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.     

Technical Uncertainty in Quantitative Policy Analysis — A Sulfur Air Pollution Example

Expert judgments expressed as subjective probability distributions provide an appropriate means of incorporating technical uncertainty in some quantitative policy studies. Judgments and distributions obtained from several experts allow one to explore the extent to which the conclusions reached in such a study depend on which expert one talks to. For the case of sulfur air pollution from coal-fired power plants, estimates of sulfur mass balance as a function of plume flight time are shown to vary little across the range of opinions of leading atmospheric scientists while estimates of possible health impacts are shown to vary widely across the range of opinions of leading scientists in air pollution health effects.     

Modelling age variation in survival and reporting rates for recovery models

In this paper, we focus on models for recovery data from birds ringed as young. In some cases, it is important to be able to include in these models a degree of age variation in the reporting probability. For certain models this has been found, empirically, to result in completely flat likelihood surfaces, due to parameter redundancy. These models cannot then be fitted to the data, to produce unique parameter estimates. However, empirical evidence also exists that other models with such age variation can be fitted to data by maximum likelihood. Using the approach of Catchpole and Morgan (1996b), we can now identify which models in this area are parameter-redundant, and which are not. Models which are not parameter-redundant may still perform poorly in practice, and this is investigated through examples, involving both real and simulated data. The Akaike Information Criterion is found to select inappropriate models in a number of instances. The paper ends with guidelines for fitting models to data from birds ringed as young, when age dependence is expected in the reporting probability.     

Putting modularity in business planning and control

The use of modules in constructing corporate planning systems has been reported by companies such as I.B.M. Xerox, and Standard Oil of New Jersey. The modules may be of organizational units, or of functions such as production, distribution and finance. Modules may also be used for different types of calculations and for generating report output. A module is quite simply a standard unit. Modularity becomes more important as systems grow large, because it is one means of keeping order within large systems. Modularisation is a key concept in structuring large systems, and a useful approach to use in designing procedures for Corporate Planning.