Computation of determinantal subset influence in regression

One of the important goals of regression diagnostics is the detection of cases or groups of cases which have an inordinate impact on the regression results. Such observations are generally described as influential. A number of influence measures have been proposed, each focusing on a different aspect of the regression. For single cases, these measures are relatively simple and inexpensive to calculate. However, the detection of multiple-case or joint influence is more difficult on two counts. First, calculation of influence for a single subset is more involved than for an individual case, and second, the sheer number of subsets of cases makes the computation overwhelming for all but the smallest data sets.Barrett and Gray (1992) described methods for efficiently examining subset influence for those measures that can be expressed as the trace of a product of positive semidefinite (psd) matrices. There are, however, other popular measures that do not take this form, but rather are expressible as the ratio of determinants of psd matrices. This article focuses on reducing the computation for the determinantal ratio measures by making use of upper and lower bounds on the influence to limit the number of subsets for which the actual influence must be explicitly determined.     

A reply to Mr Palloni's comments

Abstract The protracted and inconclusive debate on the cause of the post-war mortality decline in Ceylon reflects our ignorance of this complex historical event and although I am reticent to prolong this already lengthy discussion, I feel that it is necessary to reply to certain points raised by Mr Palloni. The object of my paper 'The Decline of Mortality in Ceylon and the Demographic Effects of Malaria Control'(9) was to re-examine some of the past work on this subject in order to attempt a synthesis of previous theories, was not, however, intended to provide a definitive account of all the causal mechanisms underlying the decline of mortality as it is my view that the data are insufficient for such an undertaking. In the reappraisal I was mainly concerned with the validity of Newman's regression model and, as far as the data would permit, an assessment of Meegama's thesis that there were significant disturbing variables which confounded the simple regression of mortality decline and malaria prevalence. I will try first to respond to Mr Palloni's specific substantive points and then go on to consider the broader question of regression models.     

Internationalization,Innovation and Institutions: The 3 I's Underpinning the Competitiveness of Emerging Market Firms

The past decade has seen an increase in the extent of research focused on and around emerging market firms (EMFs) and their rising levels of competitiveness in both their home markets and more importantly in the global market place. At the same time, the practitioner-oriented literature has been documenting a growing number of corporate success stories that originate in emerging market economies. We posit that the growing prominence of EMFs is a result of three interrelated phenomena: the fast-paced internationalization of EMFs into both developing and developed market economies; the rapidly increasing extent to which business enterprises in emerging economies are focusing on knowledge-intensive processes and innovation; and the continuous evolution of institutions in these markets, particularly in terms of economic liberalization.     

Performance of the weighted least squares apprdach to categorical data analysis

The weighted least squares method of Grizzle, Starmer and Koch is a common and convenient way to analyze categorical data. Tests of significance based on this method are typically performed by calculating a quadratic form which is asymptotically distrib-uted as a chi-square random variable under an appropriate null hy- pothesis.

This paper explores the validity of this distributional approximation for small samples in terms of the accuracy and power associated with this chi-square statistic. We report simulation results from the weighted least squares method applied to balanced factorial experiments, The simulations which constitute the majorpart of this work also provide insight into the relative performance of several response functions.     

Examining the historical and present energy metabolism of a Rust Belt City: Syracuse,NY 1840–2005

Early cities depended on local, solar-based energy resources for their metabolism. Over time, cities have become increasingly dependent on fossil fuels, both directly and indirectly, as they facilitate exploitation of solar resources from much farther away. Alternatives to fossil fuels, typically generated locally, often provide lower surplus energy to society. As cities consider the transition back to solar-based energy resources, it becomes necessary to understand the capability of the solar-based economy to provide e.g. energy (including food) from nearby lands. To do so, we compared the energy metabolism (respiration) of a typical rust-belt city, Syracuse, NY, with the net primary production in the surrounding county (production) over its development (1840–2005). We calculated the ratio of respiration to production (R:P) and examined how this ratio changed during the periods of industrialization, shifts in major fuel types, and deindustrialization. We found that from 1840 to 1950 respiration became increasingly centralized in the urban core; since then it has become more diffused. Urban respiration exceeded production in the county by 9:1 in 1930, and it remains just under 2:1 today. Respiration reached an absolute (67 PJ) and a per capita (339 GJ) maximum in 1970, then fell by 40 % and 20 % respectively, due to deindustrialization and population losses. Conversely, production increased 480 % from its lows in 1930 because of reforestation and improved agricultural yields. What this means is that to achieve a higher P:R ratio requires either increased production of food and fuels in areas surrounding the city, or decreased per capita energy consumption.