Spatial Analysis; The Primitives at UMBC

Geoprocessing & Spatial Analysis
GES673
at Shady Grove

Richard Heimann

Richard Heimann © 2013

Thursday, February 21, 13

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.



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


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.



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



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?


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”



Social Science Laws can be:

Anyon (1982): social science should be
empirically grounded, theoretically
explanatory and socially critical.



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.



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



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)



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!!



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



Tobler’s First Law of Geography

Teenage Birth Rates – US.



Tobler’s First Law of Geography



If TFLG weren’t true…
GIS would be impossible

Life would be impossible



TFLG

S-ZAR RAN-VAR



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?



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



A (Unofﬁcial) Second (ﬁrst) Law of Geography

LISA MAP | Crime Columbus, OH BOX MAP | Crime Columbus, OH



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



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.




Total Fertility Rate – US.




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.



Practical implications of Second (ﬁrst) Law

…a state is not a sample of the nation
…a country is not a sample of the world



…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?



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.



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.”



Candidate Laws

Montello and Fabrikant, “The First Law
of Cognitive Geography”

“People think closer things are more
similar”



Cognitive Geography [Ethnocentrisms]…



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




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.




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.




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.”




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.




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.




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.



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.




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.



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).



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



• Edge issues
• Modiﬁable areal unit problem (MAUP-zone )
– Results may depend on the speciﬁc geographic unit used in the study
– Province or county; county or city



• Edge issues
• 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


What is Special about Spatial???
…the potentials and pitfalls.
Potentials:



Potentials:
…it teaches us more about what we are studying. [1]



Potentials:

…to avoid misspeciﬁcation in our models; build better
models. (missing variables, better marginal effects,
measurement error) [2]



Potentials:


…to adhere to statistical assumptions. [3]



Potentials:


…to adhere to statistical assumptions. [3]

To be hip! To be quantitative! …and learn more about
spatial data analysis. [4]




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.




…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




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.


Spatial Autocorrelation



It DOES violate the assumptions traditional
statistics…



statistics…

Units of analysis might not be independent



statistics…


Estimated error variance is biased, which
inﬂates the observed R 2 values.



statistics…


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!


…the pitfalls.
Spatial autocorrelation (TFLG)



…the pitfalls.
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.)



…the pitfalls.

1)Biased parameter estimates



…the pitfalls.

1)Biased parameter estimates
2)Data redundancy (affecting the calculation of
conﬁdence intervals)



Spatial Heterogeneity
‘Second’ Law of Geography (Goodchild, 2003)



Simpson’s Paradox



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



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…




…the pitfalls.




…the pitfalls.

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?



…the pitfalls [scale].
…when should we accept it?

Census Tracts (White Population)



…the pitfalls [scale].
…when should we accept it?

Census Tracts (White Population) Counties (White Population)




…the pitfalls [fractals]...
…Spatial Autocorrelation is scale dependent.



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.




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




http://www.theatlantic.com/technology/archive/2013/02/the-geography-of-happiness-according-to-10-million-tweets/273286/



…the pitfalls [fractals]...

Unit = 200 km, length = 2400 km Unit = 50 km, length = 3400 km




Population Illiterates per capita
>60 years income



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




AKA: Intrinsic heterogeneity



http://www.hss.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf



Edge Effects.

Edge effects arise where an artiﬁcial boundary is imposed on
a study, often just to keep it manageable.



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.




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".



(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




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




x y




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.




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.




Modiﬁable Area (aka
Zonal Problem): Units
are arbitrary deﬁned
and different
organization of the
units may create
different analytical
results.



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



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)



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



Ecological Fallacy

Is there a relationship between
Ecological Fallacy & MAUP?



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.




In the 2000 U.S. presidential election, Al Gore, with more of the population
vote than George Bush, but failed to become president.




http://press.princeton.edu/titles/9030.html



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



Observational Studies



…the pitfalls(ish).



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



Spatial Analysis - The Primitives.

Questions?



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



Thank you…

Data Tactics Corporation
https://www.data-tactics-corp.com/
http://datatactics.blogspot.com/
Twitter: @DataTactics

Rich Heimann
Twitter: @rheimann



Spatial Analysis; The Primitives at UMBC

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