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.     

Detecting active effects in unreplicated designs

Unreplicated factorial designs pose a difficult problem in analysis because there are no degrees of freedom left to estimate the error. Daniel [Technometrics 1 (1959), pp. 311-341] proposed an ingenious graphical method that does not require σ to be estimated. Here we try to put Daniel's method into a formal framework and lift the subjectiveness that carries. A simulation study has been conducted that shows that the proposed method behaves better than Lenth's [Technometrics 31 (1989), pp. 469-473] popular method.     

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 use of savings as a family resource management strategy to meet child rearing costs

This study examines the effect of children on family savings decisions over the life cycle. The model used is a multinomial logit budget share allocation model. The data are from the 1982 Canadian Family Expenditure Survey Data. Results indicate that the addition of a child to a family results in fewer assets being accumulated than if the child was not present. As much as 43% of direct child rearing costs may be met through this substitution out of future consumption. Closer analysis reveals that accrual of housing equity is relatively unaffected by child's presence and that substitutions occur primarily out of other types of savings instruments.The authors would like to acknowledge financial support from the Social Science and Humanities Research Council of Canada (Grant #1498-85-0005), the Department of Consumer Science, University of Wisconsin, Madison and the College of Home Economics, University of Saskatchewan. However, all opinions expressed are our own and do not necessarily reflect the views of our sponsors. Special thanks is due Susan Bruns for outstanding research and computer programming assistance. The authors accept responsibility for any errors or omissions. All correspondence should be directed to Prof. Douthitt at 1300 Linden Drive, University of Wisconsin, Madison, Wisconsin 53706.Robin A. Douthitt received her Ph.D. from Cornell University. She is an Associate Professor, Department of Consumer Science and the Institute for Research on Poverty, University of Wisconsin, Madison, WI 53706. Her research interests include the relationship between child support awards and child rearing costs, and family time use.Joanne M. Fedyk received her M.S. from the University of Saskatchewan. She is currently an Assistant Professor in the College of Home Economics, University of Saskatchewan S7N OWO, Canada. Her research interests include both the cost of raising children and the valuation of homemaking services.     

Cross-Cultural Supervision

A multicultural perspective is essential in the twenty-first century. It is projected that by the year 2010 twelve of our most populous states will have significant minority populations. Thus, the supervision triad of patient, psychoanalyst, and supervisor will most likely contain persons of differing racial-ethnic backgrounds who are confronting problems and concerns in a diverse social environment. This paper uses examples to illustrate how this diverse triad is played out.     

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.     

Renyi's entropy for residual lifetime distribution

In the present paper, we introduce and study Renyi's information measure (entropy) for residual lifetime distributions. It is shown that the proposed measure uniquely determines the distribution. We present characterizations for some lifetime models. Further, we define two new classes of life distributions based on this measure. Various properties of these classes are also given.     

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.