Moran's I
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Moran's I
In statistics, Moran's ''I'' is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Spatial autocorrelation is characterized by a correlation in a signal among nearby locations in space. Spatial autocorrelation is more complex than one-dimensional autocorrelation because spatial correlation is multi-dimensional (i.e. 2 or 3 dimensions of space) and multi-directional. Global Moran's ''I'' Global Moran's ''I'' is a measure of the overall clustering of the spatial data. It is defined as : I = \frac N W \frac where * N is the number of spatial units indexed by i and j; * x is the variable of interest; * \bar x is the mean of x; * w_ is a matrix of spatial weights with zeroes on the diagonal (i.e., w_ = 0); * and W is the sum of all w_ (i.e. W = \sum_^N \sum_^N ). Defining weights matrices The value of I can depend quite a bit on the assumptions built into the spatial weights matrix w_. The matrix is required because, in order to address spatial autoc ...
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Checkerboard Pattern
Check (also checker, Brit: chequer) is a pattern of modified stripes consisting of crossed horizontal and vertical lines which form squares. The pattern typically contains two colours where a single checker (that is a single square within the check pattern) is surrounded on all four sides by a checker of a different colour. The pattern is commonly placed onto garments and is, in certain social contexts, applied to clothing which is worn to signify cultural or political affiliations. Such is the case with check in ska and on the keffiyeh. The pattern's all-pervasiveness and simple layout has lent to its practical usage in scientific experimentation and observation, optometry, technology (hardware and software), and as a symbol for responders to associate meaning with. Etymology The word is derived from the ancient Persian word ' which means "king" in the Sasanian game of Shatranj; an old form of chess which is played on a squared board of alternating coloured checkers. It is more ...
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Geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and phenomena of Earth. The first recorded use of the word γεωγραφία was as a title of a book by Greek scholar Eratosthenes (276–194 BC). Geography is an all-encompassing discipline that seeks an understanding of Earth and its human and natural complexities—not merely where objects are, but also how they have changed and come to be. While geography is specific to Earth, many concepts can be applied more broadly to other celestial bodies in the field of planetary science. One such concept, the first law of geography, proposed by Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." Geography has been called "the world discipline" and "the bridge between the human and ...
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Spatial Heterogeneity
Spatial heterogeneity is a property generally ascribed to a landscape or to a population. It refers to the uneven distribution of various concentrations of each species within an area. A landscape with spatial heterogeneity has a mix of concentrations of multiple species of plants or animals (biological), or of terrain formations (geological), or environmental characteristics (e.g. rainfall, temperature, wind) filling its area. A population showing spatial heterogeneity is one where various concentrations of individuals of this species are unevenly distributed across an area; nearly synonymous with "patchily distributed." Examples Environments with a wide variety of habitats such as different topographies, soil types, and climates are able to accommodate a greater amount of species. The leading scientific explanation for this is that when organisms can finely subdivide a landscape into unique suitable habitats, more species can coexist in a landscape without competition, a phenome ...
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Indicators Of Spatial Association
Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance, if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distribution in space. Global indicators Notable global indicators of spatial association include: * Global Moran's ''I'': The most commonly used measure of global spatial autocorrelation or the overall clustering of the spatial data developed by Patrick Alfred Pierce Moran. * Geary's ''C'' (Geary's Contiguity Ratio): A measure of global spatial autocorrelation developed by Geary in 1954. It is inversely related to Moran's ''I'', but more sensitive to local autocorrelation than Moran's ''I''. * Getis–Ord ''G'' (Getis–Ord global G, Geleral G-Statistic): Introduced by Geti ...
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Distance Decay
Distance decay is a geographical term which describes the effect of distance on cultural or spatial interactions. The distance decay effect states that the interaction between two locales declines as the distance between them increases. Once the distance is outside of the two locales' activity space, their interactions begin to decrease. It is thus an assertion that the mathematics of the inverse square law in physics can be applied to many geographic phenomena, and is one of the ways in which physics principles such as gravity are often applied metaphorically to geographic situations. Mathematical models Distance decay is graphically represented by a curving line that swoops concavely downward as distance along the x-axis increases. Distance decay can be mathematically represented as an inverse-square law by the expression I = const. \times d^ or I \propto 1/d^2, where is interaction and is distance. In practice, it is often parameterized to fit a specific situation, such ...
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Concepts And Techniques In Modern Geography
''Concepts and Techniques in Modern Geography'', abbreviated CATMOG, is a series of 59 short publications, each focused on an individual method or theory in geography. Background and impact ''Concepts and Techniques in Modern Geography'' were produced by the Study Group in Quantitative Methods of the Institute of British Geographers. Each CATMOG publication was written on an individual topic in geography rather than a series of broad topics like traditional textbooks. This à la carte approach allowed only purchasing publications on topics of interest, keeping each CATMOG relatively cheap and accessible, lowering student costs. The first of these publications was published in 1975, and the last in 1996. Each was written by someone working professionally with its topic. As they focus on core concepts of the discipline and were written by experts in the field, they are still often cited today when discussing specific topics. The Quantitative Methods Research Group (QMRG) at the Roy ...
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Geomorphology
Geomorphology (from Ancient Greek: , ', "earth"; , ', "form"; and , ', "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or near Earth's surface. Geomorphologists seek to understand why landscapes look the way they do, to understand landform and terrain history and dynamics and to predict changes through a combination of field observations, physical experiments and numerical modeling. Geomorphologists work within disciplines such as physical geography, geology, geodesy, engineering geology, archaeology, climatology, and geotechnical engineering. This broad base of interests contributes to many research styles and interests within the field. Overview Earth's surface is modified by a combination of surface processes that shape landscapes, and geologic processes that cause tectonic uplift and subsidence, and shape the coastal geography. Surface processes co ...
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Dialectology
Dialectology (from Greek , ''dialektos'', "talk, dialect"; and , ''-logia'') is the scientific study of linguistic dialect, a sub-field of sociolinguistics. It studies variations in language based primarily on geographic distribution and their associated features. Dialectology treats such topics as divergence of two local dialects from a common ancestor and synchronic variation. Dialectologists are ultimately concerned with grammatical, lexical and phonological features that correspond to regional areas. Thus they usually deal not only with populations that have lived in certain areas for generations, but also with migrant groups that bring their languages to new areas (see language contact). Commonly studied concepts in dialectology include the problem of mutual intelligibility in defining languages and dialects; situations of diglossia, where two dialects are used for different functions; dialect continua including a number of partially mutually intelligible dialects; and pluric ...
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Lithium
Lithium (from el, λίθος, lithos, lit=stone) is a chemical element with the symbol Li and atomic number 3. It is a soft, silvery-white alkali metal. Under standard conditions, it is the least dense metal and the least dense solid element. Like all alkali metals, lithium is highly reactive and flammable, and must be stored in vacuum, inert atmosphere, or inert liquid such as purified kerosene or mineral oil. When cut, it exhibits a metallic luster, but moist air corrodes it quickly to a dull silvery gray, then black tarnish. It never occurs freely in nature, but only in (usually ionic) compounds, such as pegmatitic minerals, which were once the main source of lithium. Due to its solubility as an ion, it is present in ocean water and is commonly obtained from brines. Lithium metal is isolated electrolytically from a mixture of lithium chloride and potassium chloride. The nucleus of the lithium atom verges on instability, since the two stable lithium isotopes foun ...
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Geographic Information Science
Geographic information science or geographical information science (GIScience or GISc) is the scientific discipline that studies geographic information, including how it represents phenomena in the real world, how it represents the way humans understand the world, and how it can be captured, organized, and analyzed. It can be contrasted with geographic information systems (GIS), which are the actual repositories of such data, the software tools for carrying out relevant tasks, and the profession of GIS users. That said, one of the major goals of GIScience is to find practical ways to improve GIS data, software, and professional practice. it is more focused on how gis is applied in real life British geographer Michael Goodchild defined this area in the 1990s and summarized its core interests, including spatial analysis, visualization, and the representation of uncertainty. GIScience is conceptually related to geomatics, information science, computer science, but it claims the sta ...
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Luc Anselin
Luc Anselin (born December 1, 1953) is one of the developers of the field of spatial econometrics. Life and contributions Luc Anselin was previously the Regents' Professor, Walter Isard Chair and Director of the School of Geographical Sciences and Urban Planning (ASU) where he attracted some of the leading spatial econometrics scholars. He also founded and directed the GeoDa Center for Geospatial Analysis and Computation at ASU to develop, implement, apply, and disseminate spatial analysis methods. In 2016, the GeoDa Center for Geospatial Analysis relocated to the University of Chicago.spatial.uchicago.edu. He held prior appointments at the University of Illinois, Urbana-Champaign, University of Texas at Dallas, West Virginia University, the University of California, Santa Barbara and the Ohio State University. His joint appointments included a range of disciplines, including Geography, Urban and Regional Planning, Economics, Agricultural and Consumer Economics, Political Economy a ...
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Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ...
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