Exploring multivariate data graphically:a brief review with examples

Many methods for obtaining graphical representations of multivariate data have been suggested over the last decade, but it is only relatively recently that software has become available which makes use of these procedures routine. In this paper, a number of examples are used to illustrate the application of graphical methods for the exploration of multivariate data. The diagrams produced may prove useful in consultations with clients and in examining the results from more formal methods.     

Membranes, mitochondria and amoebae: shape models

Most real-world shapes and images are characterized by high variability- they are not rigid, like crystals, for example—but they are strongly structured. Therefore, a fundamental task in the understanding and analysis of such image ensembles is the construction of models that incorporate both variability and structure in a mathematically precise way. The global shape models introduced in Grenander's general pattern theory are intended to do this. In this paper, we describe the representation of two-dimensional mitochondria and membranes in electron microscope photographs, and three-dimensional amoebae in optical sectioning microscopy. There are three kinds of variability to all of these patterns, which these representations accommodate. The first is the variability in shape and viewing orientation. For this, the typical structure is represented via linear, circular and spherical templates, with the variability accomodated via the application of transformations applied to the templates. The transformations form groups: scale, rotation and translation. They are locally applied throughout the continuum and of high dimension. The second is the textural variability; the inside and outside of these basic shapes are subject to random variation, as well as sensor noise. For this, statistical sensor models and Markov random field texture models are used to connect the constituent structures of the shapes to the measured data. The third variability type is associated with the fact that each scene is made up of a variable number of shapes; this number is not assumed to be known a priori. Each scene has a variable number of parameters encoding the transformations of the templates appropriate for that scene. For this, a single posterior distribution is defined over the countable union of spaces representing models of varying numbers of shapes. Bayesian inference is performed via computation of the conditional expectation of the parametrically defined shapes under the posterior. These conditional mean estimates are generated using jump-diffusion processes. Results for membranes, mitochondria and amoebae are shown.     

The impact of unionization,right-to-work laws,and female labor force participation on earnings inequality across states

This study examines the effect of unionization, right-to-work laws, and participation of women in the labor force on income inequality. Two distinct models are developed using 1970 and 1980 census data on the 50 states in the U.S. First, an income inequality model is specified as a beta distribution of the second kind to estimate Gini measures of income inequality. Second, these Gini estimates are used in a simultaneous equations model. The 1970 results indicate that higher unionization rates decreased inequality while right-to-work laws increased inequality. In 1980, the measure of inequality was lower in states with higher female labor force participation. We thank an unknown referee and the editor for comments and criticisms that greatly improved the paper. The usual caveat applies.     

Sources of drug information among adolescent students

A sample of 1023 eighth and tenth grade students in small to medium-sized central Texas school districts was assessed to determine the amount of information they receive from ten sources about six categories of drugs. The amount of information males reported receiving about each drug category was significantly greater than what females reported, and the amount of information that eighth graders reported receiving about each drug category was significantly greater than what tenth graders reported. Television was the primary source of drug information for all categories of drugs except inhalants, for which friends and television were equally important sources. Parents and printed media (magazines or newspapers) were of secondary importance, followed by friends and teachers. Adolescents were less likely to receive drug-related information from experience, siblings, church, doctors, and police. The reliance on the mass media for drug information in smaller school districts is a pattern which has been previously observed in larger urban districts. This consistency suggests that mass media approaches to drug education are likely to be as effective in rural areas and smaller towns as they are among urban adolescents. Implications for television programming are discussed.     

Book Review: Beyond Earth Day: Fulfilling the Promise. Gaylord Nelson with Susan Campbell and Paul Wozniak. Madison,WI: The University of Wisconsin Press, 2002: 160 pp.

Population and Environment -     

Government Risk Management Priorities: A Comparison of the Preferences of Asian Indian Americans and Other Americans

A survey was conducted of approximately 200 Asian Indian Americans and 200 other residents of New Jersey in order to understand the risk management priorities that they want government to have. We found that Asian Indian Americans, especially younger women, focused on personal/family risks, such as alcohol and drug abuse, sexual abuse, and domestic violence. The New Jersey comparison group, in contrast, placed war/terrorism and loss of health care services and insurance at the top of their priorities for government. These results suggest stressful acculturation-related issues within the Asian Indian community. Both populations want more risk management from government than they believe government is currently providing. Respondents who wanted more from government tended to dread the risk, be fearful of the consequences, trust government, and have a feeling of personal efficacy. Within the Asian Indian American sample, wide variations were observed by language spoken at home and religious affiliation. Notably, Muslims and Hindi language speakers tended not to trust government and hence wanted less government involvement. This study supports our call for studies of recent migrant populations and Johnson's for testing ethnic identity and acculturation as factors in risk judgments.     

An Experimental Evaluation of the Serial Cost Sharing Rule

This paper proposes an experimental test to evaluate the performance of the serial cost sharing rule, originally proposed by Shenker [Sigmetrics, 241–242 (1990)] and then analyzed by Moulin and Shenker [Econometrica 60, 1009–1037 (1992)]. We report measures of the performance and efficiency of the serial mechanism by comparing the choices and payoffs attained by the subjects to the expected equilibrium allocations. Experimental evidence shows that learning is needed for the subjects to converge to the equilibrium strategy. However, in terms of efficiency, the serial mechanism leads to almost efficient allocations.