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The modifiable areal unit problem (MAUP) via cluster analysis methodologies: a look at scale, zoning, and instances of foreclosure in Los Angeles County

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The modifiable areal unit problem (MAUP) via cluster analysis methodologies: a look at scale, zoning, and instances of foreclosure in Los Angeles County

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Content i

THE MODIFIABLE AREAL UNIT PROBLEM (MAUP) VIA CLUSTER ANALYSIS
METHODOLOGIES:
A LOOK AT SCALE, ZONING, AND INSTANCES OF FORECLOSURE IN LOS
ANGELES COUNTY

by

Matthew W. Davis

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE & TECHNOLOGY)

May 2012

Copyright 2012 Matthew W. Davis

ii

Acknowledgements

I must begin this by thanking the head of my committee, Jennifer Swift, for her
unerring support through all the erroneous stop-and-goes of this research. She always
looked toward the other avenues of research and encouraged me to press on. She is also
responsible for giving me the original “Parcels” dataset, for which I am especially
grateful. I must thank Daniel Goldberg for his sharp eye and for always having a
perspective I would not have considered. I must also thank Andrew Curtis for his
seemingly endless supply of knowledge on cluster analysis methods, without which I
could never have interpreted my results. I must thank Cam D’Angeles for her meticulous
attention to detail and charity, without which I would still be formatting this thesis.
Thanks must go to the Los Angeles County Assessor’s Office for providing the
raw foreclosure dataset that formed the crux of this research. Daniel Goldberg was
instrumental in obtaining these data and kindly allowed me to use it in my research. The
Census Bureau is also commended for their comprehensive parcel data throughout the
United States.
Last, but certainly not least, it goes without question that I could not have done
this without the endless support of Rob Hughes.

iii

Table of Contents

Acknowledgements

ii

List of Tables v

List of Figures vi

Abstract viii

Chapter One Introduction 1
1.1 Introduction and Rationale 1
1.2 Theoretical Framework and Questions 3

Chapter Two Literature Review 5
2.1 Problem Formulation 5
2.2 Background Theories of the Components of the MAUP 6
2.3 The Scale Effect 10
2.4 The Aggregation Effect 13
2.5 The MAUP (Both Effects 15
2.6 Critiques 20

Chapter Three Methodology 23
3.1 Data Gathering and Acquisition 23
3.2 Data Analysis Procedure 23
3.3 Data Preparation 29
3.4 Cluster Analysis Methods 30
3.5 Justification 34

Chapter Four Analysis Results 36
4.1 Hotspot Analysis (Getis-Ord general G) Results 39
4.2
Cluster and Outlier Analysis (Anselin Local Moran’s I)
Results
46
4.3 Spatial Autocorrelation (Global Moran’s I) Results 50
4.4
High/Low Clustering Results (Getis-Ord General G)
Results
53
4.5
Multi-Distance Spatial Cluster Analysis (Ripley’s K-
function) Results
56

Chapter Five Interpretation 64
5.1 Interpretation of Hotspot Results (Getis-Ord Gi*) 64
iv

5.2
Interpretation of Cluster and Outlier Analysis Results
(Anselin Local Moran’s I)
71
5.3 The Broader Results 78
5.4 Future Avenues of Research 79
5.5 Answering the Theoretical Questions 80

References 83
v

List of Tables

Table 2-1
Studies and their relation to the MAUP and other factors under
discussion
9

Table 3-1 Guide to Model Iterations and Results 25

Table 3-2 Summary of the seven studied datasets and their characteristics 30

Table 4-1 Summary of Spatial Autocorrelation results 52

Table 4-2 Summary of High/Low Clustering results 54

vi

List of Figures

Figure 2-1
Artificial example of the aggregate effect and the scale effect on
average and variance
16

Figure 3-1 Example of a group of model iterations in ModelBuilder 32

Figure 3-2
Identical sets of points that are either contained in a single cell or
split into quadrants
34

Figure 4-1 Map of LA County and all instances of foreclosures (2006-2008) 38

Figure 4-2 Map of LA County Parcels3 hotspot results (2km Distance
Threshold)
41

Figure 4-3 Map of LA County Parcels3 hotspot results (1km Distance
Threshold )
42

Figure 4-4
Map of LA County Parcels2 hotspot results (750m Distance
Threshold)
44

Figure 4-5
Map of LA County Parcels2 hotspot results (5km Distance
Threshold)
45

Figure 4-6
Map of LA County Parcels2 Cluster & Outlier results (5km
Distance Threshold)
47

Figure 4-7
Map of LA County Fishnet1 Cluster & Outlier results (5km
Distance Threshold)
48

vii

Figure 4-8
Map of LA County Fishnet2 Cluster & Outlier results (5km
Distance Threshold)
49

Figure 4-9 Ripley’s K result graph of the FC_Points dataset 58

Figure 4-10 Ripley’s K result graph of the Fishnet2 dataset 59

Figure 4-11 Ripley’s K result graph of the Parcels2 dataset 60

Figure 4-12 Ripley’s K result graph of the Parcels3 dataset 61

Figure 4-13 Ripley’s K result graph of the Fishnet3 dataset 63

Figure 5-1 Hot spot map of Parcels3 (750m distance threshold) 64

Figure 5-2 Hot spot map of Parcels3 (10km distance threshold) 66

Figure 5-3
Smaller scale hot spot map of Parcels3 (750m Distance
Threshold)
69

Figure 5-4
Smaller scale hot spot map of Parcels3 (10km Distance
Threshold)
70

Figure 5-5
Cluster and Outlier analysis map of Fishnet1 (1km Distance
Threshold)
72

Figure 5-6
Cluster and Outlier analysis map of Fishnet2 (1km Distance
Threshold)
73
Figure 5-7
Cluster and Outlier analysis map of Fishnet3 (1km Distance
threshold)
74
Figure 5-8
Cluster and Outlier analysis map of Parcels (1km Distance
Threshold)
75
viii

Figure 5-9
Cluster and Outlier analysis map of Parcels2 (1km Distance
Threshold)
76

Figure 5-10 Cluster and Outlier analysis map of Parcels3 (1km Distance
Threshold)
77

ix

Abstract

Spatial research has been plagued by the modifiable areal unit problem, or MAUP
(Openshaw, 1979), for decades. The MAUP can be broken down into two categories, the
scale or aggregation effect and the zoning or grouping effect. Recent advances in spatial
science and technology have exacerbated the effects of the MAUP prevalent in many
forms of research. In this paper, data was obtained depicting instances of foreclosures in
Los Angeles County (also the study extent) in 2006-2008. This data was spatially joined
to three sets of grids, or fishnets, covering Los Angeles County. The data was also
spatially joined to three additional datasets: the individual parcels of Los Angeles County
and two aggregations of these parcels. Five cluster analysis tools were used to analyze
each of these seven total datasets. Each permutation involved the five tools, seven
datasets, and multiple pre-selected distance thresholds to test for scale and zoning effects
of the MAUP. There were a total of 137 successful iterations illustrating the
aforementioned permutations. It was determined the MAUP is prevalent in this case
study. Suggestions are made in determining future actions to combat the effects of the
MAUP.

1

Chapter One – Introduction
1.1 Introduction and Rationale
The advent of geographic information systems, or GIS, has propelled spatial
research and analysis to new heights. Within the past few decades the acceleration of
computer technology coupled with the heightened prevalence of spatial data have forced
researchers to reexamine their assumptions regarding how best to address the inherent
flaws in such data. These flaws include: accuracy, scale, aggregation effects, and how
best to relate such data to other variables which may or may not be comprised of similar
spatial structures.
In order to understand the relationships between spatial datasets with different
extents it is necessary to aggregate data from one dataset into another. One such method
is to aggregate point data into polygon data. Methods of aggregation provide researchers
with the ability to cross-reference and analyze different types of data to see potential
spatial associations or relationships. The boundaries with which these data are
aggregated tend to have arbitrarily defined extents. For example, census tracts, city
boundaries, counties, states, and regularly gridded study areas are all artificially
constructed for various administrative or study-specific purposes. These issues are a part
of the scale effect and zoning effect commonly found in multivariate spatial analysis.
These effects fall under the umbrella term known as the modifiable areal unit problem, or
MAUP. The MAUP was coined by Openshaw & Taylor (1979) to describe the effects of
these two problems. This thesis addresses MAUP issues and includes a discussion on
how the MAUP can be taken into consideration in order to prevent its effects from
2

biasing or leading to misinterpretation of results. One of the ways this thesis proves the
existence of the MAUP is to utilize Local Indicators of Spatial Association, or LISA,
statistics (Dale et al., 2002; Ratcliffe and McCullagh, 1999; Lee and Rogerson, 2007;
Anselin, 1995). This case study examines the relationship between foreclosure points in
Los Angeles County and how they relate to spatially joined aggregated polygons. These
feature datasets share a similar extent though differ greatly among one another in terms of
polygon structure and placement. Chapter Three includes more information on these
differences and what their long term implications are in spatial research.
This thesis is comprised of five chapters including this introductory chapter.
Chapter Two is a comprehensive Literature Review that examines research related to
spatial data queries and the conception of methodological frameworks, and critiques the
methods, results, and potential areas of improvement to the aforementioned research.
Chapter Three details the methodology used to examine the MAUP using LISA statistics
and includes a case study involving the relationship between foreclosures and units of
foreclosure aggregation as they relate to multiple cluster analysis methodologies.
Chapter Four details the results of the latter case study with maps, charts, and graphs of
the results of five different cluster methods. Chapter Five interprets the LISA results
which lead into a discussion about how researchers need to include multiple permutations
to account for the effects of the MAUP. Chapter Five also includes a broader
interpretation of the overall results of this thesis project. A hypothetical example is also
included which illustrates how the effects of the MAUP need to be accounted for before
any actual research begins.
3

1.2 Theoretical Framework and Questions
Spatial research is limited to the dataset with the highest resolution or largest
extent(s) set forth to be studied (Shriner, et al., 2006). It is possible, though extremely
difficult, to disaggregate such data into smaller scales or components for analysis with
finer data (Gotway and Young, 2002). This thesis will deal specifically with the issues
that arise when point data is aggregated into larger areal units and the inherent concerns
therein.
How thoroughly a given methodology has examined the effects of the MAUP
indicates whether or not the researcher(s) have accounted for its effects. Each variable in
spatial research should require an exhaustive evaluation of the scale (or aggregation) and
the zoning effects of the MAUP. There is a trade-off in the level of uncertainty and error
in the results/conclusions that a researcher must be willing to accept based on how
thoroughly this analysis is performed. These issues necessitate an awareness of how the
MAUP issues bias and impact results based on the chosen methods of spatial calculation.
As completely as possible this thesis will answer the following questions related to
foreclosure, aggregation, and zoning issues. These questions are phrased as follows:
1) How does the modifiable areal unit problem (MAUP) affect the visual results of
aggregate data in a multiscale environment via cluster analysis methods across
multiple distance thresholds?
2) What is the best scale or aggregation unit used for running spatial analysis
involving the use of local indicators of spatial association (LISA) statistics?
4

3) How do these effects impact the way in which a research methodology is
constructed?
The impact of the MAUP can be a nuisance to any research that attempts to
spatially link discordant variables across different spatial extents and scales (Getis and
Franklin, 1987). One example of this situation includes instances of foreclosures,
represented as point data, and crime rate statistics within city boundaries, represented as
polygon data. One way to do a comparative measurement of the two variables would be
to aggregate the point foreclosure data into the city boundaries to determine how
foreclosure and crime rate correlate. However, such aggregation tends to generalize the
foreclosure data. In this example, intra-city clusters of foreclosures and trends will
unfortunately be eliminated through such aggregation methods. The fifth chapter of this
thesis will discuss how best to approach this problem in one’s research and provide
insights as to how researchers might incorporate these approaches into their analysis.

5

Chapter Two – Literature Review
2.1 Problem Formulation
There has been moderate consideration given in the literature to the role zones
and aggregation play in spatial datasets and subsequent analysis. Aggregation is defined
herein as the inclusion of point/unit level data into larger arbitrarily defined extents that
can be used for spatial analysis and statistical research (Pawitan and Steel, 2009). There
are few studies which have attempted to account for or exonerate the effects of zonal data
and spatial extent issues that plague many forms of spatial research. These sets of issues
are known as the Modifiable Areal Unit Problem or MAUP (Openshaw and Taylor, 1979;
Openshaw, 1984) and are broken up into two major effects, the scale effect (sometimes
called the aggregation effect) and the zoning effect (Amrhein and Reynolds, 2006;
Amrhein and Reynolds, 2007). This chapter details and critiques background literature
which highlights the effect that aggregation has on analytical results. One of the goals of
this chapter is to comprehensively articulate and summarize the necessary criteria for
aggregate analysis.
In order to relate point-based feature data to other data in a spatial context it is
often necessary to aggregate the attributes of those features into larger units in order to
produce viable measures and statistics. In many cases the variable to compare is already
aggregated into a larger extent, making point aggregation essential for analysis. The
most common use of aggregates usually aligns with census blocks or tracts, zip codes,
and city or county boundaries. Using established boundaries for aggregation provides the
added benefit of linking one study’s aggregates and conclusions to other studies with
6

similar extents and study areas. This literature review is intended to define and critique
prior research while also providing the necessary background to synthesize a framework
for the proposed methodology. In order to quantify the effect of the MAUP this research
focuses on the different aspects of cluster analysis methodologies applicable to
foreclosure point datasets based on total counts of foreclosure instances. The foreclosure
data is utilized to analyze the effects of the MAUP by spatially relating point data to
different feature boundaries and types.
This chapter is composed of four sections including this problem formulation
section. Section 2.2 covers the history and background theories of aggregation, including
the MAUP. Section 2.3 scrutinizes and critiques the methodologies and approaches
employed by the articles summarized in Section 2.2. Finally, Section 2.4 reviews some
pertinent research involving cluster analysis methodologies and compares them to each
other. Chapter Five concludes this inquiry by focusing on possible methods for
recognizing the impacts of the MAUP, and a discussion about future researchers might
design their studies to lessen the effects of the MAUP.

2.2 Background Theories of the Components of the MAUP
The relevance of this study to the pertinent literature requires a comprehensive
look at previous studies, in particular their contribution to understanding the MAUP, as
well as the lens some used to compensate for the MAUP. Two primary problem
paradigms are used to categorize and evaluate the MAUP which consists of the scale
problem and the zoning problem. Jelinski and Wu (1996) define the scale problem as
7

“where the same set of areal data is aggregated into several sets of larger areal units, with
each combination leading to different data values and inferences” and the zoning problem
as “where a given set of areal units is recombined into zones that are of the same size but
located differently, again resulting in variation in data values and…different
conclusions”. In order to understand the reasons why certain methodological choices
were made for this study it is necessary to evaluate the methodologies, conclusions, and
schemas used by other researchers with similar goals. By understanding preceding
research and narrowing down extraneous avenues of thought this chapter is intended to
provide clearer insight into the compositions of spatial research involving aggregate data
and the MAUP. Thus the following discussion provides the primary rationale for this
study.
The term MAUP was coined by Openshaw and Taylor (1979). A few studies
were published in the 1980s and early 1990s (with the notable exception of Openshaw in
1984) which indicated that interest in the MAUP had tapered off (Amrhein, 1993). The
MAUP has recently become more prevalent and prominent in zone and scale research.
The pronounced effect the MAUP has on research, particularly with different
hotspot/cluster methodologies, warrants a level of scrutiny that will encourage future
researchers to account for the bias, effects, and scope the MAUP. This section notes
several prominent studies (Table 2-1) and elaborates on the similarities and differences in
results and conclusions between these studies as well as the corollary of the MAUP.
Accounting for the MAUP provides the added benefit of eliminating an avenue of bias
and thus potential criticism toward one’s methodologies and conclusions.
8

Each of the studies discussed in this review have either attempted to measure the
MAUP or compensate for it in some way in order to prevent zoning or scale/aggregation
effects from warping statistical results and conclusions. The following section details the
studies focused solely on the scale effect; Section 2.4, the scale/aggregation effect; and
lastly, section 2.5 covers research on scale and aggregation (Table2-1).

9

Table 2-1: Studies related to the MAUP described in this chapter (inclusive of some background literature).
10

2.3 The Scale Effect
The scale problem, as defined previously (Jelinski and Wu, 1996), concerns how
the scale of any given data impacts the way in which they are analyzed and interpreted.
When moving from a fine scale geographic extent to one that excludes variation, certain
types of error inevitably follow. Dark and Bram (2007), Ratcliffe and McCullagh (1999),
and Shriner, et al. (2006) each attempt to approach the scale problem with different
methodologies. Scale is largely chosen by the extents and scale of the input data for any
evaluation. In many cases this involves the structure of a raster and the ‘cells’ that
constitute the data composites to be analyzed. Dark and Bram (2007) emphasize the
scale effect as seen in physical geography. Ratcliffe and McCullagh (1999) use hotspots
of crime occurrences to illustrate the scale effect. Shriner, et al (2007) use five grain
sizes, or raster extents, on richness hotspots for conservation planning regarding species
reserve network. Mu & Wang (2008) analyze different ways of mitigating the scale
effect.
Dark and Bram (2007) noted that the natural sciences were quick to recognize the
natural scales of many geographic and ecological phenomena. Determining the scale
with which to study a particular phenomenon or process requires a balance between the
scales of the different available data and considerations for future cross analyses which
utilize similar scales and extents. Dark and Bram’s (2007) study focused on creating
flow line models based on different Digital Elevation Models, or DEMs, of the same
area. The coarsest, or lowest scale resolution data, produced rough flow lines based on
30 meter DEMs. When overlain on finer scale DEMs (10 meter and 1 meter,
11

respectively) one may visually asses how the scale problem can warp resultant data when
assessing the topographical features of the flow lines. They also discuss possible
solutions to the scale effect of the MAUP that are highly relevant to the methodology and
results of this thesis.
Ratcliffe and McCullagh (1999), on the other hand, focus their study on hotspot
analysis and LISA statistics regarding instances of crime. They compare actual crime
statistics to the perceived zones of concentrated criminal activity as reported by police
officers across three police force subdivisions. They account for and mitigate the scale
effect of the MAUP by using a ‘moving windows’ approach to analyze the data. This
particular approach is comprised of a “technique [that] applies a movable sub-region
(usually a circle) over the entire study area to measure dependence in subsets of the study
area” (Ratcliffe and McCullagh, 1999). The ‘moving window’ approach allows for the
data to be analyzed without aggregation or the scale of the data creating a conflicting
framework for analysis (Rushton and Lolonis, 1996; Rushton, 1998, Ratcliffe and
McCullagh, 1999). The results of Ratcliffe and McCullagh’s (1999) study illustrate the
way in which hotspot analysis and the moving window technique can help law
enforcement agencies concentrate their resources on endemic areas proven to be
statistically significant hotbeds of crime. The moving window approach was pioneered
by Rushton and Lolonis (1996) and Rushton (1998).
Shriner, et al (2006) performed their analysis using five different raster extents on
species richness hotspot data to determine the spatial overlap of generated reserve
networks. Richness hotspot reserves are comprised of areas where species diversity is
12

delineated by hotspot concentrations of specific species. Through multiple iterations of
calculations they determined that “the number of species represented in richness hotspot
reserves increased as grid cell size decreased” (Shriner, et al., 2006). This particular
study clearly illustrated the scale effect of the MAUP since reserve network
configurations varied greatly across different grain sizes, which were meant to highlight
how the initial scale of input data affects the possible outcomes across any spatial
analysis. Shriner, et al. (2006) also noted that thoughtful consideration is required when
conceiving how fine-scale data may engender fragmentation and coarse-scale data may
lose essential accuracy.
Unlike the previously mentioned research, Mu and Wang (2008) attempt to
formulate a practical program for implementing a modified scale-space clustering
method, called MSSC. This program is intended to “account for both attribute
homogeneity and spatial contiguity” (Mu and Wang, 2008). To test this new technology
they considered a case study involving homicide rates in Chicago in 1990. Using the
MSSC method they develop and aggregate various tracts of land within the city of
Chicago into groups containing fewer and fewer units as the calculations progress
(continuous aggregation). Mu and Wang (2008) “name the process of repeatedly running
a clustering method toward the formation of one single cluster a converging effect.”
Their results clearly indicate the presence of the MAUP, especially when applying this
methodology to many different zones. This indicates how each process of a continuous
aggregation yields a dataset that is increasingly generalized and homogenous when
compared to its predecessor(s).
13

2.4 The Zoning Effect
The other category of the MAUP involves the zoning effect. This effect is
marked by the assumption that information aggregated to a specified area is true for every
subset of that area and that the resultant statistics of any calculations will change if the
zones change although the total areal extent remains constant. This effect causes loss of
the precision and accuracy of point-data. For example, this loss of precision would then
favor area-based data representation which makes for easier interpretation and calculation
(Williamson, et al., 2001). There are three additional articles in the following discussion
that exemplify the zoning effect. These articles include analysis in choropleth map
accuracy (MacEachren, 1982), different levels of neighborhood aggregate structure
analysis and crime (Hipp, 2007), and using local levels to determine crime rates (Bhati,
2005).
At the time of publication of MacEachren’s (1982) research, GIS technology did
not exist to readily critique different types of aggregate structures in order to determine
the areal units best suited for any given research. Despite this fact MacEachren (1982)
constructed a methodology around individual noncontiguous enumeration units
representing different counties across the United States. These units were overlaid on a
regular grid of points to measure compactness, data distribution variability, and unit size.
MacEachren (1982) concluded that unit size and enumeration are significant factors that
need to be considered for any choropleth map creation, since subsequent interpretation is
heavily dependent upon these factors. It can be inferred from MacEachren’s (1982)
14

research that scale and zonal measures impact not just data structures in analysis and
representation but also how information is visually assessed and interpreted.
While MacEachren (1982) took a broader view on unit configuration, Hipp (2007)
proffers a detailed discussion on the common problems associated with selecting what
constitutes ‘neighborhoods’ and how aggregating information with different zonal
locations may emphasize or obscure natural clusters of information. Hipp (2007) then
looks at various demographic characteristics as they relate to different criminological
paradigms to see how aggregations with different zones impact results and conclusions
drawn from them. Hipp (2007) concludes that there is no universally accepted
“appropriate” zone of aggregation that all researchers must follow. Rather a researcher
must take all possible zonal levels and scales into careful consideration in order to find
the one that is most appropriate for a particular study. Hipp (2007) also presents the
argument that reconciling how different people subjectively view the boundaries of a
given area can result in vast differences in how neighborhood boundaries are constructed
and analyzed. For example, how a city delineates a neighborhood boundary and how a
citizen living in a neighborhood delineates that same neighborhood boundary can and do
result in different definitions for areas and thus issues related to areal definitions.
Lastly, Bhati (2005) focuses his research on determining an analytical framework
to approach rare crimes via areal aggregation at different local levels. Data from the
census tract level was aggregated to neighborhood clusters for the analysis. Much like
Hipp (2007), Bhati (2005) utilizes various demographic variables in his study. In this
study the MAUP is only touched upon briefly, though the aggregate problem is shown to
15

be prominent in the resultant figures. Bhati (2005) goes on to assess that the two
aggregate boundaries used in his analysis (census tract and neighborhoods) yielded
statistically significant results across both sets with certain variables, while other
variables had a statistical significance that fluctuated across both aggregation levels.

2.5 The MAUP (Both Effects)
Few studies look at both aspects of the MAUP, preferring instead to focus either
on the scale effect or zoning effect. Seven primary articles were reviewed that deal with
both facets of the MAUP. These studies deal with a broad range of scale problems and
zoning problems, from poverty in Pennsylvania (Hayward and Parent, 2009) to upscaling
landscape analysis (Hay et al, 2001), to incidence rate maps (Nakaya, 2000). The
approaches that each researcher takes yield varying conclusions across a broad spectrum
of research. The following paragraphs summarize the highlights of each article and
provide a brief overview of the major conclusions.
Jelinski and Wu (1996) look at the MAUP as it relates to landscape ecology.
Using Normalized Difference Vegetation Index, or NDVI, they were able to aggregate
the units to test how the MAUP impacts spatial autocorrelation. Jelinski and Wu (1996)
created an artificial example of the MAUP effects which was reproduced by Dark and
Bram (2007) and seen here in Figure 2-1. In their analysis of landscape data Jelinski and
Wu (1996) aggregated data from the finest scale (1x1), basic units, to coarsest scale
(225x225). To measure the zoning effect they then used two aggregation procedures at
different scales but “with an equal number of pixels per zone” (Jelinski and Wu, 1996).
16

To test for spatial autocorrelation they used Moran’s I statistic and Geary’s C statistic.
The scale effect of the MAUP can be seen when comparing the results of different spatial
autocorrelation operations which utilize different scales (Fotheringham, 1989;
Fotheringham and Wong, 1991). Jelinski and Wu (1996) go on to conclude that “from a
hierarchical stand point of view, the MAUP is not really a ‘problem’…it may reflect the
‘nature’ of the real systems that are hierarchically structured” (Jelinski and Wu, 1996).
The determination that hierarchical structure is important in analyzing the MAUP and in
mitigating its effects will be discussed in more detail in section 2.6.

Figure 2-1: Artificial example of the aggregate effect and the scale effect on average and variance (Jelinski
and Wu, 1996)

17

Hayward and Parent (2009) concentrate on quantifying the effects of the MAUP
on poverty rates in Pennsylvania. To learn about the scale effect Hayward and Parent
(2009) created choropleth maps at different scales and zonal configurations which
resulted in the use of a Kolmogorov-Smirnov (K-S) test. To investigate the zoning effect
they used varying district designs to compare rates between different aggregated areas.
Aside from the statistical proofs of the MAUP they also generated several choropleth
maps of the results that showed different poverty concentrations that varied greatly in
location and distribution. They were careful to note how these proofs validated not only
the existence of the MAUP but how it affects the public interpretation of poverty
locations.
Hay et al. (2001) described their study and how they hoped to use hierarchically
nested data structures to analyze dominant landscape features via the Object-Specific
Analysis, or OSA. They worked on satellite imagery of a small 36 ha2 area of an island
in Canada. This imagery was scaled (by increasing grain size, or cell resolution) to
different scales and zones (resolutions) and calculated against the OSA and the Object-
Specific Upscaling, or OSU, techniques to determine which was more apt at negating or
controlling for the MAUP. Raster grids are composed of regularly gridded cells, each
with its own value or set of values. The OSU is “unique, in that it incorporates an
explicit multi-resolution (i.e., hierarchical) sampling and evaluation” of pixels within the
larger context of its higher-grained extent (Hay et al., 2001). Multiple upscaling
iterations were used on the base imagery which led them to conclude that, of the two
techniques, OSU is the one that is most appropriate for this type of study. They go on to
18

suggest that “multiscale image-object thresholds are often far more ‘fuzzy’ or less
discrete than the term threshold commonly implies” (Hay et al. 2001).
Nakaya (2000) studied the geographic relationship between a standard mortality
ratio (SMR) and a designation of 262 basic areal units (BSUs) for Tokyo City, Japan.
Incidence rate maps were generated based on several socioeconomic ratios comprising
Tokyo. A comprehensive analysis was then performed utilizing variables and the
geographic extent of the city and its comprising BSUs. Nakaya (2000) discusses possible
factors that may skew the results concerning population density distributions, and those
impacts on the final statistics. Nakaya (2000) concludes that “it is possible to find the
proper resolution of maps depending on the size of the data” to adequately understand
SMR rates and distributions.
Pawitan and Steel (2009) attempt to explore the MAUP using various statistical
simulations on Australian Census data. The results of this analysis indicate strong
evidence of MAUP, despite utilizing a single unaltered zone scheme. This thesis project
will utilize a similar analysis schema to Pawitan and Steel (2009). Pawitan and Steel
(2009) used two dataset aggregations while this thesis project will utilize four dataset
aggregations. Chapter Three of this project discusses the procedures involved in the
creation of the datasets used in this thesis.
Tagashira and Okabe (2002) attempt to study the MAUP from the specific
framework of fixed predetermined point analysis. Their regression model is based on
studying income and household location as a function of distance from the predetermined
point of a business district. This analysis also attempts to deal with the ecological fallacy
19

problem in which “results calculated from aggregate level data are unlikely to correspond
to those from individual level data” (Tagashira and Okabe, 2002). Through the use of
efficiency analysis of slope coefficients it was determined that the MAUP was prevalent
in this research area, and that the range of potential analyses roughly determines how best
to measure the ecological fallacy problem and the MAUP.
Chainey et al. (2008) focused on spatial analysis of crime instances and hotspot
analyses of this variable. The primary critique Chainey, et al. (2008) performs was an
analysis of five different hotspot analysis techniques to determine which is more accurate
in terms of estimating where actual future crimes will occur. They studied the London,
England area with two additional adjacent areas that fell within the jurisdiction of the
London Metropolitan Police Force. The results indicated that kernel density estimation,
or KDE, was consistently the most accurate technique available for use with hotspots.
Visualizations of the different hotspot techniques lend credence to their assertions that
hotspot analyses have not been as rigorously tested in past studies as they should be.
They also created a new prediction accuracy index, or PAI, as part of their validity testing
of hotspot analysis. It is important to note at this point that this thesis project attempts to
study hotspot techniques, though only under the paradigm of MAUP analysis and
confirmation, rather than determining the primacy or superiority of any one hotspot
technique.
Unlike the previously mentioned studies, Gotway and Young (2002) focus their
research on how best to approach the MAUP through statistical methods and evaluation
of best-fit approaches based on the scale of the data and possible aggregations therein.
20

Gotway and Young (2002) present a strong case for how the MAUP is merely a facet of
the larger Change of Support Problem, or COSP, that permeates spatial research. They
go on to define ‘support’ as “the size or volume associated with each data value, but the
complete specification of this term also includes the geometrical size, shape, and spatial
orientation of the regions associated with the measurements” (Gotway and Young, 2002).
The aggregation of any data into different scales or areal units, in turn, creates entirely
new variables that are only distantly related to the properties of the original variables.
Rather than apply their methods to a particular case study, they suggest various statistical
methods for dealing with particular COSPs.

2.6 Critiques
The following discussion deconstructs the issues involved with analyzing the
MAUP as it relates to the different methodologies inherent in each study. Gotway and
Young (2002) present examples of observations of the COSP and the nature of its
processes. The four types of COSPs include point, line, area, and surface. The nature of
each of the four COSPs may be quite different and directly affects the types of possible
analyses that can be performed. Thus COSP can be considered the umbrella set of
problems that the ecological fallacy problem and the MAUP are part of.
Of the literature reviewed some studies analyzed only one aspect of the MAUP
and failed to take into consideration the effects of the other aspects of the MAUP within
each analysis. Dark and Bram (2007), for example, make use of flow line analysis based
on fine and coarse grain resolution imagery. The aggregation effect does not play a role
21

in this type of research unless other factors are being measured against that imagery or if
the scale of the imagery changes across multiple dimensions. Dark and Bram (2007) do
not take the scale effect into account in their examination.
Gotway and Young (2002) also noted that hierarchical structures are important for
disaggregating clusters of data into more manageable units. This study reasonably asserts
that such hierarchical disaggregation may make false assumptions about the accuracy of
the areal data being dispersed. “These assumptions are much more than mathematical
and computational assumptions…they can (often surreptitiously) result in unusual or
unrealistic cross-scale relationships” (Gotway and Young, 2002). Shriner, et al. (2006)
made a similar note with the comment that “many authors that use coarse-grained data
either implicitly assume patterns detected using coarse grained data reflect those at other
grains (Rahbek and Graves 2000, Larsen and Rahbek 2004) or fail to discuss potential
consequences of extrapolating results to other scales” (Shriner, et al. 2006). More work
needs to be done to ask these kinds of questions in order to critically focus on the
framework of potential analyses that may deal with the MAUP and its impacts on
analytical methods and conclusions.
Jelinski and Wu (1996) and Ratcliffe and McCullagh (1999) both primarily deal
with the ‘moving windows’ approach in their analyses to the MAUP. The moving
window technique is defined as applying “a movable sub-region (usually a circle) over
the entire study area to measure dependence in subsets of the study area and is
particularly suited to crime hotspot detection” (Ratcliffe and McCullagh, 1999).
Utilizing the moving windows approach is similar to the way in which this thesis project
22

is constructed since it uses a distance threshold on each areal unit in some of the cluster
analysis methods. More on this methodology can be found in Chapter Three.
23

Chapter Three – Methodology
There are many potential vehicles of analysis available to those attempting to
study the MAUP in spatial research. This thesis uses foreclosure events in Los Angeles
County as the primary spatial variable. A total of 55,631 geographic locations pinpoint
instances of foreclosure over a three year period (2006-2008). The use of these points, as
well as artificially constructed boundaries, sheds a great deal of light on how pervasive
the MAUP is in spatial research and its accompanying conclusions. This chapter is
divided into five main sections: data gathering and acquisition, data analysis procedures,
data preparation, cluster analysis methods, and justification. Each section clarifies the
use of specific cluster analysis tools, data preparation techniques, distance thresholds, and
geographically aggregated boundaries (Getis and Ord, 1992).

3.1 Data Gathering and Acquisition
The Los Angeles County Assessor’s Office provided the original version of the
point dataset used to depict the instances of foreclosures in LA County for the given time
frame and the parcel boundary. All subsequent files used in this study were generated
independently as a result of spatial tool processes which combined, aggregated, merged,
joined, dissolved, or calculated cluster statistics on dataset features.

3.2 Data Analysis Procedure
The procedures involved in this research uses three main dimensions of analysis
to understand the effects of the MAUP. There are five different cluster analysis tools
24

which are used on seven different datasets (Mueller-Warrant, Whittaker and Young III,
2008). Each of these datasets is then broken down into another subset via the distance
threshold variable (Table 3-1). This variable indicates how far away a given point or
polygon will ‘look’ when performing statistical analyses to determine cluster properties.
Each tool, with the exception of Ripley’s K, utilizes this threshold variable. Multi-
Distance Spatial Cluster Analysis (Ripley’s K-function) tool uses regularly spaced
distance bands as a property of the tool itself. The procedures and model runs for this
project used eight different distance thresholds: 164 meters, 300 meters, 500 meters, 750
meters, 1 kilometer, 2 kilometers, 5 kilometers and 10 kilometers. The first distance
threshold, 164 meters, was determined to be the lowest acceptable distance threshold for
a hotspot analysis to run on the original foreclosure point dataset. Since the foreclosure
points are the base level data for each subsequent aggregation and tool iteration, this
minimum and subsequent thresholds were maintained across the other geographically
aggregated features. It is important to note that many processes were unable to utilize a
distance threshold of 164 meters or more due to limitations of analysis software (Esri
ArcGIS). Table 3-1 provides a complete reference as to which feature classes could run
each cluster analysis tool and at which distance thresholds they would function. This
table functions as a reference to the results maps in Chapter Four as well as the maps in
the Appendices.

25

Analysis
Method
Iteration Results
Foreclosure Points

Distance Yielded Results
High/Low Clustering
(Getis-Ord General G)
HTML
164m Yes
300m Yes
500m Yes
750m Yes
1km Yes
2km Yes
5km Yes
10km Yes
Multi-Distance Spatial
Cluster Analysis
(Ripley’s K Function)
N/A Yes
Spatial Autocorrelation
(Moran’s I)
HTML
164m N/A
300m N/A
500m N/A
750m N/A
1km N/A
2km N/A
5km N/A
10km N/A
Cluster and Outlier
Analysis (Anselin Local
Moran’s I)
164m N/A
300m N/A
500m N/A
750m N/A
1km N/A
2km N/A
5km N/A
10km N/A
Hotspot Analysis
(Getis-Ord Gi*)
164m N/A
300m N/A
500m N/A
750m N/A
1km N/A
2km N/A
5km N/A
10km N/A

Table 3-1: Guide to model iterations and results.
*Indicates the distance threshold was too low for the model iteration to run.
**Indicates the available hardware was unable to compute the results.

26

Analysis
Method
Iteration Results
Parcels Parcels2
Distance Yielded Results Yielded Results
High/Low Clustering
(Getis-Ord General G)
HTML
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km ** Yes
5km ** Yes
10km ** Yes
Multi-Distance Spatial
Cluster Analysis
(Ripley’s K-Function)
N/A ** Yes
Spatial Autocorrelation
(Moran’s I)
HTML
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Cluster and Outlier
Analysis (Anselin Local
Moran’s I)
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km ** Yes
Hotspot Analysis
(Getis-Ord Gi*)
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Table 3-1, continued: Guide to model iterations and results.

27

Analysis
Method
Iteration Results
Parcels3 Fishnet1
Distance Yielded Results Yielded Results
High/Low Clustering
(Getis-Ord General G)
HTML
164m * *
300m * Yes
500m * Yes
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Multi-Distance Spatial
Cluster Analysis
(Ripley’s K-Function)
N/A Yes **
Spatial Autocorrelation
(Moran’s I)
HTML
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Cluster and Outlier
Analysis (Anselin Local
Moran’s I)
164m * *
300m * *
500m * *
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Hotspot Analysis
(Getis-Ord Gi*)
164m * *
300m * Yes
500m * Yes
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Table 3-1, continued: Guide to model iterations and results.

28

Analysis
Method
Iteration Results
Fishnet2 Fishnet3
Distance Yielded Results Yielded Results
High/Low Clustering
(Getis-Ord General G)
HTML
164m * *
300m * *
500m * *
750m * *
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Multi-Distance Spatial
Cluster Analysis
(Ripley’s K-Function)
N/A Yes Yes
Spatial Autocorrelation
(Moran’s I)
HTML
164m * *
300m * *
500m * *
750m * *
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Cluster and Outlier
Analysis (Anselin Local
Moran’s I)
164m * *
300m Yes Yes
500m Yes Yes
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Hotspot Analysis
(Getis-Ord Gi*)
164m * *
300m Yes Yes
500m Yes Yes
750m Yes Yes
1km Yes Yes
2km Yes Yes
5km Yes Yes
10km Yes Yes
Table 3-1, continued: Guide to model iterations and results.

There are a total of seven feature classes analyzed in this study (Table 3-1). The
foreclosure points for Los Angeles County are utilized as the ‘base layer’ reference point
29

for aggregations and cluster analyses. The Assessor’s Parcel Number, or APN, as well as
spatial location for these parcels matched the provided foreclosure point dataset perfectly.
No parcels were dropped from either dataset upon joining.
Table 3-1 describes the seven feature classes, the five cluster analysis
methodologies, and the eight selected distance thresholds. Each possible permutation of
these factors is listed in this table. Table 3-1 is intended to highlight which combinations
of factors yielded results. Some of the results could not run due either to lack of
sufficient computational power or a distance threshold which was too low (not accepted
by the software program). Some of the results also were not applicable due to, for
example, the foreclosure point dataset not being able to run the spatial autocorrelation
tool against the foreclosure point dataset. The multi-distance spatial cluster analysis
(Ripley's K-function) tool uses its own distance threshold variables and iteration counts
when generating its functions (Cressie and Collins, 2001; Gatrell et al., 1996; Lentz,
Blackburn and Curtis, 2011; Mitchell, 2009; Perry, Miller and Enright, 2006; Ripley,
1977). The results of Table 3-1 indicate only whether or not a given process ran
successfully.

3.3 Data Preparation
To begin the dataset preparation process, parcels underwent the Dissolve process,
where each polygon was ‘blended’ with each adjacent parcel which shared its boundaries.
This new dataset is designated “Parcels2”. Another aggregation process was performed
30

on Parcels2 to combine adjacent parcels within 5 meters from one another. This
dissolution of boundaries created another new dataset referred to as “Parcels3”.
A regular grid of polygons, 300 meters by 300 meters, was created using the
Create Fishnet tool in Esri’s ArcGIS Toolbox. This tool generates a regular grid of
rectangles across a given input, in this instance the extent of Los Angeles County. This
new dataset is designated as “Fishnet1” and is comprised of 308,730 features. Another
aggregation process was performed on this dataset to create “Fishnet2” with broader
dimensions, 1 kilometer by 1 kilometer, comprised of 27,798 features. The final dataset
is referred to as “Fishnet3” and is identical in dimensions to Fishnet2, except that all
features are shifted by 500 meters along the horizontal axis to the East. This shift is
intended to illustrate how precarious cluster analysis is on aggregated features when
boundaries are even slightly altered. This shift is indicative of the zoning problem in the
MAUP. Table 3-2 provides a summary of these datasets and how they are derived from
one another.
Feature Dataset
Original
Dataset
Derivation Procedure Dimensions
No. of
Features
FC_Points Yes Original Dataset Within LA County 55,631
Parcels Yes Original Dataset LA County 2,367,742
Parcel2 No Dissolved 'Parcels' LA County 84,907
Parcels3 No Aggregated 'Parcels2' LA County 74,714
Fishnet1 Yes Original Dataset Grid covering LA County 308,730
Fishnet2 No Aggregated 'Fishnet1' Grid covering LA County 27,798
Fishnet3_Shifted No Shifted features from 'Fishnet2' Grid covering LA County 27,798

Table 3-2: Summary of the seven datasets utilized in this analysis.

31

3.4 Cluster Analysis Methods
Once all of the preparations for each dataset were completed, each dataset and its
associated tool were placed into an ArcGIS model in Model Builder. Model Builder
allows for multiple iterations of a single tool, or multiple tools, to run in sequence. A
total of 137 model iterations were run which covered each dataset, distance threshold,
and cluster analysis method, the results of which are shown in Table 3-1. Another
example, Figure 3-1, highlights five model iterations within a single model in Model
Builder which used the same input, but with different distance thresholds chosen. These
models facilitated an efficient processing environment which also provided a convenient
testing environment for the cluster tools and their outputs. Each feature class output was
stored in a file geodatabase except those tools with tabular or graphic output. All tools
used in this procedure are found in the Arc Toolbox from ESRI’s ArcGIS software suite.
Processing time varied across the different models and iterations. Z-scores were applied
to the cluster analysis (hotspot and cluster and outlier) outputs which yielded datasets.
The Z-scores for these datasets are used to generate maps of various areas of Los Angeles
County to highlight differences between the outputs. Depictions of these results tables,
graphs, datasets as well as the maps derived from them are included in Chapters Four and
Five along with information on Z-scores and P-values.

32

Figure 3-1: Example of a ModelBuilder model showing five Hotspot Analysis tools running in sequence. Yellow boxes represent the tools,
dark blue ovals are dataset inputs, aqua colored ovals show the two result fields (Z-score and P-value), the aqua oval represents varying
distance threshold inputs and the dark green ovals show the output datasets.
33

Many of the goals of this project involve illustrating areas where issues of either
aggregation or zonal configuration can be clearly shown to switch between hot and cold
spots. “Hot spots” delineate areas where the concentrations of a given variable
(foreclosures) occur at higher concentrations. Conversely, ‘cold spots’ indicate areas
where there is a marked absence of such occurrences. It must be noted that the red hot
spots and blue cold spots of the Hot Spot Analysis tool differs in definition from the
Cluster and Outlier Analysis tool. Figure 3-2 illustrates an example of the Hot Spot
Analysis phenomenon wherein the left side of the figure shows that a series of proximal
points is located within the same cell, thus that cell is highlighted in a red hue to indicate
high clustering. The right area of the figure illustrates the same points, but dissected
twice near the center of the cluster producing four equally sized cells with a similar
number of points in each cell. The result of this shift is exemplified in the 500 meter shift
between Fishnet2 and Fishnet3. This shift is meant to emphasize the zoning effect of the
MAUP on the aggregated datasets. Since Fishnet2 is a regular grid that covers Los
Angeles County indiscriminately of physical boundaries (such as lakes, freeways, and
mountains) the shift of the units will highlight the zoning effect of the MAUP.
34

Figure 3-2: Identical sets of points that are either contained in a single cell (left) which generates a hotspot,
or split into quadrants with different zonal boundaries (right) which shows even distribution.

3.5 Justification
The five different commonly used cluster analysis methods were chosen because
such tools can visually illustrate how pervasive the MAUP is in various facets of spatial
research in a statistically significant way. Each tool uses different functions to transform
and analyze the spatial properties of different features within the same dataset. The wide
variety of tools, aggregations, and distance thresholds lends credence to any possible
conclusions regarding the MAUP impacts on data visualization in a spatial context.
These permutations also exemplify how bias can play a role on how data is chosen,
processed, and evaluated at a fundamental level. Each of the following chapters will
detail specific attributes of the statistical tools used in this research endeavor.
Each of the five different methods discussed in this chapter were selected because
of their inherent similarities and contrasting differences. Each method constitutes an
aspect of analyzing clusters of spatial events within the same geometries. Examining the
35

MAUP requires looking at the same data for uniformity of experimentation while
maintaining the integrity of a given tool. It might be possible to analyze the MAUP using
only one cluster analysis method, though any results might be biased due to the nature of
the data, the extent of the study area, any presumptions a researcher may or may not
possess, and ‘natural’ clusters of spatially-oriented data. The elimination of these factors
requires a comprehensive analysis method that draws from multiple cluster analysis tools,
across multiple scales and multiple aggregations. A cross analysis encompassing
multiple cluster tools is one of the best methods available for easy comparison, therefore
it is implemented in this study.

36

Chapter Four – Analysis Results
Determining whether or not a feature’s similarity to its neighbors is random
requires statistical tools for validation. Each of the five tools utilized in this study
measure clustering in a different way. It is important to emphasize that this thesis does
not reflect on all the details regarding how each tool analyzes a given dataset nor the
specific statistical equations used to garner the results. Rather the goals of this research
emphasize the potential impact of scale and aggregation effects on clustering
methodologies and their results.
This chapter describes and illustrates the results of many of the model processes
for each tool’s iteration. To describe each result would be onerous; therefore this chapter
is broken down to convey the results of each tool individually, while Chapter Five
provides the interpretation of the results. Each tool is summarized in an individual
subsection with supporting figures, tables, maps, and tool outputs pertinent to each
analysis method. Hotspot analysis (Getis-Ord General G) and Cluster and Outlier
Analysis (Anselin Local Moran’s I) have similar mapped outputs grouped into hot (red)
and cold (blue) zones to reflect clustering, discussed in sections 4.1 and 4.2, respectively.
These tools function as local indicators of spatial association, or LISA, statistics. LISA
statistics give individual results for each unit in a dataset while global clustering tools
look at the datasets as a whole to determine whether or not clustering occurs. The
following three tools act as indicators of global clustering. Spatial autocorrelation
(Global Moran’s I) and High/Low Clustering (Getis-Ord General G) have graphic outputs
that are summarized in tables in sections 4.3 and 4.4, respectively. Finally, Multi-
37

Distance Spatial Cluster Analysis (Ripley’s K-function) graphic results are displayed in
section 4.5. Each subsection gives more detail on the functions and use of each tool as
well as any relevant limitations of the results.
Before each section details the results, Figure 4-1 will be used to show all the
instances of foreclosures in 2006-2008 in the Los Angeles County extent. Visual
examination of this figure already illustrates specific foreclosure clustering in the denser
urban areas. This figure can also be used as a guide to measure foreclosure instances
compared to sections 4.1 and 4.2 which have similarly detailed maps.
38

Figure 4-1: Overview map of the raw foreclosure instances in Los Angeles County from 2006 to 2008.
39

4.1 Hotspot Analysis (Getis-Ord general G) Results
Hotspot analysis is used to determine where spatial features cluster with respect to
each other within a user-defined distance threshold (Ceccato, Haining, and Signoretta,
2002; Prendergast et al., 1993). This tool, as well as spatial autocorrelation and Cluster
and Outlier analysis, are unable to process the foreclosure point dataset. Since hotspot
analysis requires that each feature be weighted in some way, there was no method of
running hotspot analysis on the foreclosure points without weighting them with some
other unrelated variable. Such a weight would not allow the foreclosure points to be
correlated with any of the other datasets whose weighted variable is a sum count of the
total instances of foreclosure that take place within its boundaries. This exemplifies the
aggregation effect of the MAUP. The foreclosure points cannot be compared to another
variable without aggregating them to larger areal units. This justifies why the sum count
of foreclosure instances within each polygon unit is used as the primary variable to be
tested.
All of the other datasets were able to run at least five of the selected distance
thresholds. The three parcels datasets ran successful iterations of hotspot analysis at a
distance threshold of 750 meters and above. The three Fishnet datasets ran successfully
at a distance threshold of 300 meters or more. Each iteration output resulted in a new
dataset with new attribute fields pertaining to the p-value and the z-score of each
feature’s clustering properties. The null hypothesis of this analysis tool is that there is no
inherent spatial association between the raw foreclosure points and any aggregations of
them. P-values represent the probability that the null hypothesis was falsely rejected
40

(Mitchell, 2009). Mitchell (2009) describes the Z-score as “a reference measure for the
standard normal distribution (with mean of zero and standard deviation of 1)”. The Z-
score is a useful way of determining whether or not to reject the null hypothesis.
Figure 4-2 provides an overview map of the cluster analysis for hotspots for the
Los Angeles County extent. Subsequent maps for this chapter are in a similar format.
The dark red areas represent z-scores of 2 or higher, which indicate areas with high
foreclosure instances, while the dark blue areas, with z-scores of -2 or less, showing areas
contiguously void of foreclosures. The light blue areas (z-score of 2.0 to 1.0) indicate
areas that are moderately void of foreclosures while the light red or beige areas (z-score
of -1.0 to -2.0) show areas with moderate foreclosure clustering. The white areas
represent areas of dispersion with neither high clustering nor low clustering. In this
analysis, ‘dispersion’ is defined as an area with neither a high concentration of
foreclosures nor an absence of them. Any green areas in the map are simply background
imagery service showing forested areas via green polygons. Figure 4-2 provides an
overview map of the Parcels3 dataset, 2 kilometer distance threshold, with the contiguous
Los Angeles County as the same scale.
41

Figure 4-2: Overview hotspot analysis map of Parcels3 showing all Los Angeles County with a 2
kilometer distance threshold
42

Figure 4-3: Overview hotspot analysis map of Parcels3 showing all Los Angeles County with a 1 kilometer
distance threshold.
43

At smaller scales, some results/maps illustrate interesting differences when the
distance threshold is shifted from 750 meters to 5 kilometers. Parcels2 results indicate
severe shifts in hot/cold spot locations based on the distance threshold. Figure 4-4 and
Figure 4-5 show the Parcels2 dataset zoomed into a smaller area to illustrate these shifts,
how hotspot areas dramatically change when features are aggregated into larger units.
This discussion and the following sections of this chapter are intended to highlight the
final results of model iterations. Interpretation and further discussion of these results are
provided in Chapter Five.
44

Figure 4-4: Hotspot analysis results for the Parcels2 dataset at a distance threshold of 750 meters.
45

Figure 4-5: Hotspot analysis results for the Parcels2 dataset at a distance threshold of 5 kilometers.
46

4.2 Cluster and Outlier Analysis (Anselin Local Moran’s I) Results
A cluster and outlier analysis is marked not necessarily by how individual features
rate when clustered near one another, but rather by how their weights impact their
standing in relation to all other features they are adjacent to (Mitchell, 2009). The results
from an Anselin Local Moran’s I test give a more detailed look at how features cluster to
each other depending on the weighted attribute being tested against and the same
weighted attributes from nearby features. An example of this basic principle can be
found in Figure 4-6, where the Parcels2 dataset was processed with a 5 km distance
threshold.
It is important to reiterate that this analysis does not focus on explaining the
differences between different permutations of model runs when changing certain aspects
of how an analysis tool processes a given feature with its neighbors, but rather that almost
all possible parameters remain the same with only the dataset and distance threshold
changing. Altering these parameters in this tool or in any of the other related tools with
similar parameters will result in more potential permutations than would be prudent to
address, given the scope of this project.
The outputs from the cluster and outlier analysis are indicative of spatial patterns
that can be seen across multiple scales and aggregations. For example, Figure 4-7, which
illustrates the results of the Fishnet1 dataset at a 5 kilometer distance threshold, shows
clearly defined natural clusters at the county-wide scale. Conversely, when the dataset is
shifted to Fishnet2, as in Figure 4-8, the same perspective or scale with the same distance
47

Figure 4-6: Cluster and outlier analysis of the Parcels2 dataset with a 5km distance threshold.
48

Figure 4-7: Cluster and outlier analysis of the Fishnet1 dataset with a 5km distance threshold.
49

Figure 4-8: Cluster and outlier analysis of the Fishnet2 dataset with a 5km distance threshold.

50

threshold illustrates vastly different results. There are now significantly higher numbers
of contiguous hotspots, with a few cold spots that are difficult to discern.
One must remember that while the analysis tool utilizes similar outputs to the
hotspot analysis tool (Getis-Ord General G), the interpretation of hot and cold spots is
different. This analysis looks at how similar a weighted feature is to every other feature
within its immediate vicinity while taking into account all the other features within its
distance threshold (Mitchell, 2009). Areas that are ‘cold’, or dark blue, do not
necessarily indicate areas where no foreclosures occur, but merely that the pattern of
clustering varies greatly enough in that area to warrant a negative z-score and negative
Moran’s I value. Alternately the hotspot analysis (Getis-Ord General G) determines
whether or not a unit is ‘hot’ or ‘cold’ based on the total number and respective weights
of all its neighbor features within the specified distance threshold.

4.3 Spatial Autocorrelation (Global Moran’s I) Results
The Global Moran’s I tool simultaneously measures a feature’s weighted variable
and its location to determine whether or not a pattern is dispersed, random, or clustered.
It then assigns P-values and Z-scores to show the significance of the results (Dale et al.,
2002; Mitchell, 2009). All of the results for the Global Moran’s I statistic indicated a
positive likelihood that clusters were present in discernible patterns. There was a less
than 1% chance that patterns of clusters could have been the result of random chance.
All Moran’s Index scores are supposed to be between -1 and 1 (Mitchell, 2009).
Negative Moran’s I scores represent suspected dissimilarity, with an index closer to -1
51

representing the most dissimilarity. Conversely, positive Moran’s I scores represent
suspected clustering, with values closer to 1 representing high levels of clustering with
similar values (Mitchell, 2009). The 1 kilometer distance threshold is the only model for
the Parcels dataset that ran successfully, though its results will not be considered due to
falling outside the valid range of results, see Table 4-1. The reasons for this aberration
are unknown. The remaining results from the Spatial Autocorrelation analysis are
provided in Table 4-1.
The Spatial Autocorrelation tool requires that each feature be weighted in some
way so as to indicate autocorrelation between and among various features and their
attributes. All of the aggregated datasets (except the foreclosure dataset) employed the
total count of all instances of foreclosure as the variable to be tested. Since the
foreclosure points dataset could not be tested against itself, it was exempted from this
particular analysis. This dataset could have been autocorrelated with another unrelated
variable, such as unemployment rates, though such a correlation would have had no
meaning compared to the other datasets analyzed or to their results.
All of the Moran’s I scores and associated z-scores indicated strong clustering
patterns within and amongst the various datasets. Each of these results corresponds with
the results from the Ripley’s K-function results as shown in section 4.5. This
corroboration indicates not only that the clustering of foreclosures is indicative of
inherent assemblages of foreclosure instances but that their groupings tend toward
recognizable spatial patte

52

Spatial Autocorrelation Results
Dataset Distance Z-Score Moran's Index
Parcels
164m* * *
300m* * *
500m* * *
750m* * *
1km** 105500.436** 31.702**
2km Incomplete Incomplete
5km Incomplete Incomplete
10km Incomplete Incomplete
Parcels2
164m* * *
300m* * *
500m* * *
750m 32.534 0.062
1km 41.102 0.061
2km 71.654 0.06
5km 130.716 0.054
10km 193.249 0.048
Parcels3
164m* * *
300m* * *
500m* * *
750m 33.617 0.077
1km 42.449 0.075
2km 74.593 0.074
5km 136.533 0.066
10km 202.423 0.058

Table 4-1: Summary of the Spatial Autocorrelation results.
*This particular dataset could not be run due to an insufficient distance threshold within the extent of LA
County for the tool to run properly.
**Results do not fall within acceptable parameters.

53

Spatial Autocorrelation Results
Fishnet1
164m* * *
300m* * *
500m 562.288 0.514
750m 789.443 0.476
1km 972.212 0.451
2km 1516.324 0.392
5km 2587.939 0.297
10km 3564.576 0.225
Fishnet2
164m* * *
300m* * *
500m* * *
750m* * *
1km 176.278 0.749
2km 270.711 0.691
5km 491.362 0.539
10km 682.698 0.414
Fishnet3
164m* * *
300m* * *
500m* * *
750m* * *
1km 174 0.739
2km 267.137 0.681
5km 485.489 0.532
10km 674.508 0.409

Table 4-1, continued: Summary of Spatial Autocorrelation results.
*This particular dataset could not be run due to an insufficient distance threshold within the extent of LA
County for the tool to run properly.

4.4 High/Low Clustering Results (Getis-Ord General G) Results
The High/Low Clustering tool (Getis-Ord General G) calculates a single statistic
for a given dataset at different distance thresholds, one statistic per iteration, rather than
statistical results for each feature. This tool provides the benefit of describing whether or
54

not a dataset indicates if there are concentrations of high or low values and whether or not
these values are clustered. A tool such as this works best in describing the overall trend
of a given study area, depending on the scope of one’s research and goals (Mitchell,
2009). The primary results of this analysis indicate that all successful iterations resulted
in a statistically significant indication of clustering showing a p-value of less than 0.01,
with the sole exception of Parcels2 at the 1 kilometer distance threshold, which had a p-
value of 0.06.
The results of the high/low clustering analysis match well with the results of the
spatial autocorrelation analysis. Global Moran’s I and Getis-Ord general G both measure
continuous feature values in order to ascertain an overall pattern of the dataset. These
results indicate that the local level of statistics in the results of other tools’ processes
should provide a clearer idea as to the spatial patterns involved in the instances of
foreclosures across various scales, aggregations, and datasets.
Summary of High/Low Clustering Results
Dataset Distance Z-Score Observed General G p-value
Parcels
164m * - -
300m * - -
500m * - -
750m 36971.598 0.005192 0
1km 36964.607 0.005192 0
2km ** - -
5km ** - -
10km ** - -

Table 4-2: Summary of High/Low Clustering results.
*This particular dataset could not be run due to an insufficient distance threshold for the tool to run
properly.
**This dataset could not run due to insufficient processing power of available hardware.

55

Summary of High/Low Clustering Results
Parcels2
164m * - -
300m * - -
500m * - -
750m 2.876 0 0.004029
1km 1.879 0 0.060241
2km 6.808 0.000001 0
5km 8.456 0.000002 0
10km **

Parcels3
164m *

300m *

500m *

750m 9.233 0 0
1km 8.287 0 0
2km 15.717 0.000001 0
5km 19.691 0.000002 0
10km 17.507 0.000003 0
Fishnet1
164m *

300m 425.936 0.000001 0
500m 562.338 0.000001 0
750m 789.321 0.000002 0
1km 971.59 0.000003 0
2km 1507.599 0.000006 0
5km 2407.209 0.000012 0
10km 2522.363 0.000019 0
Fishnet2
164m *

300m *

500m *

750m *

1km 176.384 0.000002 0
2km 270.669 0.000004 0
5km 482.874 0.00001 0
10km 613.982 0.000017 0

Table 4-2, continued: Summary of High/Low Clustering results.
*This particular dataset could not be run due to an insufficient distance threshold for the tool to run
properly.
**This dataset could not run due to insufficient processing power of available hardware.
56

Summary of High/Low Clustering Results
Fishnet3_Shifted
164m * - -
300m * - -
500m * - -
750m * - -
1km 174.107 0.000002 0
2km 267.102 0.000004 0
5km 477.224 0.00001 0
10km 607.364 0.000017 0

Table 4-2, continued: Summary of High/Low Clustering results.
*This particular dataset could not be run due to an insufficient distance threshold for the tool to run
properly.
**This dataset could not run due to insufficient processing power of available hardware.

4.5 Multi-Distance Spatial Cluster Analysis (Ripley’s K-function) Results
Haase (1995) and Diggle et al. (2003) both note how the Ripley’s K statistic tests
against a null hypothesis which supposes that a distribution of points is completely
random. When the Ripley’s K statistic is run on a dataset of spatial points it can be
determined whether or not there is any inherent clustering of said points. A procedure
involving the production of random points within the same extent of the dataset and then
running simulations to determine a ‘confidence envelope’ is described by Haase (1995).
This confidence envelope is used to illustrate a 95%, 99%, or 99.9% confidence level of
statistical accuracy based on the number of simulations run per dataset. This project used
a 99% confidence envelope for the five datasets which could be processed.
Unlike the other tools utilized in this project, the Multi-Distance Spatial Cluster
Analysis tool has multiple distance thresholds built into the overall structure of the tool
processes (Dale et al., 2002; Gatrell et al, 1996; Lentz, Blackburn and Curtis; 2011). The
57

foreclosure points dataset has a much higher Observed K than the Expected K, which
indicates a strong clustering pattern, see Figure 4-9. There is no statistically significant
difference between the expected and observed K-values for either of the two Fishnet
datasets capable of being calculated, see Figure 4-10 and Figure 4-10. Fishnet2 and
Fishnet3 had similar results due to their almost identical features and extents (in terms of
total area and dimensions). This is to be expected given the nature of the Fishnet
composition. Without variations in the perimeter or area of each polygon, it will be
difficult for clustering to occur outside of an expected range. Unfortunately, the Parcels
and Fishnet1 datasets were unable to be computed given the nature of the dataset and the
processes involved in using this tool.

58

Figure 4-9: Ripley’s K graph showing the Expected K, Observed K, and Confidence Interval for the Foreclosure Points dataset.
59

Figure 4-10: Ripley’s K graph showing the Expected K, Observed K, and Confidence Interval for the Fishnet2 dataset.
60

Figure 4-11: Ripley’s K graph showing the Expected K, Observed K, and Confidence Interval for the Parcels2 dataset.
61

Figure 4-12: Ripley’s K graph showing the Expected K, Observed K, and Confidence Interval for the Parcels3 dataset.
62

The Parcels2, Parcels3, Fishnet2, and Fishnet3 K-functions show a clear
indication of strong clustering within the instances of foreclosure in Los Angeles County.
These results prove that the null hypothesis is false which lends credence and validity to
the other cluster analysis results. The Multi-Distance Spatial Cluster Analysis tool
utilizes a beginning distance threshold (in this project, 500 meters is utilized) with a total
of ten iterations per dataset, each with an additional 500 meter distance threshold. The
latter is shown in Figure 4-9 to 4-13 as the independent variable on the X-axis. The
perpetually increasing distance thresholds in this analysis, as well as the eight distance
thresholds selected for the other tools, act as a gauge for how scale effects impact the way
in which the results can be perceived as being clustered or dispersed, depending on the
dataset and distance threshold chosen. Figures 4-10 and 4-11 illustrate this principle
when the distance threshold is between 500 meters and 1 kilometer, which indicates that
the Fishnet2 and Fishnet3 datasets have a high level of dispersion. All the distance
thresholds at or above 1 kilometer show patterns of significant clustering. Future spatial
research along similar veins must remain cognizant of how much of an impact scale has
on the final results of any cluster analysis. Overall, the Multi-Distance Spatial Cluster
Analysis illustrated the inherent clustering of the foreclosure point aggregations as well
as other clustering, based on other datasets of varying aggregations, scales, and distance
thresholds.

63

Fig 4-13: K-function graph showing the Expected K, Observed K, and Confidence Interval for the Fishnet3 dataset.
64

Chapter Five – Interpretation
5.1 Interpretation of Hotspot Results (Getis-Ord Gi*)
Much of Chapter Four dealt with assessing the individual results of each model
iteration with summaries or examples. These results varied, as indicated in this chapter
with tables, graphs, and maps. The emphasis of Chapter Five is to compare the results of
the two LISA tools (Hotspot and Cluster and Outlier Analyses). These two sets of
outputs are more easily compared to one another since they analyze features individually
rather than entire datasets. The results are shown to exemplify the effects of the MAUP
across multiple distance thresholds and areas. Datasets that share similar scales and
aggregation methodologies provide a greater understanding of how the MAUP interacts
with spatial data, analysis results, and interpretation(s) of those results.
Hotspot maps detailing a small area within Los Angeles County help provide a
means for understanding just how prevalent the MAUP is in spatial research. Figures 5-1
and 5-2 show an area near Rosemead, California that highlights some important
differences in hotspot clusters foreclosures. Figure 5-1 shows the hotspot Gi Z-score
values on a map for the Parcels3 dataset at a 750 meter distance threshold. Figure 5-2
shows the same area with the same dataset but with a 10 kilometer distance threshold.
Many of the areas in Figure 5-1 that were considered to be ‘cold’ spots are now shown to
be dispersed in Figure 5-2.

65

Figure 5-1: Hot spot analysis map of Parcels3 dataset at a distance threshold of 750 meters.
66

Figure 5-2: Hot spot analysis map of Parcels3 dataset at a distance threshold of 10 kilometers.
67

Particular interest should be paid to the red hotspot near the center of Figure 5-1.
This area is shown with greater detail in Figures 5-3 and 5-4. Figure 5-3 shows the same
dataset, Parcels3, with a distance threshold of 750 meters while Figure 5-4 shows the area
with a 10 kilometer distance threshold. It is noteworthy how Figure 5-3 shows an area
with a few hotspots, while the rest of the surroundings appear to have a dispersed number
of foreclosures. This is indicated by the surrounding area having a GiZScore of -1.0 to
1.0 (beige coloring on the map). Figure 5-4, with its differing distance threshold, shows a
far greater shift from the previous figure, Figure 5-3. Figure 5-4 now considers the entire
area to be a ‘cold’ spot with GiZScores of less than -2.0.
Results such as these highlight the need for spatial researchers to examine exactly
how the MAUP will affect their spatial research. The examples in Figures 5-1 to 5-4 do
stress opposite ends of a distance threshold continuum, the lowest distance threshold
compared to much higher distance threshold, though the results of this change are
significant in several regards. These figures call attention to how drastic the scale effect
of the MAUP can be in terms of how readily assemblages of spatial features can be
subjectively illustrated and measured. Whether or not a group of features are considered
“clusters” continues to depend on the scale with which the features are viewed. It is
therefore imperative that any spatial research having to deal with cluster analysis consider
employing multiple scales to analyze spatial data. Such considerations might promote
awareness of the widespread effects of the MAUP. The rest of this section details some
of the most noteworthy effects of the Cluster and Outlier analysis through analyses at
68

multiple scales and with different datasets in order to illustrate the resulting aggregation
effects.

69

Figure 5-3: Smaller-scale close up of Hotspot analysis map of Parcels3 with a 750 meter distance
threshold.
70

Figure 5-4: Smaller-scale close up of Hotspot analysis map of Parcels3 with a 10 kilometer distance
threshold.
71

5.2 Interpretation of Cluster and Outlier Analysis Results (Anselin Local Moran’s I)
The previous section dealt with what happens when the distance threshold
changes in a given area in a hotspot analysis, whereas this section describes what happens
when the distance threshold remains the same while the datasets vary. Such variation
will highlight how scale/aggregation and zoning effects alter the results of a Cluster and
Outlier analysis. When comparing Figures 5-5 and 5-6 or Figures 5-5 and 5-7 to each
other, the shift depicted by the variation in hot, cold, or dispersed is indicative of how
much zoning affects the results. Cluster and outlier analysis looks at how features relate
to other neighborhood features. There are two blue cells above the legend in Figure 5-5.
These features are dark blue not just because there is a lack of foreclosures within their
boundaries, but also because surrounding cells containing more than one instance of
foreclosure. When compared to Figures 5-6 and 5-7 their presence is completely lost
when this information was aggregated into shifted zonal units.
Figures 5-8, 5-9, and 5-10 illustrate a similar point. Each of the figures, when
compared to one another, gives different results. Due to the increasing aggregation of the
Parcels features where tracts of land were merged into one another, some features are
often only separated by a single street. A strong example of this can be viewed in the
way that certain areas have several ‘clusters’ of foreclosures (depending on scale), though
the Parcels dataset does not distinguish naturally occurring neighborhoods, merely
(non)adjacent boundaries. The question of which scale and aggregation method work
best is discussed in the next section.
72

Figure 5-5: Cluster and outlier analysis map of Fishnet1 with a 1 kilometer distance threshold.
73

Figure 5-6: Cluster and outlier analysis map of Fishnet2 with a 1 kilometer distance threshold.
74

Figure 5-7: Cluster and outlier analysis map of Fishnet3 with a 1 kilometer distance threshold.
75

Figure 5-8: Cluster and outlier analysis map of Parcels with a 1 kilometer distance threshold.
76

Figure 5-9: Cluster and outlier analysis map of Parcels2 with a 1 kilometer distance threshold.
77

Figure 5-10: Cluster and outlier analysis map of Parcels3 with a 1 kilometer distance threshold.
78

5.3 The Broader Results
The overall pattern of the results indicates strong clustering in the foreclosure
points and the various aggregations of those points. The tools which analyze the global
patterns of clustering and dispersion clearly indicate a prevalence of clustering across
multiple datasets and distance thresholds. When reviewing the mapped results of the
hotspot analysis and the cluster and outlier analysis, results show the strongest instances
of variation with the datasets. Areas with high distance thresholds are shown to be
clustered while the same areas indicate disorder when lower distance thresholds are
chosen. This type of variation exists across all mapped datasets where any single input is
altered. There is very little homogeneity between and amongst the different mapped
outputs.
The implications of these varying outputs are far reaching. They not only confirm
the existence of the MAUP but also how difficult it can be to determine the most
appropriate approach spatial research would need to take to account for its effects. These
outputs highlight the importance of running various types of analyses to make certain that
results accurately reflect the true physical topic of interest, and not skewed results that
aggregation and zoning effects will create.
As a hypothetical example, a city planner wants to know what areas of a city need
more street lights for its citizens. The planner would need to delineate how he or she
characterizes the areal units in this type of study. Are they constructed of parcel units,
regular grids, commonly-accepted neighborhood delineations, or some other artificially
constructed boundary? Perhaps it is a combination of multiple types of boundaries in
79

order to find the least luminous areas. Does the planner also account for population
density so that more lights are needed in denser areas? It would also need to be
determined how many lights a given areal unit would need in order to be considered
sufficiently luminous. This hypothetical example is riddled with questions that need to
be answered by generating multiple outputs to thoroughly answer the questions the
analysis puts forward.

5.4 Future Avenues of Research
The scope of this project is based upon the exemplification of the effects of the
MAUP using cluster analysis methods on instances of real foreclosures in Los Angeles
County, between 2006 and 2008, and various aggregations of these events. There are a
number of avenues of exploration remaining for future appropriate inquiry into this area
of research. This project researched only instances of foreclosures and their spatially
joined counts as the primary variable studied. In the future, it would be interesting to
examine the regression and autocorrelation results of the foreclosure data with
demographic data, such as household income, residential age groups, and crime rates. In
addition to such analyses, yet more research possibilities include determining the ‘true’
aggregation effects when factoring in non-Euclidian distance measures. An example of
this approach would be to include two foreclosures happening within 500 meters from
one another, but separated geographically by elevation. Another possible avenue of
research may be in the replication of cluster analysis results with point features from
highly different fields of spatial research, such as locations of infected flora or locations
80

of street lights signifying ‘clusters’ of illumination and thus light pollution. Although
these additional avenues of research could be used to further validate the analyses of the
MAUP and shed more light on the best practices, they do not necessarily encompass the
scope of a typical thesis project.

5.5 Answering the Theoretical Questions
Chapter One introduced the modifiable areal unit problem, or MAUP, and the
scale and aggregation problems which comprise it. Subsequent sections gave information
on just how much of an impact scale and aggregation have on analysis results. It was
determined from the results of this research project that issues of scale and zoning affect
conceptualization as well as the results of such analyses. The scale of what is utilized –
large/small, many/few, coarse/fine, and high/low distance thresholds – impacts how a
project is formulated and executed, and in turn the results.
To answer the first thesis question of this project, the effects of the MAUP on the
visual results are clearly shown in the maps and stress the importance of looking at wide
ranges of areal scales and zonal configurations in order to best fit avenues of research. It
is challenging to navigate the visual differences in the maps of areas of Los Angeles
County that result from the cluster analysis tools and their varying datasets and distance
thresholds.
The second thesis question, regarding best scale or zonal unit of analysis, assumes
that all spatial research can and should use a standard zonal scheme. This project looked
at regularly gridded areas at different scales and zonal configurations (Fishnet1, Fishnet2,
81

and Fishnet3) as well as more realistic structures that represent actual urban geographies
(Parcels, Parcels2, Parcels3). The unit selected should be comparable to the size of the
phenomenon being studied. Researchers have to use intuition and educated guessing to
know what this is or use a variety of scales and see which one gives results that are close
to what should be expected. The questions that each spatial researcher attempt to answer
require multifaceted approaches to deal with the scale effect and the zoning effect.
More research should be conducted to highlight known methods of MAUP
mitigation. One of the strongest conclusions that can be drawn from this research is that
most forms of spatial analysis must be sure to at least acknowledge the assorted impacts
of the MAUP by varying analyses at different scales relevant to the given study area,
aggregation units, and perspectives in order to fully comprehend all the possible
consequences of the MAUP on their research.
The final question this research attempted to answer was how the MAUP affects
the way in which a methodology should be constructed. Any and all measures should be
taken in order to account for the MAUP in research projects. Steps should always be
taken to mitigate the effects of the MAUP in spatial research (Mu and Wang, 2008).
Certain approaches, such as the ‘moving window’ approach, can be used to help mitigate
some aspects of the MAUP in spatial research (Jelinski and Wu, 1996; Ratcliffe and
McCullagh, 1999). Acknowledging the MAUP in published research can go a long way
towards cultivating the thought processes needed to ensure the future development of
sound methodologies which account for the inherent biases of preselected boundaries,
scales, extents, and the limitations of aggregated data in spatial research (Hipp, 2007).
82

The surest way of imparting the impacts of the MAUP on those performing
spatial research is through rigorous education and training. The development of GIS
technology coupled with the ever-increasing advances in computer and network
capabilities is generating spatial data at an unprecedented rate. One need only look at the
various spatial data repositories on the internet to recognize the variety of potential
avenues of analysis available to everyone.
Persistent effects generated by the MAUP will continue to plague spatial research
until large scale efforts are taken to understand, quantify, and evaluate all facets of the
MAUP. An even greater effort is required to educate those who would perform spatial
research on how to anticipate the MAUP and mitigate its effects, if possible. It must be
proposed that the first step in such educational efforts include mention of the MAUP in
more research and literature than is currently present. Perhaps such educational efforts
will include the introduction of the background and prevalence of the MAUP. When
enough researchers and students are made aware of the MAUP and its effects become
known to a wider audience it will then permeate guidebooks, textbooks, and the technical
literature which will influence generations of GIS professionals. Such permeation will
saturate the GIS community which will enable understanding of the MAUP and hopefully
generate a level of enthusiasm needed to help mitigate it on an institutional level.

83

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from Research and Practice. London: Taylor and Francis, pp. 187-202.

Abstract (if available)

Abstract Spatial research has been plagued by the modifiable areal unit problem, or MAUP (Openshaw, 1979), for decades. The MAUP can be broken down into two categories, the scale or aggregation effect and the zoning or grouping effect. Recent advances in spatial science and technology have exacerbated the effects of the MAUP prevalent in many forms of research. In this paper, data was obtained depicting instances of foreclosures in Los Angeles County (also the study extent) in 2006-2008. This data was spatially joined to three sets of grids, or fishnets, covering Los Angeles County. The data was also spatially joined to three additional datasets: the individual parcels of Los Angeles County and two aggregations of these parcels. Five cluster analysis tools were used to analyze each of these seven total datasets. Each permutation involved the five tools, seven datasets, and multiple pre-selected distance thresholds to test for scale and zoning effects of the MAUP. There were a total of 137 successful iterations illustrating the aforementioned permutations. It was determined the MAUP is prevalent in this case study. Suggestions are made in determining future actions to combat the effects of the MAUP.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Davis, Matthew W. (author)

Core Title The modifiable areal unit problem (MAUP) via cluster analysis methodologies: a look at scale, zoning, and instances of foreclosure in Los Angeles County

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 05/04/2012

Defense Date 02/22/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag hotspot,modifiable areal unit problem (MAUP),OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Swift, Jennifer N. (committee chair), Curtis, Andrew J. (committee member), Goldberg, Daniel (committee member)

Creator Email m.w.davis1984@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-27983

Unique identifier UC11289471

Identifier usctheses-c3-27983 (legacy record id)

Legacy Identifier etd-DavisMatth-748.pdf

Dmrecord 27983

Document Type Thesis

Rights Davis, Matthew W.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA