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Spatial Analysis; The Primitives at UMBC
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GES673 Spring 2013 UMBC MPS in GIS: Lecture from Week 2
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Spatial Analysis; The Primitives at UMBC
1.
Geoprocessing & Spatial
Analysis GES673 at Shady Grove Richard Heimann Richard Heimann © 2013 Thursday, February 21, 13
2.
Review Locational Invariance (Goodchild
et al): Fundamental property of spatial analysis Results change when location changes. Two Data Models: Raster Model & Vector Model Components of Spatial Analysis: -Visualization Showing Interesting Patterns. -Exploratory Spatial Data Analysis Finding Interesting Patterns. -Spatial Modeling, Regression Explaining Interesting Patterns. Richard Heimann © 2013 Thursday, February 21, 13
3.
Review Description versus Analysis:
Process, Pattern and Analysis Four levels of Spatial Analysis: Spatial Data Description Exploratory Spatial Data Analysis - ESDA Spatial statistical analysis and hypothesis testing Spatial modeling and prediction Why is Spatial Data Special; Potentials and Pitfalls. Spatial Autocorrelation, MAUP (scale & zone), Scale effects, Ecological Fallacy, Non-uniformity of space, Edge Effects. Big Data Geographic Knowledge Discovery Experimentation Richard Heimann © 2013 Thursday, February 21, 13
4.
What will we
discuss…? Laws of Spatial Science - the primitives of spatial analysis!! …what are they and why are they important? …how do we begin to measure and quantify the existence of such laws? Contemporary Examples... Spatial is Special -- The Potentials & Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
5.
The value of
Laws Teaching Laws allow courses to be structured from first principles Laws provide the basis for predicting performance, making design choices An asset of a strong, robust discipline Richard Heimann © 2013 Thursday, February 21, 13
6.
Are Laws of
Spatial Science… Deterministic? Does a counterexample defeat a law? Empirical statements? Verifiable with respect to the real world? Do the Social Sciences have Physics Envy? Richard Heimann © 2013 Thursday, February 21, 13
7.
Candidate for the
First Law of Social Science Can there be laws in the social sciences? Ernest Rutherford: “The only result that can possibly be obtained in the social sciences is: some do, and some don’t” Richard Heimann © 2013 Thursday, February 21, 13
8.
Social Science Laws
can be: Anyon (1982): social science should be empirically grounded, theoretically explanatory and socially critical. Richard Heimann © 2013 Thursday, February 21, 13
9.
Social Science Laws
ought to be empirically grounded... Anyon (1982): [T]hat one collects data and uses it to build one's explanations. Ideally one's explanations are related to the data in that they emerge from it. Yet, they attempt to explain it by recourse to categorically different types of constructs: not by other data [...] (p. 35) It is not sufficient to 'explain' patterns in data using a method that was designed to define patterns in data. Richard Heimann © 2013 Thursday, February 21, 13
10.
Social Science Laws
ought to be theoretically explanatory : Anyon (1982): [T]hat one does not rely, for one's reasons for things, on empirically descriptive regularities or generalizations, or on deductions or inferences there from one's theory must be socially explanatory. It must situate social data in a theory of society. (p. 35) ...still theory-poor Richard Heimann © 2013 Thursday, February 21, 13
11.
Social Science Laws
ought to be socially critical: Anyon (1982): To be critical will mean, then, to go beyond the dominant ideology or ideologies, in one's attempt to explain the world. To be critical is to challenge social legitimations, and fundamental structures [...] to seek to explicate, and to seek to eliminate structurally induced exploitation and social pain. (pp. 35-6) Richard Heimann © 2013 Thursday, February 21, 13
12.
Social Science Laws
can be: Based on empirical observation Observed to be generally true Sufficient generality to be useful as a norm Deviations from the law should be interesting Dealing with geographic process rather than form Understanding of social process in context …the Nomothetic & Idiographic debate in geography is solved!! Richard Heimann © 2013 Thursday, February 21, 13
13.
Tobler’s First Law
of Geography (TFLG) TFLG: “All things are related, but nearby things are more related than distant things” W.R.Tobler, 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46: 234-240 Richard Heimann © 2013 Thursday, February 21, 13
14.
Tobler’s First Law
of Geography Teenage Birth Rates – US. Richard Heimann © 2013 Thursday, February 21, 13
15.
Tobler’s First Law
of Geography Richard Heimann © 2013 Thursday, February 21, 13
16.
Tobler’s First Law
of Geography Richard Heimann © 2013 Thursday, February 21, 13
17.
Tobler’s First Law
of Geography Richard Heimann © 2013 Thursday, February 21, 13
18.
Tobler’s First Law
of Geography Richard Heimann © 2013 Thursday, February 21, 13
19.
If TFLG weren’t
true… GIS would be impossible Life would be impossible Richard Heimann © 2013 Thursday, February 21, 13
20.
Tobler’s First Law
of Geography Richard Heimann © 2013 Thursday, February 21, 13
21.
TFLG
S-ZAR RAN-VAR Richard Heimann © 2013 Thursday, February 21, 13
22.
A Second (first?)
Law of Geography TFLG describes a second-order effect (Properties of places taken two at a time) …is there a law of places taken one at a time? Richard Heimann © 2013 Thursday, February 21, 13
23.
A Second (first?)
Law of Geography TFLG describes a second-order effect (Properties of places taken two at a time) …is there a law of places taken one at a time? Yes, its named Spatial heterogeneity Richard Heimann © 2013 Thursday, February 21, 13
24.
A (Unofficial) Second
(first) Law of Geography LISA MAP | Crime Columbus, OH BOX MAP | Crime Columbus, OH Richard Heimann © 2013 Thursday, February 21, 13
25.
A Second (first)
Law of Geography The geography of the 2004 US presidential election results (48 contiguous states) Spatial heterogeneity Non-stationarity / Regional Variation Uncontrolled variance / Equilibrium Richard Heimann © 2013 Thursday, February 21, 13
26.
Implications of Second
(first) Law Stationarity Extreme Heterogeneity Single Equilibria: A Multiple Equilibrium: One singular process over process for every space and across observation over space. study area. Richard Heimann © 2013 Thursday, February 21, 13
27.
A Second (first)
Law of Geography Total Fertility Rate – US. Richard Heimann © 2013 Thursday, February 21, 13
28.
A Second (first)
Law of Geography Richard Heimann © 2013 Thursday, February 21, 13
29.
A Second (first)
Law of Geography Richard Heimann © 2013 Thursday, February 21, 13
30.
A Second (first)
Law of Geography Globalization is thought of a homogenizing the world, but it cannot and will not happen. The underlying processes that drive these systems both look for unevenness and produce unevenness. Homogeneous processes cannot happen, which necessitate the development of methods to describe the unevenness and account for it when describing process. Richard Heimann © 2013 Thursday, February 21, 13
31.
Practical implications of
Second (first) Law …a state is not a sample of the nation …a country is not a sample of the world Richard Heimann © 2013 Thursday, February 21, 13
32.
Practical implications of
Second (first) Law …no average person or place. With the global population distribution being ~50% male and ~50% female would the average be a person with one uterus and one testis? Richard Heimann © 2013 Thursday, February 21, 13
33.
Practical implications of
Second (first) Law Spatial Simpson’s Paradox; Small Theory & Stylized Facts Global standards will always compete with local social phenomenon. Violence in the Violence in the north north Violence Violence in the south Violence in the south Global models average regionally variant Local models account for regional variation. phenomenon. Richard Heimann © 2013 Thursday, February 21, 13
34.
Candidate Laws
By adding demographics to Tobler’s law we can define as the first law of Spatial Demographics: “…people who live in the same neighborhood are more similar than those who live in a different neighborhood, but they may be just as similar to people in another neighborhood in a different place.” Richard Heimann © 2013 Thursday, February 21, 13
35.
Candidate Laws
Montello and Fabrikant, “The First Law of Cognitive Geography” “People think closer things are more similar” Richard Heimann © 2013 Thursday, February 21, 13
36.
Cognitive Geography [Ethnocentrisms]…
Richard Heimann © 2013 Thursday, February 21, 13
37.
Cognitive Geography [Ethnocentrisms]…
Richard Heimann © 2013 Thursday, February 21, 13
38.
Cognitive Geography [Ethnocentrisms]…
Richard Heimann © 2013 Thursday, February 21, 13
39.
Cognitive Geography [Ethnocentrisms]…
Richard Heimann © 2013 Thursday, February 21, 13
40.
Contemporary Examples of
Spatial Analysis Fuller (1974) argues that political decisions regarding the location of clinics is decided on the basis of aspatial analysis, and therefore family planning programs may not have the expected impact on fertility levels. The results of his study could be used as a guidance to optimize the number and location of clinics in communities. http://scholarspace.manoa.hawaii.edu/bitstream/handle/10125/22661/PapersOfTheEastWestPopulationInstituteNo.056SpatialFertilityAnalysisInALimitedDataSituation1978%5Bpdfa%5D.PDF?sequence=1 Richard Heimann © 2013 Thursday, February 21, 13
41.
Contemporary Examples of
Spatial Analysis Paul Krugman loosely defines economic geography as the study of economic issues in which location matters. Economic theory usually assumes away distance. Krugman argues that it is time to put it back - that the location of production in space is a key issue both within and between nations. Richard Heimann © 2013 Thursday, February 21, 13
42.
Contemporary Examples of
Spatial Analysis Paul Krugman loosely defines economic geography as the study of economic issues in which location matters. Economic theory usually assumes away distance. Krugman argues that it is time to put it back - that the location of production in space is a key issue both within and between nations. New Economic Geography implies that instead of spreading out evenly around the world, production will tend to concentrate in a few countries, regions, or cities, which will become densely populated but will also have higher levels of income. Richard Heimann © 2013 Thursday, February 21, 13
43.
Contemporary Examples of
Spatial Analysis Paul Collier in his book The Bottom Billion argues that being landlocked in a poor geographic neighborhood is one of four major development "traps" that a country can be held back by. In general, he found that when a neighboring country experiences better growth, it tends to spill over into favorable development for the country itself. For landlocked countries, the effect is particularly strong, as they are limited from their trading activity with the rest of the world. "If you are coastal, you serve the world; if you are landlocked, you serve your neighbors.” Richard Heimann © 2013 Thursday, February 21, 13
44.
Contemporary Examples of
Spatial Analysis The Social Disorganization Theory: An ecological perspective on crime, dealing with places, not people, as the reason crime happens: where one lives is causal to criminality; the physical and social conditions a person is surrounded by create crime. The assumption of this theory is that people are inherently good, but are changed by their environment. According to this theory, five types of change are most responsible for criminality. They are: urbanization, migration, immigration, industrialization, and technological change. If any one of these aspects occurs rapidly, it breaks down social control and social bonds, creating disorganization. Richard Heimann © 2013 Thursday, February 21, 13
45.
Contemporary Examples of
Spatial Analysis In The Truly Disadvantaged: The Inner City, the Underclass, and Public Policy (1987), William Julius Wilson was an early exponent, one of the first to enunciate at length the spatial mismatch theory for the development of a ghetto underclass in the United States. Spatial mismatch is the sociological, economic and political phenomenon associated with economic restructuring in which employment opportunities for low-income people are located far away from the areas where they live. Richard Heimann © 2013 Thursday, February 21, 13
46.
Contemporary Examples of
Spatial Analysis Schelling Tipping Model was first developed by Thomas C. Schelling (Micromotives and Macrobehavior, 1978) … and represents one of the first constructive models explicitly designed to explore social issues. Richard Heimann © 2013 Thursday, February 21, 13
47.
Contemporary Examples of
Spatial Analysis Proximate casualty hypothesis; (Gartner, Segura, and Wilkening 1997) Time and space provide new insight on the multiple processes underlying opinion change in today’s complex information environment. A case study of the “proximate casualties” hypothesis (Gartner and Segura 2000; Gartner, Segura, and Wilkening 1997), the idea that popular support for American wars is undermined at the individual level more by the deaths of American personnel from nearby areas than by the deaths of those from far away. Richard Heimann © 2013 Thursday, February 21, 13
48.
Contemporary Examples of
Spatial Analysis Harvey developed the idea of spatial fix and the second the idea of accumulation by dispossession. The spatial fix is something much more flexible, consisting in the geographical expansions and restructurings used as temporary solutions to over accumulation crises. As Harvey points out, spatial fixes are available even in a world that is more or less fully incorporated in capitalism. Spatial fixes make use of geographical unevenness, but unevenness is not simply a product of "underdevelopment". Capitalism produces its own unevenness, often plunging already “developed” regions into destructive devaluations. The idea implied here is that processes of primitive accumulation are turned not only against the remaining few non-capitalist formations but also against parts of capitalism itself. Richard Heimann © 2013 Thursday, February 21, 13
49.
Contemporary Examples of
Spatial Analysis The Easterlin Theory (Easterlin 1987) suggests a link between cohort sizes and fertility, was tested in a multiregional context using Italy as a case study (Waldorf and Franklin 2002). An elaborated spatial autoregressive model (Anselin 1988) was formulated, showing that: (i) the space-time components are highly significant and therefore cannot be neglected in studies to assess Easterlin’s theory, (ii) diffusion does play a major role and cannot be neglected either, and (iii) the link between cohort sizes and fertility varies across regions and time (some southern regions, for example, do not substantiate Easterlin’s theory). Richard Heimann © 2013 Thursday, February 21, 13
50.
Critical Issues in
Spatial Analysis Richard Heimann © 2013 Thursday, February 21, 13
51.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other Richard Heimann © 2013 Thursday, February 21, 13
52.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other • Scale effects and measurement pitfalls – Cities may be represented as points or polygons – Results depend on the scale at which the analysis is conducted: province or county – MAUP—scale effect Richard Heimann © 2013 Thursday, February 21, 13
53.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other • Scale effects and measurement pitfalls – Cities may be represented as points or polygons – Results depend on the scale at which the analysis is conducted: province or county – MAUP—scale effect • Non-uniformity of Space – Phenomena are not distributed evenly in space – Be careful how you interpret results! Richard Heimann © 2013 Thursday, February 21, 13
54.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other • Scale effects and measurement pitfalls – Cities may be represented as points or polygons – Results depend on the scale at which the analysis is conducted: province or county – MAUP—scale effect • Non-uniformity of Space – Phenomena are not distributed evenly in space – Be careful how you interpret results! • Edge issues – Edges of the map, beyond which there is no data, can significantly affect results Richard Heimann © 2013 Thursday, February 21, 13
55.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other • Scale effects and measurement pitfalls – Cities may be represented as points or polygons – Results depend on the scale at which the analysis is conducted: province or county – MAUP—scale effect • Non-uniformity of Space – Phenomena are not distributed evenly in space – Be careful how you interpret results! • Edge issues – Edges of the map, beyond which there is no data, can significantly affect results • Modifiable areal unit problem (MAUP-zone ) – Results may depend on the specific geographic unit used in the study – Province or county; county or city Richard Heimann © 2013 Thursday, February 21, 13
56.
Critical Issues in
Spatial Analysis • Spatial autocorrelation – Data from locations near to each other are usually more similar than data from locations far away from each other • Scale effects and measurement pitfalls – Cities may be represented as points or polygons – Results depend on the scale at which the analysis is conducted: province or county – MAUP—scale effect • Non-uniformity of Space – Phenomena are not distributed evenly in space – Be careful how you interpret results! • Edge issues – Edges of the map, beyond which there is no data, can significantly affect results • Modifiable areal unit problem (MAUP-zone ) – Results may depend on the specific geographic unit used in the study – Province or county; county or city • Ecological fallacy – Results obtained from aggregated data (e.g. provinces) cannot be assumed to apply to individual people – MAUP—individual effect Richard Heimann © 2013 Thursday, February 21, 13
57.
What is Special
about Spatial??? …the potentials and pitfalls. Potentials: Richard Heimann © 2013 Thursday, February 21, 13
58.
What is Special
about Spatial??? …the potentials and pitfalls. Potentials: …it teaches us more about what we are studying. [1] Richard Heimann © 2013 Thursday, February 21, 13
59.
What is Special
about Spatial??? …the potentials and pitfalls. Potentials: …it teaches us more about what we are studying. [1] …to avoid misspecification in our models; build better models. (missing variables, better marginal effects, measurement error) [2] Richard Heimann © 2013 Thursday, February 21, 13
60.
What is Special
about Spatial??? …the potentials and pitfalls. Potentials: …it teaches us more about what we are studying. [1] …to avoid misspecification in our models; build better models. (missing variables, better marginal effects, measurement error) [2] …to adhere to statistical assumptions. [3] Richard Heimann © 2013 Thursday, February 21, 13
61.
What is Special
about Spatial??? …the potentials and pitfalls. Potentials: …it teaches us more about what we are studying. [1] …to avoid misspecification in our models; build better models. (missing variables, better marginal effects, measurement error) [2] …to adhere to statistical assumptions. [3] To be hip! To be quantitative! …and learn more about spatial data analysis. [4] Richard Heimann © 2013 Thursday, February 21, 13
62.
What is Special
about Spatial??? …the potentials and pitfalls. Pitfalls: Many of the standard techniques and methods documented in standard statistics textbooks have significant problems when we try to apply them to the analysis of the spatial distributions. Richard Heimann © 2013 Thursday, February 21, 13
63.
What is Special
about Spatial??? …the potentials. TFLG: “All things are related, but nearby things are more related than distant things” W.R.Tobler, 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46: 234-240 Richard Heimann © 2013 Thursday, February 21, 13
64.
What is Special
about Spatial??? Pitfalls: Paradoxically Spatial autocorrelation (TFLG) Many of the standard techniques and methods documented in standard statistics textbooks have significant problems when we try to apply them to the analysis of the spatial distributions. Richard Heimann © 2013 Thursday, February 21, 13
65.
Spatial Autocorrelation
Richard Heimann © 2013 Thursday, February 21, 13
66.
Spatial Autocorrelation
It DOES violate the assumptions traditional statistics… Richard Heimann © 2013 Thursday, February 21, 13
67.
Spatial Autocorrelation
It DOES violate the assumptions traditional statistics… Units of analysis might not be independent Richard Heimann © 2013 Thursday, February 21, 13
68.
Spatial Autocorrelation
It DOES violate the assumptions traditional statistics… Units of analysis might not be independent Estimated error variance is biased, which inflates the observed R 2 values. Richard Heimann © 2013 Thursday, February 21, 13
69.
Spatial Autocorrelation
It DOES violate the assumptions traditional statistics… Units of analysis might not be independent Estimated error variance is biased, which inflates the observed R 2 values. If spatial effects are present, and you don’t account for them, your model is not accurate! Richard Heimann © 2013 Thursday, February 21, 13
70.
Spatial Autocorrelation
…the pitfalls. Spatial autocorrelation (TFLG) Richard Heimann © 2013 Thursday, February 21, 13
71.
Spatial Autocorrelation
…the pitfalls. Spatial autocorrelation (TFLG) The nonrandom distribution of phenomena in space has various consequences for conventional statistic analysis. Traditional statistics often assume independent and identically distributed (i.i.d.) Richard Heimann © 2013 Thursday, February 21, 13
72.
Spatial Autocorrelation
…the pitfalls. Spatial autocorrelation (TFLG) The nonrandom distribution of phenomena in space has various consequences for conventional statistic analysis. Traditional statistics often assume independent and identically distributed (i.i.d.) 1)Biased parameter estimates Richard Heimann © 2013 Thursday, February 21, 13
73.
Spatial Autocorrelation
…the pitfalls. Spatial autocorrelation (TFLG) The nonrandom distribution of phenomena in space has various consequences for conventional statistic analysis. Traditional statistics often assume independent and identically distributed (i.i.d.) 1)Biased parameter estimates 2)Data redundancy (affecting the calculation of confidence intervals) Richard Heimann © 2013 Thursday, February 21, 13
74.
Spatial Autocorrelation
Spatial Heterogeneity ‘Second’ Law of Geography (Goodchild, 2003) Richard Heimann © 2013 Thursday, February 21, 13
75.
Simpson’s Paradox
Richard Heimann © 2013 Thursday, February 21, 13
76.
Spatial Simpson’s Paradox
‘Second’ Law of Geography (Goodchild, 2003) Global Models may be inconsistent with regional models (i.e. Spatial Simpson’s Paradox) Global standards will always compete with local standards Crime in the north Crime in the north Crime Crime in the south Crime in the south Richard Heimann © 2013 Thursday, February 21, 13
77.
Spatial Autocorrelation
Richard Heimann © 2013 Thursday, February 21, 13
78.
Spatial Autocorrelation
Statistical Inference for Spatial Data An important consequence of spatial dependence is that statistical inferences on this type of data won’t be as efficient as in the case of independent samples of the same size. In other words, the spatial dependence leads to a loss of explanatory power. In general, this reflects on higher variances for the estimates, lower levels of significance in hypothesis tests and a worse adjustment for the estimated models, compared to data of the same dimension that exhibit independence. Generally lower p values are required… Richard Heimann © 2013 Thursday, February 21, 13
79.
Spatial Autocorrelation
…the pitfalls. Statistical Inference for Spatial Data Richard Heimann © 2013 Thursday, February 21, 13
80.
Spatial Autocorrelation
…the pitfalls. Statistical Inference for Spatial Data TFLG: “All things are related, but nearby things are more related than distant things” Then what is Negative Spatial Autocorrelation? / Type II Error or is it possible? Richard Heimann © 2013 Thursday, February 21, 13
81.
Spatial Autocorrelation
…the pitfalls [scale]. …when should we accept it? Census Tracts (White Population) Richard Heimann © 2013 Thursday, February 21, 13
82.
Spatial Autocorrelation
…the pitfalls [scale]. …when should we accept it? Census Tracts (White Population) Counties (White Population) Richard Heimann © 2013 Thursday, February 21, 13
83.
Spatial Autocorrelation
…the pitfalls [fractals]... …Spatial Autocorrelation is scale dependent. Richard Heimann © 2013 Thursday, February 21, 13
84.
Scale Effects and
Measurement Pitfalls. Gregory Bateson, in "Form, Substance and Difference," from Steps to an Ecology of Mind (1972), elucidates the essential impossibility of knowing what the territory is, as any understanding of it is based on some representation: We say the map is different from the territory. But what is the territory? Operationally, somebody went out with a retina or a measuring stick and made representations which were then put on paper. What is on the paper map is a representation of what was in the retinal representation of the man who made the map; and as you push the question back, what you find is an infinite regress, an infinite series of maps. The territory never gets in at all. […] Always, the process of representation will filter it out so that the mental world is only maps of maps, ad infinitum. Richard Heimann © 2013 Thursday, February 21, 13
85.
Scale Effects and
Measurement Pitfalls. Another basic quandary is the problem of accuracy. In "On Exactitude in Science", Jorge Luis Borges describes the tragic uselessness of the perfectly accurate, one-to-one map: In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guild drew a Map of the Empire whose size was that of the Empire, coinciding point for point with it. The following Generations, who were not so fond of the Study of Cartography saw the vast Map to be Useless and permitted it to decay and fray under the Sun and winters. In the Deserts of the West, still today, there are Tattered Ruins of the Map, inhabited by Animals and Beggars; and in all the Land there is no other Relic of the Disciplines of Geography. http://en.wikipedia.org/wiki/On_Exactitude_in_Science Richard Heimann © 2013 Thursday, February 21, 13
86.
Scale Effects and
Measurement Pitfalls. http://www.theatlantic.com/technology/archive/2013/02/the-geography-of-happiness-according-to-10-million-tweets/273286/ Richard Heimann © 2013 Thursday, February 21, 13
87.
Scale Effects and
Measurement Pitfalls. …the pitfalls [fractals]... Unit = 200 km, length = 2400 km Unit = 50 km, length = 3400 km Richard Heimann © 2013 Thursday, February 21, 13
88.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
89.
Scale Effects and
Measurement Pitfalls. Population Illiterates per capita >60 years income Richard Heimann © 2013 Thursday, February 21, 13
90.
Scale Effects and
Measurement Pitfalls. Population Illiterates per capita >60 years income Richard Heimann © 2013 Thursday, February 21, 13
91.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
92.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
93.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
94.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
95.
Scale Effects and
Measurement Pitfalls. Richard Heimann © 2013 Thursday, February 21, 13
96.
Non-Uniformity of Space Cranshaw,
J., Schwartz, R., Hong, J., & Sadeh, N. (2012). The livehoods project: Utilizing social media to understand the dynamics of a city. … the Advancement of Artificial …. Retrieved from http://www.aaai.org/ocs/index.php/ICWSM/ICWSM12/paper/download/4682/4967 Richard Heimann © 2013 Thursday, February 21, 13
97.
Non-Uniformity of Space
AKA: Intrinsic heterogeneity Richard Heimann © 2013 Thursday, February 21, 13
98.
Non-Uniformity of Space
Richard Heimann © 2013 Thursday, February 21, 13
99.
Non-Uniformity of Space
http://www.hss.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf Richard Heimann © 2013 Thursday, February 21, 13
100.
Edge Effects.
Edge effects arise where an artificial boundary is imposed on a study, often just to keep it manageable. Richard Heimann © 2013 Thursday, February 21, 13
101.
Modifiable Areal Unit
Problem A classic early paper is Gehlke and Biehl (1934) who found that the magnitude of the correlation between two variables tended to increase as districts formed from Census tracts increased in size. Richard Heimann © 2013 Thursday, February 21, 13
102.
Modifiable Areal Unit
Problem Waller & Gotway (2004) describe it as a "geographic manifestation of the ecological fallacy in which conclusions based on data aggregated to a particular set of districts may change if one aggregates the same underlying data to a different set of districts". Richard Heimann © 2013 Thursday, February 21, 13
103.
Modifiable Areal Unit
Problem (on Robinson 1950) ...for each of the 48 states in the US as of the 1930 census, he computed the literacy rate and the proportion of the population born outside the US. He showed that these two figures were associated with a positive correlation of 0.53 — in other words, the greater the proportion of immigrants in a state, the higher its average literacy. However, when individuals are considered, the correlation was 0.11 — immigrants were on average less literate than native citizens. Robinson showed that the positive correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or ecological data Richard Heimann © 2013 Thursday, February 21, 13
104.
Modifiable Areal Unit
Problem The paper by Openshaw and Taylor (1979) described how they had constructed all possible groupings of the 99 Counties in Iowa into larger districts. When considering the correlation between %Republican voters and %elderly voters, they could produce "a million or so" correlation coefficients. A set of 12 districts could be contrived to produce correlations that ranged from -0.97 to +0.99. 99 counties of Iowa % Republican voters, % over 65 48 regions: -.548 to +.886 12 regions: -.97 to +.99 Richard Heimann © 2013 Thursday, February 21, 13
105.
Modifiable Areal Unit
Problem x y Richard Heimann © 2013 Thursday, February 21, 13
106.
Modifiable Areal Unit
Problem Richard Heimann © 2013 Thursday, February 21, 13
107.
Modifiable Areal Unit
Problem Openshaw and Taylor (1979) showed that with the same underlying data it is possible to aggregate units together in ways that can produce correlations anywhere between -1.0 to +1.0. Richard Heimann © 2013 Thursday, February 21, 13
108.
Modifiable Areal Unit
Problem Scale issue: involves the aggregation of smaller units into larger ones. Generally speaking, the larger the spatial units, the stronger the relationship among variables or often a reverse in autocorrelation. Richard Heimann © 2013 Thursday, February 21, 13
109.
Modifiable Areal Unit
Problem Modifiable Area (aka Zonal Problem): Units are arbitrary defined and different organization of the units may create different analytical results. Richard Heimann © 2013 Thursday, February 21, 13
110.
Modifiable Areal Unit
Problem The choice of an appropriate scale for the study of spatial processes is an extremely important one because mechanisms vital to the spatial dynamics of a process at one scale may be unimportant or inoperative at another. Moreover, relationships between variables at one scale may be obscured or distorted when viewed from another scale. This is particularly true in the study of human, animal, and plant populations and has led many researchers in agriculture, geography, sociology, statistics, ecology, and the earth and environmental sciences to consider scale issues in detail Richard Heimann © 2013 Thursday, February 21, 13
111.
Ecological Fallacy
The Ecological Fallacy is a situation that can occur when a researcher or analyst makes an inference about an individual based on aggregate data for a group. (Reference: http://jratcliffe.net/research/ecolfallacy.htm) Richard Heimann © 2013 Thursday, February 21, 13
112.
Ecological Fallacy
Example: We might observe a strong relationship between income and crime at the county level, with lower-income areas being associated with higher crime rate. Conclusion: 1) Lower-income persons are more likely to commit crime 2) Lower-income areas are associated with higher crime rates 3) Lower-income counties tend to experience higher crime rates Richard Heimann © 2013 Thursday, February 21, 13
113.
Ecological Fallacy
Is there a relationship between Ecological Fallacy & MAUP? Richard Heimann © 2013 Thursday, February 21, 13
114.
Ecological Fallacy
Is there a relationship between Ecological Fallacy & MAUP? The smoothing effect that results from averaging is the underlying cause of both the scale problem in the MAUP and aggregation bias in ecological studies. As heterogeneity among units is reduced through aggregation, the uniqueness of each unit and the dissimilarity among units is also reduced. Richard Heimann © 2013 Thursday, February 21, 13
115.
Modifiable Areal Unit
Problem In the 2000 U.S. presidential election, Al Gore, with more of the population vote than George Bush, but failed to become president. Richard Heimann © 2013 Thursday, February 21, 13
116.
Modifiable Areal Unit
Problem http://press.princeton.edu/titles/9030.html Richard Heimann © 2013 Thursday, February 21, 13
117.
Modifiable Areal Unit
Problem Richard Heimann © 2013 Thursday, February 21, 13
118.
Ecological Fallacy
Is there a converse to Ecological Fallacy? Conclusions regarding spatial grouped data being sought based on the measured characteristics of sampled individuals? If so, the sample must be entirely or highly representative of the grouping in order to avoid the so-called atomistic fallacy — ascribing characteristics to members of a group based on a potentially unrepresentative sample of members Richard Heimann © 2013 Thursday, February 21, 13
119.
Observational Studies
Richard Heimann © 2013 Thursday, February 21, 13
120.
Observational Studies
Richard Heimann © 2013 Thursday, February 21, 13
121.
Observational Studies
Richard Heimann © 2013 Thursday, February 21, 13
122.
…the pitfalls(ish).
Richard Heimann © 2013 Thursday, February 21, 13
123.
Spatial Analysis is
harder than Sabermetrics Thiel, J., & Hogan, J. (2011). The Statistical Irrelevance of American SIGACT Data: Iraq Surge Analysis Reveals Reality. Retrieved from http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA546546 Richard Heimann © 2013 Thursday, February 21, 13
124.
Spatial Analysis -
The Primitives. Questions? Richard Heimann © 2013 Thursday, February 21, 13
125.
Personal Notes
Richard Heimann Office: UMBC Common Faculty Area 3rd Floor Phone: 571-403-0119 (C) Office hours: Tues. 6:30-7:00 (Virtual); or by appointment (send e-mail) I promptly respond to emails. Phone calls are another matter. Email: rheimann@umbc.edu or heimann.richard@gmail.com Richard Heimann © 2013 Thursday, February 21, 13
126.
Thank you…
Data Tactics Corporation https://www.data-tactics-corp.com/ http://datatactics.blogspot.com/ Twitter: @DataTactics Rich Heimann Twitter: @rheimann Richard Heimann © 2013 Thursday, February 21, 13