Influential observations in principal component analysis:a case study

A number of results have been derived recently concerning the influence of individual observations in a principal component analysis. Some of these results, particularly those based on the correlation matrix, are applied to data consisting of seven anatomical measurements on students. The data have a correlation structure which is fairly typical of many found in allometry. This case study shows that theoretical influence functions often provide good estimates of the actual changes observed when individual observations are deleted from a principal component analysis. Different observations may be influential for different aspects of the principal component analysis (coefficients, variances and scores of principal components); these differences, and the distinction between outlying and influential observations are discussed in the context of the case study. A number of other complications, such as switching and rotation of principal components when an observation is deleted, are also illustrated.     

Variations in carambola infestation rates byBactrocera carambolae drew and hancock (Diptera: Tephritidae) with fruit availability in a carambola orchard

The relationship between the infestation rate of carambola fruits byBactrocera carambolae Drew and Hancock was investigated in a carambola orchard. Phenology of the fruits was found to influence percentage infestation of fruits byB. carambolae. The proportion of unbagged or susceptible fruits infested varied with time of year and tended to decrease with the increase of unbagged fruits available on the tree. The number of ovipunctures per fruit varied with fruit size and was also found to be indicative of the number of adult insects (B. carambolae and parasitoids) that will emerge from each fruit. Higher number of susceptible fruits available on each tree also decreased both the number of ovipunctures per fruit and the number of eggs laid per fruit, which could possibly be due to the strategy of spreading the risk adopted by the femaleB. carambolae or a result of random selection with more hosts available. The main parasitoids recorded wereBiosteres vandenboschi (Fullaway) andB. arisanus (Sonan). The mean percentage of parasitism was 38.3% and it followed roughly that of infestation of fruits.     

Bayes and empirical Bayes shrinkage estimation of regression coefficients

For a moderate or large number of regression coefficients, shrinkage estimates towards an overall mean are obtained by Bayes and empirical Bayes methods. For a special case, the Bayes and empirical Bayes shrinking weights are shown to be asymptotically equivalent as the amount of shrinkage goes to zero. Based on comparisons between Bayes and empirical Bayes solutions, a modification of the empirical Bayes shrinking weights designed to guard against unreasonable overshrinking is suggested. A numerical example is given.     

Finnish incomes policy: Unions and other constraints

This paper charts the evolution of incomes policy in Finland. Especial emphasis is placed on the constraints on incomes policy that have operated here, as indeed in other Nordic countries, ultimately to curb the corporatist experiment.     

Plague mortality rates by age and sex in the parish of St. Botolph's without Bishopsgate, London, 1603

Abstract The Bills of Mortality for London were instituted at least as early as 1528 but only a few figures survive before the extant annual series that begins in 1603. Ages at death, even in broad groups of ages, are not generally available until 1728, which is more than 50 years too late to give us any inkling of the ages, if any, at which people were specially susceptible to plague. There are reports, it is true, that suggest that children suffered from plague more severely than adults, at least on certain occasions (as in 1361 or 1418 for example), but nothing more precise. The legend of the Pied Piper of Hamelin may be a folk-memory of a plague (possibly in 1284) that killed mainly the children of the town, for the connection between infestation of rats and the loss of children suggests some kind of plague outbreak. Pollitzer concludes that no particular age group is specially liable to plague, and attributes all differences observed to different risks of exposure. The determinants of the severity of an outbreak would therefore be the environmental details and social customs.     

Bayesian break-point forecasting in parallel time series,with application to university admissions

A regular supply of applicants to Queen's University in Kingston, Ontario is provided by 65 high schools. Each high school can be characterized by a series of grading standards which change from year to year. To aid admissions decisions, it is desirable to forecast the current year's grading standards for all 65 high schools using grading standards estimated from past year's data. We develop and apply a Bayesian break-point time-series model that generates forecasts which involve smoothing across time for each school and smoothing across schools. “Break point” refers to a point in time which divides the past into the “old past” and the “recent past” where the yearly observations in the recent past are exchangeable with the observations in the year to be forecast. We show that this model works fairly well when applied to 11 years of Queen's University data. The model can be applied to other data sets with the parallel time-series structure and short history, and can be extended in several ways to more complicated structures.     

Family Therapy Following the Death of a Child*

The reactions of the entire family system to the death of a child are examined. The case illustrates therapeutic interventions dealing with changes in family structure, guilt and mourning processes in parents, anxiety and other reactions of children, and the cognitive confusion of both children and adults. The problems for the therapist in working with a family following the death of a child are discussed.     

Gambling: A Social Problem?

This paper reports the results from a national survey of gambling behavior, social problems, and attitudes toward the legalization of gambling. Non-bettors perceived more negative consequences and fewer positive consequences associated with the legalization of gambling than did bettors. One negative consequence perceived by a majority of both groups was an increase in political corruption. The level of gambling activity was positively associated with several social problems such as divorce, absenteeism, and frequency of alcohol consumption. Respondents who were classified as probable compulsive gamblers reported more family problems.