On the Geographical Interpretation of Eigenvalues

Gould, Peter

doi:10.2307/621372

Cited by 160 publications

(70 citation statements)

References 30 publications

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“…Networks were plotted with the Fruchterman and Reingold (39) algorithm. Eigenvector centrality (EC) was estimated as described (40), and Kolmogorov-Smirnov tests were used to test for differences in distributions (41,42). Differences in the number of isolated nodes were analyzed by comparing the number of nodes of degree #1.…”

Section: Discussionmentioning

confidence: 99%

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Compromised Gut Microbiota Networks in Children With Anti-Islet Cell Autoimmunity

et al. 2014

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The gut microbiome is suggested to play a role in the pathogenesis of autoimmune disorders such as type 1 diabetes. Evidence of anti-islet cell autoimmunity in type 1 diabetes appears in the first years of life; however, little is known regarding the establishment of the gut microbiome in early infancy. Here, we sought to determine whether differences were present in early composition of the gut microbiome in children in whom anti-islet cell autoimmunity developed. We investigated the microbiome of 298 stool samples prospectively taken up to age 3 years from 22 case children in whom anti-islet cell autoantibodies developed, and 22 matched control children who remained islet cell autoantibody–negative in follow-up. The microbiome changed markedly during the first year of life, and was further affected by breast-feeding, food introduction, and birth delivery mode. No differences between anti-islet cell autoantibody–positive and –negative children were found in bacterial diversity, microbial composition, or single-genus abundances. However, substantial alterations in microbial interaction networks were observed at age 0.5 and 2 years in the children in whom anti-islet cell autoantibodies developed. The findings underscore a role of the microbiome in the pathogenesis of anti-islet cell autoimmunity and type 1 diabetes.

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Section: Discussionmentioning

confidence: 99%

“…EC is a measure of the relative importance and connectivity of each node in a network (40). EC of a node accounts for the centrality of its neighbors, assuming that a node is more central if the surrounding neighbors also have high centrality (43).…”

Section: Anti-islet Cell Autoantibodies and Bacterial Interaction Netmentioning

confidence: 99%

Compromised Gut Microbiota Networks in Children With Anti-Islet Cell Autoimmunity

et al. 2014

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“…In order to be orthogonal to the first, the remaining eigenvectors must contain positive and negative elements. Gould (1967) The results of following Gould's (1967) approach using the second to sixth eigenvectors (after which the signal to noise ratio makes it impossible to uncover further structure) divides the market into eight distinct sub-markets. Figure Three shows the overall market with the eight sub-markets superimposed.…”

Section: Modelling Market Structurementioning

confidence: 99%

“…We then divide this network in to a series of submarkets, using an approach pioneered by Gould (1967), and subsequently widely used in geography (see, for example, Cliff, Haggett & Ord, 1979, Boots, 1985, O'hUallachain, 1985and Straffin, 1980. The network is first converted into an adjacency matrix; a symmetric, zero-one matrix where a zero in the ij th position indicates that nodes i and j are not connected, and a one indicates that they are.…”

Section: Modelling Market Structurementioning

confidence: 99%

Gasoline Price Cycle Drivers: An Australian Case Study

Bloch

Wills‐Johnson²

2010

SSRN Journal

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In many retail gasoline markets, prices follow a saw-toothed cycle first posited by Edgeworth (1925) and formalised by Maskin & Tirole (1988). A growing literature explores driving factors behind such cycles, most particularly in Canada and the US. This paper explores price cycles in a retail gasoline market in Australia with a unique regulatory environment that provides a census of data. We make use of a threshold regression model, and pay particular attention to local market effects and market structure. Both are novel in the study of retail petroleum prices. *corresponding author 3Gasoline Price Cycle Drivers: An Australian Case Study IntroductionRetail gasoline prices in many jurisdictions follow a saw-toothed pattern, shown in Figure Two and called an Edgeworth Cycle. Figure Figure One about hereNote that prices all seem to rise together, and often to roughly the same level. Clearly, Shell head-office in Perth plays a major role in determining when and by how much each Shellbranded outlet increases its price.Wang (2009) Section Two of this paper briefly reviews the empirical price cycle literature, while SectionThree provides an explanation of threshold regression models. Section Four provides an 4 overview of the approach we take to obtain a structural measure of local market competition.Section Five provides a brief overview of the Perth data used. Section Six introduces the model and its results. Section Seven concludes. Edgeworth Cycles and Threshold Regression ModelsPrice Cycles were first posited as an equilibrium of a dynamic game by Edgeworth (1925) and formalised by Maskin & Tirole (1988), who named the cycles after Edgeworth . Their distinctive pattern is shown in Figure Two. Figure Two about hereMaskin & Tirole (1988) show that Edgeworth Cycles are one equilibrium of a repeated, alternate move game when symmetric duopolists produce an homogenous good and who use Markovperfect strategies to choose prices from a finite grid, provided that the discount rate is sufficiently high.. The cycles arise because, for prices above the minimum, a small reduction in price is sufficient to capture the whole market from a rival until it moves again. At the minimum, it is in the interests of both parties for prices to move up again, but not for either party to be the firstmover. They thus play a war of attrition. However, once one firm moves, since the optimal response by its rival will be a slight undercut, the initiator of the price rise has an incentive to increase price by as much as possible in order to maximise its benefits over the price cycle.The model has been extended by Eckert (2003), who allows firms to be of different sizes, by Lau do so by allowing the coefficients to vary over the four phases of the cycle they identify in their work. Noel (2007aNoel ( ,b, 2008Noel ( , 2009) uses a Markov-Switching regression, which is more computationally intensive. Here, we are able to utilise Hansen's (1996Hansen's ( , 1999Hansen's ( , 2000 threshold regression model as we have a census of data, not a...

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“…It expresses a given MI value as a weighted sum of the eigenvalues of matrix (I -1lT/n)C(I -llT/n). Gould (1967) provides a useful interpretation of eigenvalues and eigenfunctions in a geographic setting. Griffith (2000a) outlines his filtering procedure in considerable detail, and includes selected empirical applications to illustrate its use and effectiveness.…”

Section: The Getis Filtering Approach (Seementioning

confidence: 99%

Comparative Spatial Filtering in Regression Analysis

Getis¹,

Griffith²

2002

Geographical Analysis

256

140

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One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order toThe need to account for temporal andlor spatial autocorrelation is well known among regression analysts. Many texts on time series detail the way temporal autocorrelation can be identified and modeled. The literature on spatial autocorrelation is less well developed. One approach to dealing with spatial autocorrelation in regression analysis involves filtering, which seeks to undertake data analyses within the context of the study of stochastic error characteristic of time series analysis. In time series analysis, ARIMA and impulse-response functions are often employed to filter autocorrelation. In the spatial domain, Haining (1991), for example, shows that the temporal-type filtering approach is equivalent to a spatial autocorrelation adjustment for the case of bivariate correlation. This paper compares two additional filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models in which parameters are estimated by ordinary least squares (OLS). It outlines the mechanics of filtering, leaving a researcher to conceptually establish the underlying source of spatial autocorrelation (for example, spatial process, misspecification).

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On the Geographical Interpretation of Eigenvalues

Cited by 160 publications

References 30 publications

Compromised Gut Microbiota Networks in Children With Anti-Islet Cell Autoimmunity

Compromised Gut Microbiota Networks in Children With Anti-Islet Cell Autoimmunity

Gasoline Price Cycle Drivers: An Australian Case Study

Comparative Spatial Filtering in Regression Analysis

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