A Guide to Legal Research in the University of Michigan Law Library (3rd ed.)

In preparing this revision of the Guide to Legal Research in the University of Michigan Law Library, we have followed respectfully the precepts established in previous editions. As before, the Guide has been written to be primarily of benefit to the students at the University of Michigan School of Law. We hope, however, that it will also be helpful to anyone who uses this collection extensively. It is not meant to be a comprehensive treatise on all, or even a few, forms of legal research. That has been done elsewhere, many times, and need not be repeated here. Instead, our purpose has been to give our readers a thorough listing of this library\u27s services and rules, a basic overview of American legal research, and a succinct explanation of some of the more important, or baffling, aspects of legal research. All of this is related, of course, to this library; consequently, we have devoted little space to describing material that we do not have

Customer-Base Analysis using Repeated Cross-Sectional Summary (RCSS) Data

We address a critical question that many firms are facing today: Can customer data be stored and analyzed in an easy-to-manage and scalable manner without significantly compromising the inferences that can be made about the customers’ transaction activity? We address this question in the context of customer-base analysis. A number of researchers have developed customer-base analysis models that perform very well given detailed individual-level data. We explore the possibility of estimating these models using aggregated data summaries alone, namely repeated cross-sectional summaries (RCSS) of the transaction data. Such summaries are easy to create, visualize, and distribute, irrespective of the size of the customer base. An added advantage of the RCSS data structure is that individual customers cannot be identified, which makes it desirable from a data privacy and security viewpoint as well. We focus on the widely used Pareto/NBD model and carry out a comprehensive simulation study covering a vast spectrum of market scenarios. We find that the RCSS format of four quarterly histograms serves as a suitable substitute for individual-level data. We confirm the results of the simulations on a real dataset of purchasing from an online fashion retailer

New Perspectives on Customer “Death” Using a Generalization of the Pareto/NBD Model

Several researchers have proposed models of buyer behavior in noncontractual settings that assume that customers are “alive” for some period of time and then become permanently inactive. The best-known such model is the Pareto/NBD, which assumes that customer attrition (dropout or “death”) can occur at any point in calendar time. A recent alternative model, the BG/NBD, assumes that customer attrition follows a Bernoulli “coin-flipping” process that occurs in “transaction time” (i.e., after every purchase occasion). Although the modification results in a model that is much easier to implement, it means that heavy buyers have more opportunities to “die.” In this paper, we develop a model with a discrete-time dropout process tied to calendar time. Specifically, we assume that every customer periodically “flips a coin” to determine whether she “drops out” or continues as a customer. For the component of purchasing while alive, we maintain the assumptions of the Pareto/NBD and BG/NBD models. This periodic death opportunity (PDO) model allows us to take a closer look at how assumptions about customer death influence model fit and various metrics typically used by managers to characterize a cohort of customers. When the time period after which each customer makes her dropout decision (which we call period length) is very small, we show analytically that the PDO model reduces to the Pareto/NBD. When the period length is longer than the calibration period, the dropout process is “shut off,” and the PDO model collapses to the negative binomial distribution (NBD) model. By systematically varying the period length between these limits, we can explore the full spectrum of models between the “continuous-time-death” Pareto/NBD and the naïve “no-death” NBD. In covering this spectrum, the PDO model performs at least as well as either of these models; our empirical analysis demonstrates the superior performance of the PDO model on two data sets. We also show that the different models provide significantly different estimates of both purchasing-related and death-related metrics for both data sets, and these differences can be quite dramatic for the death-related metrics. As more researchers and managers make managerial judgments that directly relate to the death process, we assert that the model employed to generate these metrics should be chosen carefully

Estimating CLV Using Aggregated Data: The Tuscan Lifestyles Case Revisited

The Tuscan Lifestyles case (Mason, 2003) offers a simple twist on the standard view of how to value a newly acquired customer, highlighting how standard retention-based approaches to the calculation of expected customer lifetime value (CLV) are not applicable in a noncontractual setting. Using the data presented in the case (a series of annual histograms showing the aggregate distribution of purchases for two different cohorts of customers newly “acquired” by a catalog marketer), it is a simple exercise to compute an estimate of “expected 5 year CLV.” If we wish to arrive at an estimate of CLV that includes the customer\u27s “life” beyond five years or are interested in, say, sorting out the purchasing process (while “alive”) from the attrition process, we need to use a formal model of buying behavior that can be applied on such coarse data. To tackle this problem, we utilize the Pareto/NBD model developed by Schmittlein, Morrison, and Colombo (1987). However, existing analytical results do not allow us to estimate the model parameters using the data summaries presented in the case. We therefore derive an expression that enables us to do this. The resulting parameter estimates and subsequent calculations offer useful insights that could not have been obtained without the formal model. For instance, we were able to decompose the lifetime value into four factors, namely purchasing while active, dropout, surge in sales in the first year and monetary value of the average purchase. We observed a kind of “triple jeopardy” in that the more valuable cohort proved to be better on the three most critical factors

A New Method for Laminar Boundary Layer Transition Visualization in Flight: Color Changes in Liquid Crystal Coatings

The visualization of laminar to turbulent boundary layer transition plays an important role in flight and wind tunnel aerodynamic testing of aircraft wing and body surfaces. Visualization can help provide a more complete understanding of both transition location as well as transition modes; without visualization, the transition process can be very difficult to understand. In the past, the most valuable transition visualization methods for fight applications included sublimating chemicals and oil flows. Each method has advantages and limitations. In particular, sublimating chemicals are impractical to use in subsonic applications much above 20,000 feet because of the greatly reduced rates of sublimation at lower temperatures (less than -4 degrees Fahrenheit). Both oil flow and sublimating chemicals have the disadvantage of providing only one good data point per flight. Thus, for many important flight conditions, transition visualization has not been readily available. This paper discusses a new method for visualizing transition in fight by the use of liquid crystals. The new method overcomes the limitations of past techniques, and provides transition visualization capability throughout almost the entire altitude and speed ranges of virtually all subsonic aircraft flight envelopes. The method also has wide applicability for supersonic transition visualization in flight and for general use in wind tunnel research over wide subsonic and supersonic speed ranges

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single twodimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: (1) we allow for non-linear projection manifolds (the basic building block is the Generative Topographic Mapping – GTM), (2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, (3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold’s local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.Final Accepted Versio

Counting Your Customers the Easy Way: An Alternative to the Pareto/NBD Model

Today’s managers are very interested in predicting the future purchasing patterns of their customers, which can then serve as an input into “lifetime value” calculations. Among the models that provide such capabilities, the Pareto/NBD “counting your customers” framework proposed by Schmittlein et al. (1987) is highly regarded. However, despite the respect it has earned, it has proven to be a difficult model to implement, particularly because of computational challenges associated with parameter estimation. We develop a new model, the beta-geometric/NBD (BG/NBD), which represents a slight variation in the behavioral “story” associated with the Pareto/NBD but is vastly easier to implement. We show, for instance, how its parameters can be obtained quite easily in Microsoft Excel. The two models yield very similar results in a wide variety of purchasing environments, leading us to suggest that the BG/NBD could be viewed as an attractive alternative to the Pareto/NBD in most applications

Bayesian Inference for the Negative Binomial Distribution via Polynomial Expansions

To date, Bayesian inferences for the negative binomial distribution (NBD) have relied on computationally intensive numerical methods (e.g., Markov chain Monte Carlo) as it is thought that the posterior densities of interest are not amenable to closed-form integration. In this article, we present a “closed-form” solution to the Bayesian inference problem for the NBD that can be written as a sum of polynomial terms. The key insight is to approximate the ratio of two gamma functions using a polynomial expansion, which then allows for the use of a conjugate prior. Given this approximation, we arrive at closed-form expressions for the moments of both the marginal posterior densities and the predictive distribution by integrating the terms of the polynomial expansion in turn (now feasible due to conjugacy). We demonstrate via a large-scale simulation that this approach is very accurate and that the corresponding gains in computing time are quite substantial. Furthermore, even in cases where the computing gains are more modest our approach provides a method for obtaining starting values for other algorithms, and a method for data exploration

AAS, growth hormone, and insulin abuse: psychological and neuroendocrine effects

The nontherapeutic use of prescription medicines by individuals involved in sport is increasing. Anabolic-androgenic steroids (AAS) are the most widely abused drug. Much of our knowledge of the psychological and physiological effects of human growth hormone (hGH) and insulin has been learned from deficiency states. As a consequence of the Internet revolution, previously unobtainable and expensive designer drugs, particularly recombinant human growth hormone (rhGH) and insulin, have become freely available at ridiculously discounted prices from countries such as China and are being abused. These drugs have various physiological and psychological effects and medical personnel must become aware that such prescription medicine abuse appears to be used not only for performance and cosmetic reasons, but as a consequence of psychological pre-morbidity