PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA-BINOMIAL DISTRIBUTION

A three-parameter generalisation of the beta-binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.     

From Amazon to Apple: Modeling Online Retail Sales,Purchase Incidence,and Visit Behavior

In this study, we propose a multivariate stochastic model for Web site visit duration, page views, purchase incidence, and the sale amount for online retailers. The model is constructed by composition from carefully selected distributions and involves copula components. It allows for the strong nonlinear relationships between the sales and visit variables to be explored in detail, and can be used to construct sales predictions. The model is readily estimated using maximum likelihood, making it an attractive choice in practice given the large sample sizes that are commonplace in online retail studies. We examine a number of top-ranked U.S. online retailers, and find that the visit duration and the number of pages viewed are both related to sales, but in very different ways for different products. Using Bayesian methodology, we show how the model can be extended to a finite mixture model to account for consumer heterogeneity via latent household segmentation. The model can also be adjusted to accommodate a more accurate analysis of online retailers like apple.com that sell products at a very limited number of price points. In a validation study across a range of different Web sites, we find that the purchase incidence and sales amount are both forecast more accurately using our model, when compared to regression, probit regression, a popular data-mining method, and a survival model employed previously in an online retail study. Supplementary materials for this article are available online.     

Music and Social Movements

Music is a key component of social movements. This article addresses the relationship between music and social movements through four foci: collective identity, free space, emotions, and social movement culture. Collective identity is developed and nurtured within free spaces through the use of music. These spaces are often rife with emotions that are instrumental in development of collective identity. A social movement culture may develop as these processes unfold. Music is part of this culture and serves as an important mechanism for solidarity when participants move beyond free spaces to more contested ones. Examples of song lyrics demonstrate these processes. Research on music and social movements, it is argued here, can be enhanced by addressing technology and popular culture.     

The rudiments of an Internet-based health plan for consumers: an interview with John Danaher, MD, MBA. Interview by Richard L. Reece

Richard L. Reece, MD, interviewed John Danaher, MD, MBA, on August 16, 2000, to discuss how his new company is preparing for the perfect storm--the looming convergence of demanding consumers, defined contributions, and Internet-based health plans. He describes how his firm is putting financial and clinical tools in the hands of consumers and physicians, so consumers can be more enlightened in their health care choices. Danaher says, "We're not about buying goods and services online. We are transforming the way consumers buy health care and seek insurance. We're trying to be a 401 k where people get on, knowing their risk profile and return horizons. We aim to motivate consumers to be proactive in making health care choices. How do we make consumers responsible and motivated enough to take control of managing their health care costs? How well we articulate this call to consumer action will be the key to our success."     

How Parents Communicate Right and Wrong: A Study of Memorable Moral Messages Recalled by Emerging Adults

The family communication process through which emerging adults form their moral outlook is examined through the lenses of Negotiated Morality Theory and Vygotskian Developmental Theory. Analyses were performed on the context, content, and type of 470 memorable messages reported by 303 emerging adults. Results indicated that messages were spontaneously delivered rather than planned, communicated at home, and received at around 16 years of age. Messages most often concerned relational ethics, self-honoring, honesty/fraudulence, careless/harmful acts, and personal qualities. Eleven distinct forms of communication were used by parents, including forecasting the future, empathy-enhancing, virtue-prioritizing, commanding, and identity-making. As expected, the nature of the messages varied by the gender of the parent and the age of the child at the time of the message. Parental messages appear to be influential as young adults negotiate cultural, religious, and peer sources of morality. Implications for parents and moral educators are explored.     

Simulating Media Exposure Distributions

We examine three media exposure distribution (e.d.) simulation methods. The first is based on the maximum likelihood estimate of an individual's exposure, the second on ‘personal probability’ (Greene 1970) and the third on a dependent Bernoulli trials model (Klotz 1973). The last method uses population exposure probabilities rather than individual exposure probabilities, thereby markedly reducing computation time. Magazine exposure data are used to compare the accuracy and computation times of the simulation methods with a log–linear e.d. model (Danaher 1988b) and the popular Metheringham (1964) model based on the beta–binomial distribution (BBD). The results show that the simulation methods are not as accurate as the log– linear model but are more accurate than Metheringham's model, However, all the simulation methods take less computation time than the log–linear model for schedules with more than six magazines, making them viable competitors for large schedule sizes     

A MARKOV CHAIN MODEL FOR MAGAZINE EXPOSURE

Klotz's (1973) Markov chain model for dependent Bernoulli trials is applied to magazine exposure distributions. Simple parameter estimates are derived and are shown to compare well with the maximum likelihood estimates. The Markov model is fitted to forty magazines from a large print media survey and compares favourably with the most popular non-proprietary magazine model, the beta-binomial model. In addition, the Markov model is used to simulate magazine exposure distributions.     

An application of canonical expansions to media exposure distributions

A model for media exposure probabilities is developed which has the joint probability of exposure proportional to the product of the marginal probabilities. The model is a generalization of Goodhardt & Ehrenberg's ‘duplication of viewing law’, with the duplication constant computed from a truncated canonical expansion of the joint exposure probability. The proposed model is compared on the basis of estimation accuracy and computation speed with an accurate and quick ‘approximate’ log-linear model (as noted previously)and the popular Metheringham beta-binomial model. Our model is shown to be more accurate than the approximate log-linear model and four times faster. In addition, it is much more accurate than Metheringham's model.     

AFDC AND WORK: MAGNETS OR ANCHORS FOR THE POOR?

Literature analyzing the linkage between welfare and interstate migration is divided. Lack of consistent findings partially depends on sample used and time period when studies are done. Choice of analytical modeling technique has also led to divergent findings. This paper addresses these issues by comparing the effects of welfare and work on poor/nonpoor migration patterns using contemporary structural and household data. Findings offer no support for the welfare magnet hypothesis. Effects of Aid to Families with Dependent Children (AFDC) differ by poverty status at the place of destination for 1985 and 1990. Householders are migrating to states with lower AFDC benefits. Effects of work also differ by poverty status. For 1985, householders are moving to states with lower unemployment rates. For 1990, householders are moving to states with lower wages. In general, householders remain in states with lower AFDC benefits giving more credence to an anchor effect of higher welfare benefits.     

Parameter estimation for the dirichlet-multinomial distribution using supplementary beta-binomial data

We develop estimates for the parameters of the Dirichlet-multinomial distribution (DMD) when there is insufficient data to obtain maximum likelihood or method of moment estimates known in the literature. We do, however, have supplemetary beta-binomial data pertaining to the marginals of the DMD, and use these data when estimating the DMD parameters. A real situation and data set are given where our estimates are applicable.