Inference in model-based cluster analysis

A new approach to cluster analysis has been introduced based on parsimonious geometric modelling of the within-group covariance matrices in a mixture of multivariate normal distributions, using hierarchical agglomeration and iterative relocation. It works well and is widely used via the MCLUST software available in S-PLUS and StatLib. However, it has several limitations: there is no assessment of the uncertainty about the classification, the partition can be suboptimal, parameter estimates are biased, the shape matrix has to be specified by the user, prior group probabilities are assumed to be equal, the method for choosing the number of groups is based on a crude approximation, and no formal way of choosing between the various possible models is included. Here, we propose a new approach which overcomes all these difficulties. It consists of exact Bayesian inference via Gibbs sampling, and the calculation of Bayes factors (for choosing the model and the number of groups) from the output using the Laplace–Metropolis estimator. It works well in several real and simulated examples.     

Kurtosis and spread

An increase in kurtosis is achieved through the location- and scale-free movement of probability mass from the “shoulders” of a distribution into its centre and tails. We introduce a coherent structure of ordering and measures, requiring no symmetry assumption, that represent different formalizations of this movement. For this purpose spread functions and spread-spread plots are defined. The orderings impose growth patterns on the spread-spread plot of the distributions involved, and the weakest involve both a specific scale-matching technique and placement of “shoulders”. The role of existing kurtosis orderings and measures in this general context is identified and examples discussed throughout.     

The Time Squeeze: Parental Statuses and Feelings About Time With Children

Policy makers, parents, and the public are concerned with perceived declines in parents’ time with children. Data from two national surveys (N = 1,159 and N = 821) used in this study show that nearly half of parents report feeling too little time with children. Work hours are strongly related to these feelings, even controlling for time spent with children, and explain why fathers more than mothers feel time strain. For fathers, those whose youngest child is an adolescent feel more strain than similarly situated mothers. Controlling for work hours, single parents are not more likely than married parents to feel that they spend insufficient time with children.     

ASYMPTOTIC LIKELIHOOD APPROXIMATIONS USING A PARTIAL LAPLACE APPROXIMATION

Elimination of a nuisance variable is often non‐trivial and may involve the evaluation of an intractable integral. One approach to evaluate these integrals is to use the Laplace approximation. This paper concentrates on a new approximation, called the partial Laplace approximation, that is useful when the integrand can be partitioned into two multiplicative disjoint functions. The technique is applied to the linear mixed model and shows that the approximate likelihood obtained can be partitioned to provide a conditional likelihood for the location parameters and a marginal likelihood for the scale parameters equivalent to restricted maximum likelihood (REML). Similarly, the partial Laplace approximation is applied to the t‐distribution to obtain an approximate REML for the scale parameter. A simulation study reveals that, in comparison to maximum likelihood, the scale parameter estimates of the t‐distribution obtained from the approximate REML show reduced bias.     

Momentum and the growth-free segment of a population

In the scenario of a sudden drop in fertility to replacement level. Preston (1986) argued that the population segment under age T, the length of generation, remained growth-free. Here we first present a new relationship for the momentum of any observed population as the ratio of 1) the proportion of the observed population under the mean age at childbearing to 2) the proportion of its life table population under that mean age. We then use that relationship to demonstrate Preston's approximation. Growth factors for other population segments are also presented. When the initial population is stable, momentum can be approximated as a function of the net reproduction rate alone.     

Peer influence and drug use among adolescents in rural areas

A sample of 1,004 eighth and tenth grade students in twenty-three small Central/East Texas communities was assessed to determine 1) their perception of the number of their friends who use drugs, 2) the amount of information they received about drugs from their friends, and 3) the connection between those perceptions and drug use. A multiple regression model which included grade, gender, the degree to which friends are perceived to use drugs and the amount of information about drugs received from friends explained 39 percent of the variance in the degree to which rural adolescents were involved in drug use. An item specific analysis of the subcomponents of these composite variables explained 44 percent of the variance in the degree to which rural adolescents were involved in drug use. This same four-factor model accurately classified over 81 percent of non-drug-users and 67 percent of users using discriminant analysis. Students who perceived a higher degree of drug use among their friends and who received more information about drugs from their friends used drugs more frequently. Lower marijuana use in these rural areas as compared to the nation, both as a peer perception and as a fact, may protect these students to a degree from broader patterns of drug use. The findings of this study support the theory that peer pressure is related to drug abuse, even in rural areas.     

Union survival strategies for the twenty-first century

Clearly, the necessary changes in the law and culture will not come easily or quickly. But, transcending all forms of these labor market segments is a set of concerns that arguably should spur a search for common ground between labor and management. The proliferation of automated technologies, together with the continuing impact of foreign competition with cheap labor markets, has led some to predict that, over the next quarter century, we will witness the elimination of the blue-collar, mass assembly-line worker from the production process.¹⁴ Moreover, the theory that those losing jobs in the manufacturing sector will be generally absorbed into the service sector is losing currency as it is becoming clear that service jobs are, themselves, not invulnerable either to offshore outsourcing (e.g., telephone operators, data processors) or to automated technology (e.g., bank tellers, office secretaries). Nor is it realistic to expect the new “knowledge sector” to absorb more than a fraction of the unemployed and underemployed casualties of this transformation. As a result, the widening gap between the haves and have nots will only continue to grow. As the trend accelerates, certain possibilities for a labor-management accommodation emerge. For one thing, although corporations may be enjoying short-term gains from present wage stagnation, downsizing, outsourcing, and casting off of permanent employees, the longer term effects include a work force with considerably diminished consumer purchasing power. In some industries, corporations are already acknowledging the adverse effects of this trend. Furthermore, as employers are contributing into pension funds on behalf of fewer and fewer “employees,” the forced savings pool that has for many years constituted a primary financing source of capital investments in our economy, will gradually be depleted.¹⁵ At the same time as employers are coming face to face with the disadvantages of the union-free environment they have so long sought, employers are also rediscovering the contributions to productivity, quality, and efficiency that can be gained from a truly empowered work force with an independent voice in the workplace. All of this should lead an enlightened management to place less currency on resisting unionization and other legitimate forms of independent employee representation, and to join labor in advocating strong labor standards and effective labor law for all four of the labor market segments that exist today and will exist tomorrow. The authors wish to convey their deep appreciation for the invaluable contributions to this paper made by David Silberman of Bredhoff & Kaiser and Craig Becker, Associate General Counsel, Service Employees International Union. Another version of this paper was published in Labor Lawyer.