classes of marketing problems: (1) uncovering heterogeneity, (2) flexibly modeling nonlinearities and dynamics, (3) handling high-dimensional and unstructured data, and (4) addressing missingness, often via data fusion. We also discuss promising directions in enriching marketing models, reflecting recent developments in representation learning, causal inference, experimentation and decision-making, and theory-based behavioral modeling.

Recent criminal court reforms have required prosecutors to provide defense attorneys with broader and earlier discovery of evidence. For these discovery reforms to fulfill their aims of improved fairness and efficiency, defense attorneys must take advantage of the evidence disclosed by the prosecution. Prior studies suggest, however, that a range of factors, including low pay and high caseloads, impede effective defense representation. If similar factors hinder defense attorneys from reviewing discovery, discovery reforms would fail to meet their goals, and defendants would receive sub-standard representation. The recent adoption of digital evidence platforms by local jurisdictions allows us to study whether defense attorneys consistently fulfill their duty to review discovery. Analyzing data from digital evidence platforms used in felony cases in four Texas counties between 2018 and 2020, we examine whether and when defense attorneys fail to access evidence disclosed by the prosecution. We find that a substantial number of defense attorneys never access the discovery. The access rate varies by county, year, offense seriousness, attorney category, attorney experience, and file type. Drawing on review of prior scholarship and Bayesian analysis of the data, we discuss plausible interpretations of these variations.

Marketers use online advertising platforms to compare user responses to different ad content. But platforms’ experimentation tools deliver different ads to distinct and undetectably optimized mixes of users that vary across ads, even during the test. Because exposure to ads in the test is non-random, the estimated comparisons confound the effect of the ad content with the effect of algorithmic targeting. This means experimenters may not be learning what they think they are learning from ad A-B tests. The authors document these “divergent delivery” patterns during an online experiment for the first time. They explain how algorithmic targeting, user heterogeneity, and data aggregation conspire to confound the magnitude, and even the sign, of ad A-B test results. Analytically, the paper extends the potential outcomes model of causal inference to treat random assignment of ads and user exposure to ads as separate experimental design elements. Managerially, the authors explain why platforms lack incentives to allow experimenters to untangle the effects of ad content from proprietary algorithmic selection of users when running A-B tests. Given that experimenters have diverse reasons for comparing user responses to ads, the authors offer tailored prescriptive guidance to experimenters based on their specific goals.

In recent decades, many states have expanded discovery in criminal cases. These reforms were designed to make the criminal process fairer and more efficient. The success of these changes, however, depends on whether defense attorneys actually use the new discovery opportunities to represent their clients more effectively. Records from digital evidence platforms reveal that defense attorneys sometimes fail to carry out their professional duty to review discovery. Analyzing a novel dataset we obtained from digital evidence platforms used in Texas, we found that defense attorneys never accessed any available electronic discovery in a substantial number of felony cases between 2018 and 2020. We also found that the access rate varied by county, year, offense type, attorney category, attorney experience, and file type.

Digital advertising platforms have emerged as a widely utilized data source in consumer research; yet, the interpretation of such data remains a source of confusion for many researchers. This article aims to address this issue by offering a comprehensive and accessible review of four prominent data collection methods proposed in the marketing literature: informal studies, multiple-ad studies without holdout, single-ad studies with holdout, and multiple-ad studies with holdout. By outlining the strengths and limitations of each method, we aim to enhance understanding regarding the inferences that can and cannot be drawn from the collected data. Furthermore, we present seven recommendations to effectively leverage these tools for programmatic consumer research. These recommendations provide guidance on how to use these tools to obtain causal and non-causal evidence for the effects of marketing interventions, and the associated psychological processes, in a digital environment regulated by targeting algorithms. We also give recommendations for how to describe the testing tools and the data they generate and urge platforms to be more transparent on how these tools work.

Networks are ubiquitous in life, structuring options available for choice and influencing their relative attractiveness. In this article, we propose an integration of network science and choice theory beyond merely incorporating metrics from one area into models of the other. We posit a typology and framework for “network-choice models” that highlight the distinct ways choices occur in and influence networked environments, as well as two specific feedback processes that guide their mutual interaction, emergent valuation and contingent options. In so doing, we discuss examples, data sources, methodological challenges, anticipated benefits, and research pathways to fully interweave network and choice models.

Despite recent advances in high-speed computing, Bayesian inference in high dimensional hierarchical models remains a non-trivial undertaking. Markov chain Monte Carlo (MCMC) methods have come a long way in resolving several problems in this regard, but these methods have, in turn, introduced a different set of computational issues like monitoring convergence rates. Such issues, typically, get accentuated in marketing research and practice when non- conjugate Bayesian hierarchical models are used. Here, we use a new method to generate independent samples from posterior distributions in these types of Bayesian models, obviating many of the difficulties associated with MCMC algorithms. Challenging illustrative analysis exemplifies the ease with which one can implement this method.

When definitions of two distinct criminal offenses overlap, power to decide which definition to apply to an arrest devolves to local law enforcement agencies. This discretion can lead to unequal treatment and denial of due process, especially when disadvantaged populations are arrested for nonviolent property crimes. We present a Bayesian analysis of arrests under a vaguely worded statutory scheme for retail theft in Texas, in which a shoplifter who is guilty of property theft is also guilty of organized retail theft. Using arrest data from the Texas Department of Public Safety, we find wide variation across law enforcement agencies in initial charging categories, with black and Hispanic arrestees being charged for the more serious crime more than white arrestees. The racial discrepancy is greater for agencies serving cities with higher per-capita income. These results highlight consequences of ambiguous provisions of criminal codes, and suggest a method for identifying agencies whose policies may have disparate impact across racial and ethnic groups.

Sparse Hessian matrices occur often in statistics, and their fast and accurate estimation can improve efficiency of numerical optimization and sampling algorithms. By exploiting the known sparsity pattern of a Hessian, methods in the sparseHessianFD package require many fewer function or gradient evaluations than would be required if the Hessian were treated as dense. The package implements established graph coloring and linear substitution algorithms that were previously unavailable to R users, and is most useful when other numerical, symbolic or algorithmic methods are impractical, inefficient or unavailable.

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across indi- vidual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from a large number of units. We develop a new method to sample from posterior distributions of Bayesian models, without using MCMC. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. The algorithm is scalable under the weak assumption that individual units are conditionally independent, making it applicable for large data sets. It can also be used to compute marginal likelihoods.

Dynamic customer targeting is a common task for marketers actively managing customer relationships. Such efforts can be guided by insight into the return on investment from marketing interventions, which can be derived as the increase in the present value of a customer’s expected future transactions. Using the popular latent attrition framework, one could estimate this value by manipulating the levels of a set of nonstationary covariates. We propose such a model that incorporates transaction-specific attributes and maintains standard assumptions of unobserved heterogeneity. We demonstrate how firms can approximate an upper bound on the appropriate amount to invest in retaining a customer and demonstrate that this amount depends on customers’ past purchase activity, namely the recency and frequency of past customer purchases. Using data from a B2B service provider as our empirical application, we apply our model to estimate the revenue lost by the service provider when it fails to deliver a customer’s requested level of service. We also show that the lost revenue is larger than the corresponding expected gain from exceeding a customer’s requested level of service. We discuss the implications of our findings for marketers in terms of managing customer relationships.

Trust region algorithms are nonlinear optimization tools that tend to be stable and reliable when the objective function is non-concave, ill-conditioned, or exhibits regions that are nearly flat. Additionally, most freely-available optimization routines do not exploit the sparsity of the Hessian when such sparsity exists, as in log posterior densities of Bayesian hierarchical models. The trustOptim package for the R programming language addresses both of these issues. It is intended to be robust, scalable and efficient for a large class of nonlinear optimization problems that are often encountered in statistics, such as finding posterior modes. The user must supply the objective function, gradient and Hessian. However, when used in conjunction with the sparseHessianFD package, the user does not need to supply the exact sparse Hessian, as long as the sparsity structure is known in advance. For models with a large number of parameters, but for which most of the cross-partial derivatives are zero (i.e., the Hessian is sparse), trustOptim offers dramatic performance improvements over existing options, in terms of computational time and memory footprint.

Online advertising campaigns often consist of multiple ads, each with different creative content. We consider how various creatives in a campaign differentially affect behavior given the targeted individual’s ad impression history, as characterized by the timing and mix of previously seen ad creatives. Specifically, we examine the impact that each ad impression has on visiting and conversion behavior at the advertised brand’s website. We accommodate both observed and unobserved individual heterogeneity and take into account correlations among the rates of ad impressions, website visits, and conversions. We also allow for the accumulation and decay of advertising effects, as well as ad wearout and restoration effects. Our results highlight the importance of accommodating both the existence of multiple ad creatives in an ad campaign and the impact of an individual’s ad impression history. Simulation results suggest that online advertisers can increase the number of website visits and conversions by varying the creative content shown to an individual according to that person’s history of previous ad impressions. For our data, we show a 12.7% increase in the expected number of visits and a 13.8% increase in the expected number of conversions.

Under the sociological theory of homophily, people who are similar to one another are more likely to interact with one another. Marketers often have access to data on interactions among customers from which, with homophily as a guiding principle, inferences could be made about the underlying similarities. However, larger networks face a quadratic explosion in the number of potential interactions that need to be modeled. This scala- bility problem renders probability models of social interactions computationally infeasible for all but the smallest networks. In this paper, we develop a probabilistic framework for modeling customer interactions that is both grounded in the theory of homophily and is flexible enough to account for random variation in who interacts with whom. In particular, we present a novel Bayesian nonparametric approach, using Dirichlet processes, to moderate the scalability problems that marketing researchers encounter when working with networked data. We find that this framework is a powerful way to draw insights into latent similarities of customers, and we discuss how marketers can apply these insights to segmentation and targeting activities.

Customer retention and customer churn are key metrics of interest to marketers, but little attention has been placed on linking the different reasons for which customers churn to their value to a contractual service provider. In this paper, we put forth a hierarchical competing-risk model to jointly model when customers choose to terminate their service and why. Some of these reasons for churn can be influenced by the firm (e.g., service problems or price–value trade-offs), but others are uncontrollable (e.g., customer relocation and death). Using this framework, we demonstrate that the impact of a firm’s efforts to reduce customer churn for controllable reasons is mitigated by the prevalence of uncontrollable ones, resulting in a “damper effect” on the return from a firm’s retention marketing efforts. We use data from a provider of land-based telecommunication services to demonstrate how the competing-risk model can be used to derive a measure of the incremental customer value that a firm can expect to accrue through its efforts to delay churn, taking this damper effect into account. In addition to varying across customers based on geodemographic information, the magnitude of the damper effect depends on a customer’s tenure to date. We discuss how our framework can be used to tailor the firm’s retention strategy to individual customers, both in terms of which customers to target and when retention efforts should be deployed.

Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact inference is often intractable. Markov chain Monte Carlo techniques make approximate inference possible, but the computational cost is prohibitive on the large datasets now becoming routinely available. Variational methods provide a deterministic alternative for approximation of the posterior distribution. We derive variational procedures for empirical Bayes and fully Bayesian inference in the mixed multinomial logit model of discrete choice. The algorithms require only that we solve a sequence of unconstrained optimization problems, which are shown to be convex. One version of the procedures relies on a new approximation to the variational objective function, based on the multivariate delta method. Extensive simulations, along with an analysis of real-world data, demonstrate that variational methods achieve accuracy competitive with Markov chain Monte Carlo at a small fraction of the computational cost. Thus, variational methods permit inference on datasets that otherwise cannot be analyzed without possibly adverse simplifications of the underlying discrete choice model. Appendices C through F are available as online supplemental materials.

Virtual advisors often increase sales for those customers who find such online advice to be convenient and helpful. However, other customers take a more active role in their purchase decisions and prefer more detailed data. In general, we expect that websites are more preferred and increase sales if their characteristics (e.g., more detailed data) match customers’ cognitive styles (e.g., more analytic). “Morphing” involves automatically matching the basic “look and feel” of a website, not just the content, to cognitive styles. We infer cognitive styles from clickstream data with Bayesian updating. We then balance exploration (learning how morphing affects purchase probabilities) with exploitation (maximizing short-term sales) by solving a dynamic program (partially observable Markov decision process). The solution is made feasible in real time with expected Gittins indices. We apply the Bayesian updating and dynamic programming to an experimental BT Group (formerly British Telecom) website using data from 835 priming respondents. If we had perfect information on cognitive styles, the optimal “morph” assignments would increase purchase intentions by 21%. When cognitive styles are partially observable, dynamic programming does almost as well—purchase intentions can increase by almost 20%. If implemented system-wide, such increases represent approximately $80 million in additional revenue.

We’ve long been able to personalize what information the Internet tells us — but now comes Website Morphing, and an Internet that personalizes how we like to be told. For companies, it means that communicating — and selling — will never be the same.

We examine optimal insurance purchase decisions of individuals that ex- hibit behavior consistent with Regret Theory. Our model incorporates a utility function that assigns a disutility to outcomes that are ex post suboptimal, and predicts that individuals with regret-theoretical preferences adjust away from the extremes of full insurance and no insurance coverage. This prediction holds for both coinsurance and deductible contracts, and can explain the frequently observed preferences for low deductibles in markets for personal insurance.