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Evaluating the MAUP scale effects on property crime in San Francisco, California

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Evaluating the MAUP scale effects on property crime in San Francisco, California

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EVALUATING THE MAUP SCALE EFFECTS ON PROPERTY CRIME
IN SAN FRANCISCO, CALIFORNIA

by

Benecia Zahrani

A Thesis Presented to the
FACULTY OF THE USC DORNSIFE COLLEGE OF LETTERS, ARTS AND SCIENCES
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOGRAPHIC INFORMATION SCIENCE AND TECHNOLOGY)

August 2020

Copyright 2020 Benecia Zahrani
ii

Dedication

To my family

iii

Acknowledgments
I am grateful to all the professors who taught me throughout this program, you have helped make
a longtime goal a reality. Thank you to Professors Ruddell and Oda, who helped me start and end
my thesis journey. Professor Oda provided invaluable support and guidance throughout the
process. I would also like to thank my thesis committee members, Professors Wilson and
Fleming, whose critiques helped me better formulate why the MAUP matters. Writing is a
painstaking process for me, and without the support and patience of my advisor and thesis
committee, this thesis would be challenging to read. I appreciate the time and effort they spent
proofreading my manuscript.

iv

Table of Contents
Dedication ....................................................................................................................................... ii
Acknowledgments ......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................. vi
List of Figures ............................................................................................................................... vii
Abbreviations ............................................................................................................................... viii
Abstract .......................................................................................................................................... ix
Chapter 1 Introduction .................................................................................................................... 1
1.1. Why MAUP Matters ...........................................................................................................2
1.2. Geography and Scale and MAUP .......................................................................................3
1.3. MAUP Definition and Examples ........................................................................................5
1.3.1. Scale and Zoning Effects of MAUP ..........................................................................6
1.3.2. MAUP’s relative – The Ecological Fallacy ...............................................................9
1.4. Application of the MAUP to the Case Study ....................................................................10
1.5. Thesis Organization ..........................................................................................................11
Chapter 2 Related Work ............................................................................................................... 12
2.1. MAUP ...............................................................................................................................12
2.1.1. Statistical Analysis Sensitivity to the MAUP ..........................................................13
2.1.2. MAUP Effect on Cluster Analysis ...........................................................................16
2.1.3. MAUP Effect on Regression Analysis ....................................................................18
2.1.4. Attempts to Solve the MAUP ..................................................................................21
2.2. Crime Theory and the Variables .......................................................................................22
2.2.1. Crime Types and Property Crime Definition ...........................................................22
2.2.2. Independent Variables –Demographic Factors and their Relation to Crime ...........22

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Chapter 3 Methods and Data ........................................................................................................ 25
3.1. Data Acquisition, Assessment and Preparation ................................................................25
3.1.1. Study Area and Boundary Data ...............................................................................26
3.1.2. Crime Data ...............................................................................................................29
3.1.3. Demographic Data ...................................................................................................30
3.1.4. Data Normalization ..................................................................................................32
3.2. Methods Workflow ...........................................................................................................33
3.2.1. Optimized Hot Spot Analysis ..................................................................................34
3.2.2. Regression Analysis .................................................................................................36
Chapter 4 Results .......................................................................................................................... 39
4.1. Optimized Hot Spot Analysis Results ..............................................................................39
4.2. Regression Analyses Results ............................................................................................42
4.2.1. Exploratory Regression Results ...............................................................................42
4.2.2. Descriptive Statistics of Final Variables ..................................................................45
4.2.3. Generalized Linear Regression Results ...................................................................46
Chapter 5 Discussion and Conclusions ......................................................................................... 51
5.1. Limitations and Recommendations...................................................................................55
5.1.1. Assessing Model Significance to Property Crime in San Francisco........................55
5.1.2. Future Work and Avenues for Research ..................................................................55
5.2. Final Thoughts ..................................................................................................................56
References ..................................................................................................................................... 58
Appendix A Optimized Hot Spot Analysis Results Windows ..................................................... 62

vi

List of Tables
Table 1 Datasets and data sources ................................................................................................ 26
Table 2 Variables used for regression analysis ............................................................................. 33
Table 3 Final demographic variables used in regression models ................................................. 43
Table 4 Census block groups & tracts exploratory regression summaries ................................... 44
Table 5 Exploratory regression results at the census block group and census tract scales ........... 45
Table 6 Descriptive statistics of model variables ......................................................................... 46
Table 7 Generalized linear regression model diagnostics............................................................. 47
Table 8 Generalized linear regression results ............................................................................... 48

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List of Figures
Figure 1 Map of San Francisco County, California. Source: Esri 2020 ......................................... 2
Figure 2 MAUP examples. Source: Bolstad 2016, pg. 392 ............................................................ 6
Figure 3 Scale and zoning effects. Source: Lloyd 2014, pg. 30 ..................................................... 7
Figure 4 MAUP Scale effect on Jefferson County, Alabama population density .......................... 8
Figure 5 MAUP Zone effect on Jefferson County, Alabama population density ........................... 9
Figure 6 Optimized hot spot analysis of crime in Strathclyde, Scotland. Source: McKay 2018,
pg.89.............................................................................................................................................. 17
Figure 7 Variation in regression results due to scale. Source: Louvet et al., 2015, pg. 68 ........... 19
Figure 8 San Francisco unclipped TIGER/Line census tract boundaries ..................................... 27
Figure 9 Final study area............................................................................................................... 28
Figure 10 Spatial location of 2018 San Francisco masked crime incidents ................................. 30
Figure 11 Research question and methods workflow ................................................................... 34
Figure 12 Ordinary least squares: Predicted values in relation to observed values. Source: Esri
2019b............................................................................................................................................. 37
Figure 13 Property crime optimized hot spot analysis at the census block group scale ............... 40
Figure 14 Property crime optimized hot spot analysis at the census tract scale ........................... 41
Figure 15 GLR census block group standardized residuals .......................................................... 49
Figure 16 GLR census tract standardized residuals ...................................................................... 50

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Abbreviations
AICc Corrected Akaike Information Criterion
ACS American Community Survey
CA California
CPS Current Population Survey
FBI Federal Bureau of Investigation
GEOID Geographic Identity Codes
GIS Geographic Information System
GISci Geographic Information Science
GLR Generalized Linear regression
GWR Geographically Weighted Regression
LISA Local Spatial Autocorrelation Method
MAUP Modifiable Aerial Unit Problem
MGWR Multiscale Geographically Weighted Regression
OA Output Area
OLS Ordinary Least Squares
SD Standard Deviation
SF San Francisco
SSI Spatial Sciences Institute
USC University of Southern California
MTC Metropolitan Transportation Commission

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Abstract
The Modifiable Areal Unit Problem (MAUP) is a phenomenon that occurs when data is
arbitrarily aggregated or partitioned to spatial boundaries or units. This phenomenon occurs in
most, if not all, spatial analysis efforts. The MAUP effects on analytical results cannot be
predicted. The MAUP can cause analysis results, especially statistical results, to vary depending
on the scale, aggregation, or partition used for analysis. This fact implies that inferences made
based upon the results may not exist if the scale, aggregation unit, or partition change. Yet, in
most spatial analysis efforts, there is no consideration of the MAUP. This study explored the
MAUP scale effects on the results of optimized hot spot analysis and generalized linear
regression analysis by using sociodemographic data and 2017 property crime incidents data
in San Francisco, California. A comparative study was conducted at the census block group and
census tract scales. The results suggested the presence of the MAUP in the statistical analyses.
This thesis provides a framework for geospatial analysts to evaluate the MAUP. It also serves to
highlight how the MAUP is present with commonly used analytical methods and data. The
results of this research contribute to the body of literature regarding the MAUP effects on cluster
and regression analysis.

1

Chapter 1 Introduction
This study aims to evaluate the effect of the modifiable unit area problem, known as
MAUP, on optimized hot spot analysis and generalized linear regression analysis using San
Francisco demographic factors and property crime for 2017 as a case study. The MAUP causes
spatial analysis results to vary depending on the scale and aggregation unit used. These
differences persist even though the study area, data, and methods are the same. Accurate research
is essential. Understanding how or if statistical results vary depending on scale and aggregation
methods is something all researchers should be informed.
In regression analysis, relationships between the independent and dependent variables
may be present at the census block scale, but not present at the census tract scale because of the
MAUP effect. The MAUP can cause relationship strengths, whether they are positive or
negative, and correlations between variables to vary at different scales. The MAUP effect can
also apply to hot spot analysis. Hot or cold spots may be present at one scale or appear more
substantial than the phenomenon they are representing, due to aggregation. The goal is to
demonstrate if and how unit and scale affect optimized hot spot analysis and generalized linear
regression results statistically and visually. This research also provides a framework for
geospatial analysts to evaluate MAUP in a commonly used Geographic Information System
(GIS) software, Esri’s ArcGIS Pro, Version 2.3.
To explore the scale effects of MAUP, San Francisco was chosen as the case study area.
San Francisco was chosen because of its high property crime rate. Per the Federal Bureau of
Investigation (FBI), in 2017, San Francisco had the highest rate of property crime in the country
(Cassidy and Ravani, 2018). San Francisco is an interesting use case due to its compact shape
and urban character. San Francisco is both a city and a county with the same area (Figure 1).

2

Figure 1 Map of San Francisco County, California. Source: Esri 2020
1.1. Why MAUP Matters
The MAUP is a known issue for geographic, health, socioeconomic, and environmental
researchers, yet there is no agreed-upon or right way to model or address. While there is no
agreed-upon way to research or model MAUP (Montello and Sutton, 2013), researchers must
understand that the selection of scale and analysis unit or zone is one of the most integral parts or

3

their research process (Saib et al., 2014). Due to the MAUP, results can change depending on the
scale or zone used for analysis, thus introducing the risk that inferences made based upon those
results may not be complete or correct. The MAUP will be present in most spatial analysis and
should be considered in all analysis efforts (Swift, Lin, and Uber, 2014). Understanding the
impacts of the MAUP on data aggregation at different scales, such as nested census boundaries,
is essential. For example, census data is commonly used in regression analysis to help explain
rates of crime (Hart and Waller, 2013). Knowing if statistical relationships between explanatory
variables, and their contribution to the dependent variable, change as aggregation scales change,
contributes to the validity of the research (Flowerdew, 2011).
Understanding the MAUP is critical, especially at the onset of a project when considering
what scale and delineation to use, as well as the spatial unit of the data being input into the
models. The impacts and intricacies of the MAUP effect on phenomena modeled in statistics and
spatial analysis are best described below by Ariba and Petrarca (2011). They suggest the MAUP
arises due to aggregation and causes changes to statistical measures. If the scale changes, the
statistical measures and inferences made based upon them also change. Not understanding if the
MAUP may be an issue in one’s spatial analysis and statistics can lead to bias in hypothesis
testing and therefore making wrong conclusions.
1.2. Geography and Scale and MAUP
Due to the MAUP, it is crucial to understand how relationships between phenomena
change as scales or boundaries change. We use geography and maps to understand the world
around us. Maps are representations of geographic concepts or events at a specific scale. How we
see geographic space or phenomena changes with the scale at which viewed. To view geographic
concepts or events at a scale of 1 to 1 is impossible. Geographic concepts, phenomena, or events

4

are often generalized, combined, or aggregated, as the likelihood of the information being similar
or homogenous increases with proximity. This is captured in First Law of Geography, which
states, “all things are related, but nearby things are more related than distant things” (Tobler,
1970). Scale, as it relates to Tobler’s law, is important in spatial analysis, because as the scale or
aerial unit used for analysis increases, there is less chance that the phenomena are homogenous
and the spatial dependence may decrease.
Geographers not only look at geographic space or phenomena. Geographers use the scale
as a mechanism to identify patterns and processes that are taking place within that space
(Mackaness, 2007). It is crucial to understand how patterns and processes change as the scale
used for identification changes. In most cases, understanding geographic patterns or operations is
not accomplished at the individual point level. Often point data is aggregated or joined to other
spatial structures or boundaries for spatial analysis and statistical modeling. This practice often
occurs due to model variables being available within boundaries, such as census data, and a
common spatial structure is needed to make assessments. Depending on the boundaries and the
scale used to aggregate the data for spatial analysis, the results may differ. When the schemes of
aggregations are changed, the analytical results may vary. Changes can occur even if the same
data, study area, and spatial analysis methods are used, and are an effect of the MAUP.
Phenomena represented by data may have patterns, and cause and effect relationships at one
scale that are or are not apparent at another scale due to the MAUP.
The likelihood of finding correlations between data increases as aggregation increases.
For example, when evaluating relationships between two variables for a regression model at two
nested hierarchal scales, at the smaller aggregation unit, they may not be statistically correlated.
However, as the aggregation level or unit increases in size, the likelihood that those two

5

variables will be correlated increases (Montello & Sutton, 2013). The increase in correlation is
an effect of the MAUP due to aggregation to larger enumeration units, and a reason why
understanding how the MAUP impacts statistical and analytical results matters.
1.3. MAUP Definition and Examples
The two main problems that MAUP has, when data is aggregated or partitioned to
boundaries or aerial units, are the scale effect and the zoning effect. These effects occur when the
values of aggregated data change depending on how the data is grouped or classified to polygons
or partitioned to aerial units (Bolstad, 2016). Factors that play a role in these effects are the
shape, size, delineation, and location of the aerial units (Bolstad, 2016). The MAUP is a direct
effect of changes in the unit used in spatial analysis. It thus impacts statistical results,
highlighting the issue that statistical results are sensitive to boundary changes (Duque, Laniado,
and Polo, 2018). Compounding the MAUP issue is that typically spatial data is a representation
of some phenomenon taking place that may or may not apply to a whole study area. It is
common to use point data to represent geographic events. Then the point data is partitioned into
arbitrary spatial units or aggregated to census boundaries for analysis. Often point data is
aggregated or partitioned to aerial units that have no relationship to the phenomena it represents
(Mennis, 2019).
Figure 2 depicts examples of the scale and zoning effects of MAUP using median age
data. In the top left, the figure illustrates the median age by census block and the bottom left by a
different aerial unit. In the top right, the data is aggregated to zones that are somewhat equal in
size, the same with the bottom left, but the delineation of the zones changed, so they have
different median age values. On the top right, the left-most zone has a median age of 39.8, but if
the census block data is referred to, the bottom half of the area contains many census blocks with

6

a median age ranging from 0-30. All of these examples use the same underlying data. None are
represented in the same way or show the same results (Bolstad 2016).

Figure 2 MAUP examples. Source: Bolstad 2016, pg. 392
1.3.1. Scale and Zoning Effects of MAUP
Though similar, there are differences between the scale and aggregation effect and zoning
effect of MAUP. The scale effect is regarded as a size problem (Lloyd, 2014). Scale effects
occur when data is “partitioned” to larger areas than initially captured. A scale effect example is
when census data obtained at the household level is represented at the census block level and
then aggregated and analyzed at the census tract level (Mennis, 2019). Figure 3 shows the scale
effect on the top left and right. The study area is broken into quadrants on the left with select
values in each; on the right, each quadrant is broken down into another series of quadrants. This
partitioning results in a total of 16 with a complete change in the units compared to the top left
representation of the data. The bottom left, and right of Figure 3 shows the zone effect. The
delineation and arrangement of the study area changes, while the number of shapes stays the

7

same. The zone effect of MAUP is, therefore, thought of as a shape problem (Lloyd, 2014).
When data within a study area has changes to its boundaries, the information within those
boundaries change. Previous studies show that the zone effect in boundary changes can cause a
range of -1 to 1 in the correlations of variables in regression analysis (Flowerdew, 2011).
Although the study area is the same, and the number of zones or partitions that separate the data
is the same, the counts per area or zone change, as illustrated in Figure 3.

Figure 3 Scale and zoning effects. Source: Lloyd 2014, pg. 30
The population density depicted in Figure 4 at two different areal units highlights the
scale effect of the MAUP. On the left, one value represents the population density at the county
level scale. On the right, the census tract scale represents population density, and visible
differences appear. The area around Birmingham is dense, and the population density declines as
one moves farther away from the city center. While the data and study area stay the same, a

8

change in scale provides a very different representation of population density in Jefferson
County.

Figure 4 MAUP Scale effect on Jefferson County, Alabama population density

Figure 5 shows an example of the zone effect of MAUP. The same information,
household density, is being mapped, but when the delineation of boundaries changes, the result is
an entirely different thematic map. The households per square mile range from 91 to 120 using
school districts. On the other hand, aggregation based on planning districts shows a higher range
from 121 to 150.

9

Figure 5 MAUP Zone effect on Jefferson County, Alabama population density

The zone effect results change because of the changes in the delineation of boundaries
and how data is aggregated; the scale effect changes results due to the shift in spatial units at
each scale. The MAUP causes “variance and covariance of variables” due to the zone and scale
effects. An example of the MAUP effect would be seen in a decrease in variance values when
aggregating data, resulting in increased correlations. Aggregation results in a “smoothing effect,”
and if outliers are present, they pull toward the mean (Lee et al., 2016).
1.3.2. MAUP’s relative – The Ecological Fallacy
The opposite of the MAUP is the ecological fallacy, which is another type of effect that
should be taken into consideration when designing a research project. The ecological fallacy
occurs when information or data that applies to a group is attributed to an individual that belongs

10

to the group (Mennis, 2019). Like the MAUP, the ecological fallacy is a cross-scale inference
problem. With the ecological fallacy, inferences about the group or aggregate are applied to
conclusions on the individual (Lloyd, 2014). With spatial data, an example of ecological fallacy
would be inferring that a census tract value is representative of all the households within that
census tract. While the ecological fallacy is not part of this case study, it is a concept to be aware
of while conducting spatial analysis and models because statistical results based on inferences
from a group may not apply to the individual.
1.4. Application of the MAUP to the Case Study
Evaluating demographic data at multiple scales and their statistical relationship to crime
can help guide crime interventions. For example, if an indicator of crime is a statistically
significant indicator at one scale but not at another scale, how will authorities be able to make
inferences about crime, address incidents, or adequately allocate resources to combat crime? The
unit of analysis and geography plays a key role in understanding why crime is occurring in a
geographic area. Relationships between independent variables that explain crime incidence can
change depending on the aggregate units, and these relationships may switch from positive to
negative (Porter, 2011).
The MAUP effect in regression analysis can result in changes in the explanatory power of
variables and their relationship to the dependent variable. Generally, the effects that the MAUP
causes in statistical analysis vary and are often unpredictable. The statistical significance of a
variable can depend on the scale of analysis used. Missing essential insights is a possibility if
there is no effort to evaluate the effects of scale changes. Researchers should always consider the
MAUP when they conduct spatial analysis. The scale of analysis has a direct impact on statistical
analysis results. For example, correlations between crime and the variables that constitute

11

explanatory factors of crime may be different at the census block group and census tract scales.
Statistical results also may depend on the zone or configuration that is used for analysis, even if
the scale is the same (Flowerdew, 2011). Though both scale and zone are effects of the MAUP,
this case study explores the scale effect. The zone effect of the MAUP is not considered in this
case study.
The MAUP can also affect hot spot analysis depending on the aerial unit and scale used.
For example, if hot spot analysis is performed at the census block group scale, and then repeated
at the census tract scale, there can be completely different results. Clusters of hot spots or cold
spots can disappear, or estimation of hot spots or cold spot areas can increase or decrease in size,
as the area or scale increases.
1.5. Thesis Organization
The remainder of this document contains four chapters. The next chapter discusses how
the MAUP affects statistical, cluster, and regression analysis. Recent attempts to solve the
MAUP are also reviewed. Also discussed in Chapter 2 are crime theories and associated
variables that are used to explain property crime. Chapter 3 provides a detailed overview of the
data used in this thesis, its preparation for analysis, and the methods which explored the scale
effects of the MAUP. Chapter 4 discusses the cluster and regression analysis results. Last,
Chapter 5 provides a discussion on the significance of the results and limitations of this study
and recommendations for future work.

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Chapter 2 Related Work
This chapter provides an overview of the MAUP and various aspects of crime theory relevant to
the methods used in this case study. The literature review suggests the MAUP is an issue that
should be considered and explored in every project that deals with geography, scale, and
statistical analysis. Implications of why the MAUP is important are seen in how statistical,
cluster, and regression analysis results vary depending on the scale or zone used. It is critical to
understand how the MAUP effects spatial analysis results.
The discussion is organized into two sections. The first discusses the origins of the
MAUP and the MAUP’s effect on statistics, regression, and cluster analysis. Recent
advancements in attempts to solve the MAUP are also discussed. The second section provides an
overview of the crime theories used in this study to guide the selection of regression analysis
variables. Crime theories mostly focus on specific categories of crime, and the underlying
motivations or socioeconomic processes in an area that can predict its occurrence.
2.1. MAUP
The origins of the MAUP date back to Gehlke and Biehl (1934), who found that
correlation coefficients in regression analysis increased as the aggregation unit of the data
increased when contiguously census tracts were combined. When the census tracts were not
contiguously grouped, but randomly arranged the coefficients did not increase in the same
manner. The researchers’ analysis demonstrated the way data is grouped influences correlation
coefficients due to the MAUP. Even though the origins of the MAUP can be traced to 1934,
Openshaw and Taylor (1979) coined the term. They determined that regression correlation
coefficients of Republican and elderly voters in Iowa varied from 0.98 to -0.81. The range in
correlation coefficients changed depending on the scale and enumeration units used to aggregate

13

data. Their analysis supported the results of Gehlke and Biehl (1934). The MAUP is an
acknowledged research problem, especially in the statistics and spatial analysis fields. An
extensive body of research, focusing on the MAUPs scale effect on statistical analysis,
acknowledges the MAUP’s presence and variability in modeling are challenging to predict
unless the analysis is conducted at multiple scales. Openshaw and Taylor (1979) laid the
foundation for which a growing body of MAUP research is based on by highlighting the MAUP
effect on correlation analysis (Wong, 2009). The MAUP is a problem for statistical analysis
when data based upon aerial units are used. Thus, the MAUP is present when correlation and
regression analysis have a spatial component (Wong, 2009).
The following sections provide a literature review of studies related to the topics and
methods addressed in this thesis, the MAUP scale effect on forms of statistical analysis, such as
correlation analysis, regression analysis, and cluster analysis. Most research on the MAUP
focuses on correlation and regression analysis. Recently cluster analysis has become a topic of
interest, as well as advancements in attempts to solve or account for the MAUP.
2.1.1. Statistical Analysis Sensitivity to the MAUP
The MAUP is present in all statistical and spatial analysis research, because of the scale
and zone effects. The nature of scale or zone can lead to changes in analytical results and derived
patterns (Openshaw, 1977). Statistical analysis results are sensitive regarding the aerial unit in
which the data was collected. Due to statistical analysis sensitivity to the MAUP, results using
data that has been aggregated to areal units or partitioned to zones may not be reliable
(Fotheringham and Wong, 1991). As a result, MAUP has become a topic of interest in health,
crime, and economic modeling because these subjects rely heavily on assessing neighborhood
effects and processes, both of which can be impacted by the MAUP. Spatial analysis relies

14

heavily on statistical and mathematical equations. Scale impacts statistics and mathematical
equations that are used in spatial analysis (Openshaw, 1977). The impacts often emerge when
data is aggregated into higher hierarchal aerial units. The results of statistics depend on the
values of the aggregated data and the values around them. For example, when an area that has a
low value is surrounded by areas with high values, upon aggregation, the value for the area
increases due to the MAUP scale effects. The opposite occurs when an area has a high value
surrounded by areas with low values, upon aggregation the scale effects result in decreased
values (Wong, 2009). The correlation among variables and their statistical results will strengthen
as a result of data aggregation at coarser scales (Mennis, 2019). The MAUP effects on statistical
analysis results depend on the data, study area, and scale used for analysis.
Comparing the descriptive statistics of variables at different scales is a way to evaluate
the MAUP. A study by Flowerdew (2011) evaluating the MAUP effect on the 2001 Census of
England examined the strength of the MAUP between variables at three different scales. The
researcher calculated the standard deviations, means, and bivariate correlation coefficients of 18
variables and compared at three sets of census enumeration units. The researcher then classified
them based upon mean scale difference, which is the ratio of the mean to the standard deviation.
Where there were higher mean scale differences, there was a higher expectation of seeing the
MAUP affect the relationship (Flowerdew, 2011). The effects of the MAUP were not as
impactful in the study area as predicted. However, the author stated that the MAUP effects seen
in the study could be dependent on the spatial autocorrelation of the variables at each scale.
Flowerdew (2011), concluded the MAUP could be impactful and yet hard to predict when it will
be.

15

Correlation analysis is sensitive to the MAUP. Changes in correlation results depend on
the scale and data format used. Pietrzak (2014) conducted correlation and regression analysis at
two scales to examine the MAUP scale effect on the relationships for numerous economic
variables. The author explored two dependent variables; total investment outlays in enterprises
per capita and the number of entities of the national economy per capita in Poland. The
explanatory variables were the number of unemployed, the size of the economically active
population, the total investment outlays in enterprises, and the total population. Correlation
coefficient increases were seen as the aerial unit increased for data expressed in absolute
quantities (i.e., for the variables that were not normalized). On the other hand, correlation
coefficients for variables that were normalized per capita data did not lead to changes in the
correlation means, but the standard deviation increased significantly (Pietrzak, 2014). Regression
analysis was performed on the normalized data. The analysis resulted in large increases and
significant changes in regression parameter values and standard error values. The changes of
standard error values indicated a high level of variance in the statistical significance of the
regression parameters. Based on the results, the authors confirmed the MAUP was introduced to
the correlation and regression analysis, when a change of scale was implemented. The authors
suggest that analysis using non-normalized and normalized variables should also be considered.
As stated earlier, the MAUP can have effects on statistical results, but those effects can
change depending on the data, study area, and unit or partition used for analysis. Swift, Liu, and
Uber (2008) conducted a correlation analysis to explore the scale and aggregation effects of the
MAUP on relationships between water quality and gastrointestinal (GI) illness. Pearson’s r
correlation analysis was performed on multiple sets of aerial units: census boundaries, grids, and
Voroni tessellations. The correlation values increased from 0.47 to 0.81 as the aerial unit

16

increased in size. Their findings are similar to the findings of Ghelke and Biehl (1934). The
correlation values increasing with the larger aerial units may be due to the smoothing effect of
the MAUP, which caused a decrease in the heterogeneity of the data.
2.1.2. MAUP Effect on Cluster Analysis
Another type of statistical analysis the MAUP affects is cluster analysis. The MAUP
effect on cluster analysis has recently become a topic of interest for researchers. Clusters are
groups of phenomena or data points that are more similar than other groups of events or data in
an area. Hot spot clusters are areas where the mean of the data or phenomena modeled is higher
than the mean values of other clusters in the area (McKay, 2018). Performing cluster analysis at
multiple scales can help with understanding how the MAUP affects cluster analysis.
To evaluate the MAUP scale effect, McKay (2018) used four different clustering
methods to identify crime hot spots at two scales: the data zone level and the output area level.
The four methods were: k-means, finite mixture models, Local Moran’s I, and Getis-Ord Gi*.
These cluster methods produced different results, and within each technique, results changed
depending on the scale used. For example, the optimized hot spot analysis method using the
Getis Ord Gi* statistic produced different results of Strathclyde, Scotland, at each scale using the
same crime data (Figure 6). The data zone level deemed the southernmost eastern region as not
significant, but when the scale changed to output areas, the same area turned into a crime hot
spot, indicated in red. Other areas in Strathclyde at the data zone level contain large cold spots,
indicated in blue, but at the output area level, they are not present. The results of this study
confirm MAUP presence, and that cluster analysis is sensitive to the scale used for data
aggregation. McKay (2018) suggested that the MAUP can cause an incorrect understanding of
where crime hot spots persist. Therefore, MAUP can also affect crime mitigation efforts.

17

Figure 6 Optimized hot spot analysis of crime in Strathclyde, Scotland. Source: McKay 2018,
pg.89
Another study assessing the scale effect of the MAUP on cluster analysis identifies
clusters based on industry type. The authors examined the scale effects on cluster analysis by
implementing the local spatial autocorrelation method (LISA). Workplace location point data
was aggregated to three different nested administrative boundary scales. The workplace types
used were advertisement, construction, and stock trading locations. The LISA analysis results
were different at each administrative boundary scale for construction workers. At the lowest
scale, statistically high valued clusters, significant at the 95% confidence level, were present. At
the middle scale, the clusters disappeared, then reappeared again at the next scale up. Nielsen and
Hennderdal (2014) confirmed their hypothesis that cluster analysis results of the different
business location types would be affected by the MAUP. They acknowledged cluster analysis in
the field of economic geography is important for policy and regional development planning, and
that the MAUP scale issues in the field are often ignored. They also stressed that the presence of
the MAUP should always be considered in cluster analyses.

18

2.1.3. MAUP Effect on Regression Analysis
One of the first efforts to document the scale and zone effect of the MAUP on
multivariate regression analysis was by Fotheringham and Wong (1991). When examining the
effect of the MAUP on multivariate regression analysis, they found that the relationship between
variables in their model would change depending on the aggregation scale and zone used.
Regression models of the Buffalo Metropolitan Area were developed at the census block group
and census tract levels. The model hypothesized mean family income would be positively related
to homeownership and negatively related to blue-collar workers, the black population, and the
elderly. The results of the models at both scales showed differences in parameter strength,
significance, and explanatory power. At the census block group level, the black population was
significant; however, at the census tract level, it was not. At the census block group level, the R²
value, representing the explanatory power of the variance toward the dependent variable, was
37%. At the census tract level, the R² value was 81%, more than twice the value at the census
block group level. Their discovery was significant because it indicated that multivariate
regression analysis results were unpredictable. They stressed that even in a simple multivariate
regression model, with a few variables, this would be the case. One of their implications is that
researchers should be aware of issues due to the MAUP since they commonly aggregate point
data to aerial units, especially in multivariate regression. Fotheringham and Wong (1991)
suggested it would be difficult to use the results produced at one scale to inform policy; instead,
an analysis should be conducted at multiple scales.
Geographically weighted regression (GWR) has been thought of as a way to lessen the
effects of the MAUP because it uses a local regression model instead of a global model. Cheng
and Fotheringham (2013), explored educational attainment at two scales, in Northern and the
Republic of Ireland through the global ordinary least squares (OLS) regression and local GWR.

19

The two scales were nested enumeration units at the output area (OA), and ward levels. The
GWR model had slightly better results than the OLS model; however, there were still differences
in the model parameter estimates, parameter significance, and adjusted R² values in both models.
The OLS model resulted in adjusted R² values of 0.8 at the OA level and 0.85 at the ward level.
In the OLS model, the social class and employment rate variables were statistically significant
predictors of educational attainment at the OA level, but employment rates were not at the ward
level. The GWR model improved the adjusted R² values to 0.87 at both the OA and ward scales.
The study results imply that GWR for multivariate analysis may mitigate the scale effects of the
MAUP compared to the OLS model.
Descriptive statistics and regression analysis were generated by Louvet et al. (2015) in R
to illustrate the MAUP scale and data aggregation issues. The study was implemented at multiple
scales using normalized and non-normalized variables to explore forest fire incidents. Larger
changes in mean-variance and R² values were seen in models using non-normalized data.

Figure 7 Variation in regression results due to scale. Source: Louvet et al., 2015, pg. 68
R² values were different for all scales and increased in value as the size of the aerial unit
increased. The descriptive and regression analysis results imply that non-normalized variables
are more sensitive to changes in scale than normalized variables. Figure 7 depicts the regression

20

analysis differences at each scale. Louvet et al. (2015) illustrated the results varied at each scale
as a result of data aggregation and confirmed the presence of the MAUP.
The MAUP effect on regression analysis may be a result of spatial non-stationarity
among multiple predictors and their relationship to a response variable (Parenteau and Sawada,
2011). Spatial non-stationarity is an issue because variable relationships may operate at different
scales throughout a study area. The MAUP is a concern for health geography because studies
often use census tracts as proxies for neighborhoods, which may not be accurate representations
of health processes. The authors state there is a lack of consensus in health geography in terms of
which scale is best to model health processes and wondered if the MAUP is a cause. To better
understand the MAUP effect on health geography, Parenteau and Sawada (2011) explored the
relationship of nitrogen dioxide exposure to respiratory health at three scales. They performed
multivariate stepwise regression analysis using 23 variables, selecting the best-fit model for each
scale. There was a wide variation in variable coefficient values between the three scales. The
number and types of variables that provided the best fit model for each of the three scales were
different. The best-fit model for the first scale used six of the 23 variables. The second scale had
a best-fit model using four of the 23 variables, and the third scale had a best fit model using
seven of the 23 variables. The differences between the best fit models for each scale confirmed
the authors’ hypothesis that the lack of consensus of the best scale for analysis in the field may
be due to the MAUP. The results show how regression analysis of respiratory health issues is
sensitive to scale structures and vulnerable to the scale effects of the MAUP.
Saib et al. (2014) provide another health study on the scale effects of MAUP. The authors
conducted correlation, local, and global regression analyses at three scales by analyzing the
relationship between the mortality of oral and pleural cancer on the one hand and socio-

21

economic deprivation and environmental exposure via inhalation or ingestion on the other hand.
The correlation analysis resulted in adjusted R² values ranging from 0.24 to 0.28 for pleural
cancer mortality and from 0.11 to 0.22 for oral cancer mortality at the three scales. Correlation
coefficients for both cancer types and the explanatory variables were different at all three scales.
The relationship for two of the variables changed direction at different scales. The regression
analysis showed that the local regression model performed better than the global model. Both
types of regression models for both types of cancer had differences in the adjusted R² values, an
indicator of model performance, at all the three scales. Saib et al. (2014) attributed the
differences in correlation coefficient strength and adjusted R² values to the MAUP and related
data aggregation issues.
2.1.4. Attempts to Solve the MAUP
Some recent research efforts have proposed new ways to test for this. Duque, Laniado,
and Polo (2018), for example, have developed the S-maup test. The S-maup test is the first
unique statistic created as a way to measure variables and their sensitivity to the MAUP. S-maup
is a computation-based method that works by determining the maximum level of aggregation in
which a variable can maintain its original characteristics. Fotheringham, Yang, and Kang (2017),
on the other hand, have proposed a new version of GWR, called multiscale geographically
weighted regression (MGWR), to address computational processes within a study area that may
operate at different neighborhoods or scales. MGWR addresses the varying scale of the processes
by supporting the use of two or more bandwidths being used in models, instead of choosing one
bandwidth, as seen in traditional GWR.

22

2.2. Crime Theory and the Variables
2.2.1. Crime Types and Property Crime Definition
In the U.S., crime incidents are categorized by the FBI Uniform Crime Reporting
Program, UCR, as Part I or Part II offenses. Part I offenses are criminal homicide, rape, robbery,
aggravated assault, burglary, larceny-theft, motor vehicle theft, arson, and human trafficking.
Part II offenses are simple assaults, forgery and counterfeiting, fraud, embezzlement, buying,
receiving and possessing stolen property, vandalism, carrying weapons, prostitution, sex offenses
not including rape, drug abuse violations, gambling, offenses against family and children, driving
under the influence, liquor law violations, drunkenness, disorderly conduct, vagrancy, violating
curfew and loitering laws, and suspicion of committing an offense.
Part I offenses are considered serious crimes and are cleared by arrest or other means.
They are classified into two categories, a crime against people and crime against property (FBI
Uniform Crime Reporting Program, 2017). Property crime offenses are categorized as burglary,
larceny-theft, motor vehicle theft, and arson. Property crime occurrence in San Francisco was
selected for this case study due to the city having the highest rate in the country in 2017 (Cassidy
and Ravani, 2018). San Francisco also had the highest crime rate per capita amongst the largest
cities in the United States in 2017 (Cassidy and Ravani, 2018).
2.2.2. Independent Variables –Demographic Factors and their Relation to Crime
Crime incidents typically occur at the neighborhood level and can be tied to demographic
and socioeconomic factors in efforts to explain the propensity for crime in an area. There are two
main crime theories regarding motivations and structures to explain crime occurrence; social
disorganization and routine activity. These theories focus on crime as a construct of social
disorganization, poverty, inequality, or a lack of capable guardians to deter crime, thus creating

23

opportunities to commit crime. Social disorganization theory explores the motivations behind
crime, such as poverty, with great differences between the haves and have nots in a study area.
Routine activity theory focuses on the premise that there are targets of opportunity in an area.
Routine activity theory is based on the premise that people who live in neighborhoods act
as guardians and that they deter crime (Wickes et al. 2016). Routine activity theory focuses on
three concepts that are present in space and time for crime to occur: motivation, lack of
guardianship, and a suitable target (Moriarty and Williams, 1996). Routine activity theory is
based on the premise that crime will occur when offenders believe they will not get caught (Lee
and Alshalan, 2005). This would most likely occur when people are away from their homes
during the day, or in areas that have suitable targets. Variables commonly used to test routine
activity theory are poverty, employment status, presence of multiple housing units, population
density, house ownership status, age, and marital status (Lee and Alshalan, 2005).
In contrast to routine activity theory, social disorganization theory is based upon the
premise that crime is a result of an unstable neighborhood and an inability to govern. Social
disorganization theory assumes crime occurs if the following conditions are present: economic
deprivation, residential mobility or population turnover, and racial or ethnic heterogeneity
(Cahill and Mulligan, 2007). Variables typically used to test social disorganization theory are
poverty, income, number of rental units, percent of single parents, employment rate, population
density, ethnic heterogeneity, and education attainment (Andersen, 2006).
Neither social disorganization, nor routine activity theory have been proven alone or
together to explain property crime occurrence in an area completely. Moriarty and Williams
(1996) and Andresen (2006) stress that it is valuable to look at multiple crime theories when
exploring crime occurrence. Andresen (2006) hypothesized crime occurrence in Victoria, British

24

Colombia, could be best explained using both theories. With this hypothesis in mind, a
combination of variables from both social disorganization and routine activity theory was
selected for multivariate regression analysis. The variables were ethnic heterogeneity,
unemployment rate, population change, number of single parents, average income, population,
population density, number of dwellings, young population, percent of college-educated
population, and spatial dependence. The regression analysis results incorporated variables from
both theories and confirmed the authors’ hypothesis that neither routine activity nor social
disorganization theory should be used in isolation (Andresen, 2006). The explanatory power of
the social disorganization theory was increased by adding the following variables from routine
activity theory, the average family income, percent population with a college education, number
of dwelling units, and presence of young population age 15-29.
Similarly, Moriarty and Williams (1996) used both crime theories in an attempt to
understand property crime victimization. They confirmed their hypothesis that crime occurrence
would be higher in socially disorganized areas than organized areas. In addition to this, they also
suggested that property crime correlation analysis using routine activity theory would have better
results in areas that were more socially disorganized. The correlation analysis in this work used
house value, a security index, age, race, homeownership, residential stability, home during the
day, home on the weekends, employment status, neighborhood help, marital status, and the
number of adults in the home as explanatory variables. As a consequence of the supporting
literature, variables commonly used in both theories are selected for the regression analysis part
of this thesis study and are discussed next in Chapter 3.

25

Chapter 3 Methods and Data
This chapter provides an overview of the methods and data used to analyze how the scale and
aggregation effects of the MAUP impact statistical analysis results. Based on the objective and
literature review, two spatial analysis methods (optimized hot spot analysis and generalized
linear regression) were selected to measure statistical analysis sensitivity to the MAUP on
property crime incidence in San Francisco, California. This chapter is divided into two sections.
The first describes the process taken to acquire, assess, and prepare the data for analysis. The
second describes optimized hot spot analysis, exploratory regression, and generalized linear
regression, and how they were implemented. Exploratory regression was used to explore the
relationships between the variables and finalize the variable selection for the generalized linear
regression.
3.1. Data Acquisition, Assessment and Preparation
Spatial analysis was conducted to demonstrate the effect of the MAUP on property crime
incidence at the census tract and census block group levels. The impact of the MAUP was
evaluated by performing optimized hot spot analysis and generalized linear regression analysis.
For these analyses, crime data, boundary data, and demographic data (Table 1) were first
acquired, then assessed and prepared for spatial analysis. The datasets used in the optimized hot
spot analysis were 2017 property crime incident data and the census tract and census block group
boundaries in San Francisco. For the regression analysis, the dependent variable was the 2017
property crime incident data, and the independent variables were selected from 2018
demographic indicators processed by Esri.

26

Table 1 Datasets and data sources
Dataset Spatial
Resolution
Temporal
Resolution
Data Format Data Source
Crime Data Latitude /
Longitude
2017 GeoJSON,
point
San Francisco
Government
Demographic
Data
Census Tract
& Block
Group
2018 Geodatabase,
polygon
Esri
San Francisco
Bay Region
Census Tracts &
Block Groups
Census Tract
& Block
Group
2018 Shapefile,
polygon
San Francisco
Metropolitan
Transportation
Commission

3.1.1. Study Area and Boundary Data
The TIGER/Line census boundaries are data created by the U.S. Census Bureau. They
represent hierarchal geographic entities, ranging from nation to region, state, county, census
tract, census block group, and census block. They do not contain demographic data; instead, they
have geographic identity codes (GEOID) that census data or other data sources can be linked
with. Census boundaries often cover areas that are not lived in, such as parks and large bodies of
water. The inclusion of such areas may lead to erroneous results in analysis. The unclipped
TIGER/Line boundaries covered the large water bodies to the east and west of San Francisco
(Figure 8). If the unclipped boundaries were directly used for analysis in this thesis, there would
be large areas of water with no crime events or population. The city of San Francisco uses a set
of 2018 Census TIGER/Line boundaries that have been clipped to remove water. These
boundaries were used for the optimized hot spot analysis and regression analysis in this study.
San Francisco’s clipped boundaries were joined to the Esri demographic data using an attribute
join, based on the GEOID unique identifiers of the census tracts and census block groups.

27

Figure 8 San Francisco unclipped TIGER/Line census tract boundaries
It is also important to note that this study did not include spatial outliers in San Francisco.
Golden Gate Park, Census Tract 9803, was omitted from the study because it has low population
density and a large area. There is an island group called the Farallon Islands that are part of
Census Tract 9804.01, with no population approximately 35 miles west of the conterminous San
Francisco. No crime incidents or population have been assigned to this tract. There is another
census tract, Census Tract 179.02, that has areas not contiguous to the mainland that has were
removed from the study area as well. These areas are Treasure Island, a part of Angel Island, and
a parcel of land across the bay touching Oakland. Of the regions in Census Tract 179.02,
Treasure Island was the only area containing property crime, with a count of 82 events. The
crime events for Treasure Island were deleted. Northern San Francisco also has an area that is
not within the San Francisco Police Department jurisdiction, called Presidio, Census Tract 601.
Presidio is considered a separate entity and within the jurisdiction of the California State Park
Police, because it is federal land. Presidio is not included in the study area because the crime data

28

were unavailable. All other parks in San Francisco are within the jurisdiction of the San
Francisco Police department and were included in the study area, as property crimes occurred
within their boundaries.
The resulting study area contained 59,650 property crime incidents, 192 census tracts,
and 576 census block groups. All removed census tracts shared the same size and geographic
area with the subordinate census block groups. Also removed were the coincident block groups.
In the remaining study area (Figure 9), there were eight census tracts and eight census block
groups that are entirely coincident. These enumeration areas were kept in this study since most of
them contained parks and high population counts.

Figure 9 Final study area

29

3.1.2. Crime Data
Initially, the intent was to use the 2018 crime data in this research project. Two subsets of
crime data were downloaded from the San Francisco Government open data website in
GeoJSON format because the data was not available as a single dataset for the year 2018. The
first subset was from the San Francisco legacy crime database, which ranged from January 1
st
,
2003 to May 1
st,
2018. The second subset of data was an updated crime database starting May 1
st,

2018. As of May, the city of San Francisco changed their crime database schema and started
masking crime incidents to intersections to handle privacy concerns. Instead of the crime point
being at the location where the crime incident occurred, it is at the nearest street intersection.
Due to the location modification of the crime incidents resulting in degraded spatial granularity,
the updated database was deemed not usable for analysis. There would be no way to know which
census block group or census tract the incidents should be joined to, as the intersections coincide
with the census boundaries. Due to the masking of crime incident locations starting in May of
2018, crime incidents from 2017 were used in this study. Figure 10 depicts the masked crime
incidents, with the degraded spatial granularity aligned to street intersections.
For the year 2017, there were a total of 154,773 crime incidents. Before the crime data
was appended to the census block groups and census tracts for analysis, it was filtered to contain
only property crime incidents. Burglary, larceny-theft, motor vehicle theft, and arson were then
selected, resulting in a total of 59,650 property crime incidents in the study area. These incidents
were then spatially joined to census tracts and census block groups for the optimized hot spot
analysis and regression analysis. The spatial join operation ensured that each enumeration unit
contained the sum of crime incidents.

30

Figure 10 Spatial location of 2018 San Francisco masked crime incidents
3.1.3. Demographic Data
The demographic data in this study came from the Esri curated and proprietary Popular
Demographics dataset. This dataset was part of the Living Atlas of the World, a repository of
geographic data hosted on ArcGIS Online at arcgis.com. The demographic dataset had over 50
unique variables, which were recorded at the census block group up to the state level. The
variables include population, household size, employment rate, race, poverty, income, housing
unit, housing status, and housing values. The San Francisco data was downloaded from Esri

31

ArcGIS Online. Close inspection of the demographic data showed that the polygon boundaries
did not correctly nest within each other as census block groups and census tracts should. The
block groups contained polygons in which the verticies and lines overshot the adjacent census
tract boundaries, so the data was not topologically coincident with the corresponding tract. This
type of error would cause issues when aggregating crime counts. Due to the nesting issue, the
Esri boundaries were not used, and the demographic data variables were combined, with the
clipped San Francisco 2018 Census TIGER/Line boundaries discussed in Section 3.1.1.
During the data collection phase of this project, the American Community Survey (ACS)
data was considered as a possible source for the demographic variables as well. The Esri
demographic data was selected because it had updated and refined 2018 estimates available at
the census tract and census block group scales. Esri implements a robust method using multiple
sources to create demographic data more accurately to capture yearly changes to the population
and geography. The robust method Esri employs is called the Address Based Allocation (ABA)
methodology. In an independent evaluation, a panel evaluated the data via comparisons with
different four datasets developed by other vendors. Esri’s data had the lowest precision errors for
the population and household variables. The panel acknowledged that population and household
variables are more difficult to estimate for smaller geographies like census block groups (Esri,
2012).
The Esri demographic data can be divided into population and housing characteristics.
Multiple data sources such as the 2010 Census, ACS, and Current Population Survey (CPS) and
cohort survival models are used to calculate the estimates for the population characteristics.
Housing data information is based on the 2010 Census, which was updated by Esri using sources
construction data from Metrostudy, Axiometrics, county building and home permits, US Postal

32

Service (USPS), ACS, CPS, and the Housing Vacancy Survey sources. Changes in home values
were tracked using House Price Index (HPI) and the Federal Housing Finance (FHFA)
information from mortgage loans provided by Fannie Mae or Freddie Mac. Labor Force and
Household income information were derived from the ACS, CPS, Local Area Unemployment
Statistics (LAUS), Occupational Employment Statistics (OES), Bureau of Labor Statistics
(BLS), and Bureau of Economic Analysis (BEA). Household incomes were updated by
accounting for the change in the working population.
3.1.4. Data Normalization
It is common practice to normalize data from counts to ratios before use in statistical
analysis. Normalizing data is an approach to limit the magnitude of counts by converting them
into rates, which are a measure of intensity (Dailey, 2006). For example, if a city-level crime
analysis is performed for a whole state, cities with larger populations are likely to have more
crime incidents. If the crime incidents per city are converted to ratios, it minimizes the
differences between the smaller and larger cities. Data can be normalized in two ways, by the
sum of raw total values or by another associated attribute. For example, the labor force can be
normalized by the population over age 16. All demographic variables were normalized by the
sum of the total count, resulting in a ratio in this study, except the unemployment rate, diversity
index, and median household income variables. The property crime data were also normalized by
taking the number of property crime events per tract or block group, then dividing it by the total
number of crime events in the study area. Below is a list of all the variables used for the
regression analysis (Table 2).

33

Table 2 Variables used for regression analysis
Variables Type
2017 Property Crime count
2018 Female Population count
2018 Male Population count
2018 Unemployment Rate ratio
2018 Median Household Income ratio
2018 Median Home Value ratio
2018 Diversity Index rank
2018 Owner-Occupied Housing Units count
2018 Renter Occupied Housing Units count
2018 Vacant Housing Units count
2018 Hispanic Population count
2018 White Non-Hispanic Population count
2018 Black/African American Non-Hispanic Population count
2018 Asian Non-Hispanic Population count
2018 Pacific Islander Non-Hispanic Population count
2018 Other Races Non-Hispanic Population count
2018 Multiple Races Non-Hispanic Population count
2018 Household Income $200,000 or greater count
2018 Household Income $15,000 or less count

3.2. Methods Workflow
ArcGIS Pro was utilized for data preparation and analysis in this case study. Once the
study area was determined, the data were collected, formatted, and normalized for use as inputs
in the analysis (Figure 11). All data was projected to NAD 1983 2011 San Francisco CS13
(ftUS). Optimized hot spot analysis and generalized linear regression analysis were performed at
the census block group and census tract scales to answer the research question. Exploratory
regression analysis was also conducted to explore the selection of variables for the generalized
linear regression. The dependent variable in both forms of statistical analysis was the property
crime locations in San Francisco. The demographic variables were used as the explanatory
variables for explaining the occurrence of property crime.

34

Figure 11 Research question and methods workflow
3.2.1. Optimized Hot Spot Analysis
Optimized hot spot analysis was demonstrated by using the property crime point data to
identify hot spots and cold spots at each aggregation boundary level. The optimized hot spot
analysis tool provided three options for its areal aggregation: (1) count incidents within the
fishnet grid; (2) count incidents within the hexagon grid; and (3) count incidents within the
aggregation polygons. The method used in this study was counting events within aggregation
polygons. The property crime points were input as the incidents, and the census block groups and
census tracts were input as the aggregation polygons. The number of property crime incidents
was counted in each polygon, and then, the sum was used by the tool for analysis.

35

The optimized hot spot analysis tool uses the Getis-Ord Gi* stastistic to determine where
phenomena of interest are significantly clustered. Features that have high Gi* values are
significant clusters, and features that have Gi* values close to 0 are not significant (Mitchell,
2005). Mitchell (2005) provides the Getis-Ord Gi* as the following equation:
G
i
∗ (d) =
∑ w
i
J
(d)x
J
J
∑ x
J
J

Where 𝐺 𝑖
∗
for a feature (𝑖 ), at a distance (𝑑 ) and the value of each neighbor (𝑥 ), is
multiplied by the weight for the target-neighbor pair (𝑊 𝑖𝑗
), and the results summed. Then the
sum is divided by the sum of the values of all neighbors (𝑋 𝑗 ), that is, all features in the data set.
For a location to be considered statistically significant, it has to meet the requirement of
not only having a high value, but it also has to be surrounded by other high values, or have a low
value surrounded by other low values (Esri, 2019a). Another condition is that the local sum for
each feature and its neighbors has to be proportionally higher than the sum of all features in the
study area. The optimized hot spot analysis tool automatically determines the optimal scale of
analysis to yield the best results. This determination is known as the distance band threshold. For
the optimal scale of analysis, the tool uses incremental spatial autocorrelation by computing the
intensity of clustering at each feature distance through the Global Moran’s I statistic. This
process results in a peak distance for the scale of analysis. If no peak distance is found, the
optimized hot spot analysis tool examines the distribution of each feature in relation to its
neighbors by computing the average nearest neighbor distance, to find the distance band
threshold. After the distance band threshold is determined, the Getis-Ord Gi* statistic method is
run to determine the statistically significant features.

36

The outputs of the optimized hot spot analysis tool are z-scores, p-values, and Gi-Bin
confidence levels. Gi-Bin confidence levels identify if there is significant clustering of high
values – hot spots, or low values – cold spots. Z-scores are provided as standard deviations and
are used by the tool to identify if the pattern seen is random or statistically significant. P-values
tell us whether the probability of the observed spatial pattern is random or not. A small p-values
with either of very high or very low z-score means that the pattern is not random, and indicates a
hot spot or cold spot is present (Esri, 2019a).
3.2.2. Regression Analysis
Regression analysis is commonly used to determine the relationships connecting one or
more independent variables and a dependent variable. Regression statistically assesses the
strength of relationships in the social sciences (Cheng & Fotheringham, 2013). Understanding
how the MAUP changes relationships as the scale and aggregation unit changes, will help
researchers to be more informed about their analysis and also help stakeholders with decision
making. Most regression analyses assume the data are normally distributed. The distribution of
all the variables was checked using a histogram in this study. Most of the variables were not
normally distributed with positive skews and high kurtosis values. All the variables except
median household income, the unemployment rate, and the diversity index were transformed
prior to the regression analysis itself using the log function to resolve the skewness.
Transforming data is a process in which all the data values are converted to a new scale, thus
changing the distribution (Mitchell, 2009).
In this study, two types of regression analyses were conducted. Exploratory regression
was performed first to explore the relationships among the variables to select the variables for
input into the second regression model. The second step used generalized linear regression which

37

to create the final model and evaluate the scale effects of the MAUP. Exploratory regression and
generalized linear regression use a common regression technique called ordinary least squares
(OLS). OLS is a form of linear regression that generates prediction values based on the observed
values of dependent variables in relation to explanatory variables (Figure 12). OLS is one of the
most common forms of regression and often thought of as a starting point in spatial regression
analysis (Esri, 2019b).
OLS uses the following mathematical equation to show relationships between the
dependent variable, what is being predicted, and the independent variables:
𝑦 = 𝛽 0
+ 𝛽 1
𝑥 1
+ 𝛽 2
𝑥 2
+ 𝛽 3
𝑥 3
+ 𝜀
The ordinary least squares regression equation contains the dependent variable 𝑦 ,
property crime, which is a function of the regression coefficients, β, for every explanatory
variable, 𝑥 , and represents the strength and type of the variable relationship to 𝑦 . The regression
intercept, 𝛽 0
is the expected value of the dependent variable if the independent variable is 0. The
residuals, 𝜀 , represent the difference between the observed and predicted values in the model
and the unexplained portion of the dependent variable (Esri 2019b).

Figure 12 Ordinary least squares: Predicted values in relation to observed values. Source: Esri
2019b
OLS determines the relationship between the dependent variable and independent
variables by calculating regression coefficients for every variable. The regression coefficients

38

indicate the strength and type of relationship between the dependent and explanatory variables
(Esri, 2019c.). In this study, the independent variables, demographic factors, are used to predict
property crime occurrence, the dependent variable.
3.2.2.1. Exploratory and Generalized Linear Regression Workflows
As stated in the previous section, exploratory regression was used to explore the
relationships between the model variables and to determine what independent variables were
positively or negatively correlated to property crime at the census block group and census track
scales. It resulted in a table with the variable significance rated on a scale from 0 to 100 and
multicollinearity values. The exploratory regression results were compared to evaluate
differences at each scale. The exploratory regression helped solve multicollinearity issues and
narrow down the selection of variables based on crime theories for the final generalized linear
regression model.
Generalized linear regression was run next, and the results, correlation coefficients, R
2
,
probabilities, and AIC values were used to evaluate the scale effects of the MAUP. The
correlation coefficients represent the relationship type and strength between the dependent and
explanatory variables. The R
2
values suggest how the model explains the observed dependent
variable. An R
2
value of 1 means that the model explains 100% of the variation in the dependent
variable. An R
2
of 0.50 means that 50% of the variability of the dependent variable is explained.
The probabilities identify if a variable is statistically significant. AIC values tell how well the
model fits the data, the smaller the value, the better. The results of the regression models were
evaluated and compared to determine the MAUP effects at different scales.

39

Chapter 4 Results
The results presented in this chapter explore the scale effects of the MAUP on the results from
two forms of statistical analysis; optimized hot spot analysis, and regression analysis. The
applications used two aggregation scales and property crime incidence in San Francisco,
California, as the case study. The results support findings discussed in the literature review and
confirm the study hypothesis that the aggregation of data to different scales will affect statistical
analysis results. This chapter reviews the results of these analyses in detail.
4.1. Optimized Hot Spot Analysis Results
The Optimized hot spot analysis results were different at each scale; therefore, the
assumption that there would be differences in the results at each scale due to the MAUP scale
effect was confirmed. Aggregation to aerial units at different scales produced MAUP scale
effects, even when the same data and study area were used.
The optimized hot spot analysis at the census block group scale, resulted in a larger hot
spot than at the census tract scale. The optimized hot spot analysis results are provided as maps
(Figures 13 and 14) that depict the statistically significant hot spots and cold spots, at three
confidence levels, and areas that are not statistically significant in off white. Areas in red signify
that there are clusters with high levels of property crime present. The areas in blue indicate that
there are clusters with low levels of property crime present. To be considered a hot or cold spot,
the area has to have a high or low value surrounded by similar values. When compared to the
sum of all features in the study area, the areas that have local sums higher relative to the sum of
all the features are considered statistically significant.
There was also a cold spot at the census block group scale. This cold spot is located south
of Golden Gate Park, in an area identified as the Sunset District (Figure 13). The cold spot is

40

surrounded by areas that are not significant. The census block group has a large contiguous hot
spot in northeast San Francisco. The hot spot is larger at the census block group scale extending
into the Chinatown neighborhood, whereas this area was not significant at the census tract scale.
The census block groups had approximately 2.5 square miles more territory that was deemed a
hot or cold spot than the census tracts. Not only did the change of scale from block groups to
census tracks decrease the size of the hot spots, but it also changed the confidence levels (Figure
14). At the census block group scale, the blocks on the western and northern periphery were
statistically significant at the 90 and 95% confidence levels. In contrast, the hotspot at the census
tract scale, displayed a similar confidence level only on the western periphery.

Figure 13 Property crime optimized hot spot analysis at the census block group scale

41

Figure 14 Property crime optimized hot spot analysis at the census tract scale
One reason the optimized hot spot analysis results were different at each scale is because
the Getis Ord Gi* statistic used distance band thresholds and feature weights to identify where
there were statistically significant clusters in the study area. The distance band threshold is used
to determine how many neighbors each feature has. Features that have higher weights than
nearby neighborhood features are considered significant clusters. The optimal distance band for
the block groups was 4,283 feet, and for the tracts was 4,297 feet (Appendix A). As the scale
changed, the distance band threshold changed, and this sometimes caused a change in the
number of neighbors for each feature.

42

4.2. Regression Analyses Results
Exploratory regression analysis was used to explore the relationships between the
demographic variables and property crime and to help determine what variables to keep for the
generalized linear regression.
4.2.1. Exploratory Regression Results
The results produced using the census block groups and tracts were different as expected,
confirming that regression analysis is affected by the MAUP. The relationships of some variables
to property crime changed, from the census block group to the census tract scale. Exploratory
regression was used to test for multicollinearity between all the variables by examining the VIF
values. Overall, multicollinearity increased as the aggregation scale increased from census block
groups to census block tracts. High VIF values, typically above a threshold of 7.5, mean that
there are multicollinearity issues between variables. Multicollinearity issues indicate that one or
more of the variables is redundant. Removing these variables will help to resolve the issue. In
this study, the Hispanic population variable caused multicollinearity issues with the race and sex
variables, resulting in high VIF values. Therefore, all the race variables were removed. Since
removing only one race variable did not make sense, the other race variables were removed as
well. Instead, race variations were accounted for in the Diversity Index variable.
Some census tracts had a value of 0 for median home value. These tracts were examined
in the 2014-2018 ACS and 2010 Census and finding ‘0’ values there as well, so the median home
value variable was removed in this study. Table 3 lists the remaining final variables used in the
exploratory and generalized linear regression analysis.

43

Table 3 Final demographic variables used in regression models
Final Variables
2018 Household Income $200,000 or greater (HINC200_CY_N)
2018 Household Income less than $15,000 (HINC0_CY_N)
2018 Median Household Income (MEDHINC_CY)
2018 Owner-Occupied Housing Units (OWNER_CY_N)
2018 Renter Occupied Housing Units (RENTER_CY_N)
2018 Vacant Housing Units (VACANT_CY_N)
2018 Male Population (MALES_CY_N)
2018 Female Population (FEMALES_CY_N)
2018 Unemployment Rate (UNEMPRT_CY)
2018 Diversity Index (DIVINDX_CY)

An exploratory regression analysis was repeated using the remaining variables.
Summaries of the variable significance and multicollinearity were generated (Table 4). These
summaries were used to understand what the variables were doing in the models. There were no
violations for multicollinearity except for the male population variable at the census tract scale.
The VIF value of 8.08 was slightly higher than the preferred standard of 7.5 in this instance.
However, the male population variable was kept in the regression analysis model because the
VIF violation was not present at the census block group scale. This is another indication that
regression analysis is sensitive to changes in the scale used for analysis and suffers from the
MAUP. Included in the summary of variable significance, is a significance rating on a scale of 0-
100 for each candidate variable, and whether the linear relationship of the variable to property
crime is primarily positive or negative. The higher the variable significance rating, the stronger
the variable is a predictor of property crime. Variable significance percentages and order
changed from census block group to census tract. The percentage value of whether a variable is
negatively or positively related to property crime also changed from census block group to
census tract.

44

Table 4 Census block groups & tracts exploratory regression summaries

Table 4 summarizes the differences in the exploratory regression results at each scale.

The renter-occupied housing units variable was the only variable where no changes
occurred for the variable significance, positive, and negative percentages. The renter-occupied
housing units variable was 100% significant, with a 100% positive relationship to property crime
at the census block group and census tract scales. Two other variables, the vacant housing units
and household income less than $15,000 variables retained the same rank in terms of
significance. The household income ≥ $200,000 variable saw a large change in significance rank,
significance percentage, and relationship percentage from the census block group to census tract.
The rank decreased from 6 to 10, and the percent significance decreased from 60.36 to 17.93%.
The largest change in significance was seen in the owner-occupied housing units variable. The
variable at the census block group came in last at 1.20% significant, but it rose to 8
th
position,
with a significance of 36.25%. The linear relationship of the variable changed from 43.82%

45

negative and 56.18% positive at the census block group to 81.87% negative and 18.13% positive
at the census tract.
Table 5 Exploratory regression results at the census block group and census tract scales
Variable Rank
%
Significant
%
Negative
%
Positive
Renter Occupied Housing Units (BG) 1 100 0 100
Renter Occupied Housing Units (Tract) 1 100 0 100
Diversity Index (BG) 2 80.08 3.78 96.22
Diversity Index (Tract) 3 74.5 7.17 92.83
Female Population (BG) 3 78.69 78.09 21.91
Female Population (Tract) 2 84.86 92.03 7.97
Male Population (BG) 4 72.71 12.55 87.45
Male Population (Tract) 6 61.16 24.9 75.1
Household Income ˂ $15,000 (BG) 5 65.54 0 100
Household Income ˂ $15,000 (Tract) 5 66.73 18.13 81.87
Household Income ≥ $200,000 (BG) 6 60.36 0.8 99.2
Household Income ≥ $200,000 (Tract) 10 17.93 40.64 59.36
Vacant Housing Units (BG) 7 53.98 0 100
Vacant Housing Units (Tract) 7 50.8 0 100
Unemployment Rate (BG) 8 48.8 92.23 7.77
Unemployment Rate (Tract) 9 25.1 74.5 25.5
Median Household Income (BG) 9 42.43 38.65 61.35
Median Household Income (Tract) 4 70.72 14.14 85.86
Owner Occupied Housing Units (BG) 10 1.2 43.82 56.18
Owner Occupied Housing Units (Tract) 8 36.25 81.87 18.13

4.2.2. Descriptive Statistics of Final Variables
Descriptive statistics show the differences between the variables across the two scales
(Table 6). Descriptive statistics were run on the final variables. The variable format used for the
descriptive statistics were counts, not the normalized data, except for the property crime, median
household income, unemployment rate, and Diversity Index variables. The crime variable was a
percent of all counts.

46

Table 6 Descriptive statistics of model variables
Variable
Units
Mean St. D Min Max
Crime Percent (BG)
ratio
0.173611 0.338892 0.006825 4.886955
Crime Percent (Tract)
ratio
0.520833 0.767612 0.029008 5.895401
Diversity Index (BG)
rank
62.92083 14.42841 6.3 92.1
Diversity Index (Tract)
rank
64.37135 14.42762 20.5 92.2
Median Household Income (BG)
ratio
92732.46 36972.66 10714 200001
Median Household Income (Tract)
ratio
89305.35 34586.07 12734 198062
Unemployment Rate (BG)
ratio
3.602778 2.957789 0 20.2
Unemployment Rate (Tract)
ratio
3.76875 2.216847 0.2 15.9
Owner-Occupied Housing Units (BG)
count
40.76605 23.22956 0 92.37288
Owner-Occupied Housing Units (Tract)
count
37.67807 21.82971 0 85.26104
Renter Occupied Housing Units (BG)
count
52.28878 22.42109 19 4126
Renter Occupied Housing Units (Tract)
count
55.3487 20.92732 26 6538
Vacant Housing Units (BG)
count
6.94517 4.393559 0.522778 40.93366
Vacant Housing Units (Tract)
count
6.973231 3.958612 1.151493 37.37575
Male Population (BG)
count
50.38699 4.858465 36.66667 75.46012
Male Population (Tract)
count
50.62299 5.051038 39.52711 75.46012
Female Population (BG)
count
49.61301 4.858465 24.53988 63.33333
Female Population (Tract)
count
49.37701 5.051038 24.53988 60.47289
Household Income ˂ $15,000 (BG)
count
9.370809 10.1766 0 70
Household Income ˂ $15,000 (Tract)
count
10.39659 9.943143 1.117686 58.89952
Household Income ≥ $200,000 (BG)
count
0 12.35556 0 64.53901
Household Income ≥ $200,000 (Tract)
count
0 10.95981 0 49.69072

4.2.3. Generalized Linear Regression Results
Generalized linear regression (GLR) uses the same ordinary least square regression
method as exploratory regression but differs in how the results are provided. The application
generalized linear regression at the census block group and census tract scales resulted in
differences in the coefficient linearity, probability, statistical significance, VIF values, AIC
values, and adjusted R
2
values (Tables 7 and 8). Variable coefficient linearity changed for three
of the 10 variables, and the coefficient strengths were altered for all 10 of the variables. The
unemployment rate variable was negative at the census block group scale, and positive at the

47

census tract scale (Table 8). The owner-occupied housing units variable was positive at the
census block group scale and negative at the census tract scale. The household income ≥
$200,000 variable was positive at the census block group scale and negative at the census tract
scale. The changes in linearity can be caused by changes in the values of the aggregated data, as
seen in the exploratory regression analysis results (Table 5). The VIF values increased as the
aggregation unit increased from census block groups to census tracts (Table 8). An asterisk
indicates the probability and robust probability (Robust_Pr) are statistically significant, but the
level of significance also changed when the scale changed. The vacant housing units variable at
the census tract scale had a statistically significant probability, but not at the census block group
scale. The household income ≥ $200,000 variable had a statistically significant probability and
robust probability at the census tract scale but not at the census block group scale.
Table 7 Generalized linear regression model diagnostics

The regression models’ R
2
values increased from 48% at the census block group scale to
54% at the census tract scale (Table 7). The models’ adjusted R
2
values, a better indicator of the
model performance than the multiple R
2
values, increased from 47% for the census block groups
Number of Observations (BG): 576 Akaike's Information Criterion (AICc): 1293.231623
Number of Observations (Tract): 192 Akaike's Information Criterion (AICc): 381.637326
Multiple R-Squared (BG): 0.485232 Adjusted R
2
: 0.476121
Multiple R-Squared (Tract): 0.542166 Adjusted R
2
: 0.516871
Joint F-Statistic (BG): 53.25818 Prob(>F), (10,565) degrees of freedom: 0.000000*
Joint F-Statistic (Tract): 21.433965 Prob(>F), (10,181) degrees of freedom: 0.000000*
Joint Wald Statistic (BG): 533.658364 Prob(>chi-squared), (10) degrees of freedom: 0.000000*
Joint Wald Statistic (Tract): 248.781098 Prob(>chi-squared), (10) degrees of freedom: 0.000000*
Koenker (BP) Statistic (BG): 41.024326 Prob(>chi-squared), (10) degrees of freedom: 0.000011*
Koenker (BP) Statistic (Tract): 25.539279 Prob(>chi-squared), (10) degrees of freedom: 0.004412*
Jarque-Bera Statistic (BG): 174.322857 Prob(>chi-squared), (2) degrees of freedom: 0.000000*
Jarque-Bera Statistic (Tract): 25.21975 Prob(>chi-squared), (2) degrees of freedom: 0.000003*

48

to 51% for the census tracts. The differences between the models are due to the scale effect of
the MAUP.
Table 8 Generalized linear regression results
Variable Coefficient Probability Robust_Pr VIF
Intercept (BG) -4.175816 0.000000* 0.000118*

Intercept (Tract) -4.333853 0.000000* 0.000039*

Unemployment Rate (BG) -0.000099 0.993267 0.992895 1.260365
Unemployment Rate (Tract) 0.020821 0.451028 0.462967 1.799194
Diversity Index (BG) 0.013802 0.000001* 0.000026* 1.640185
Diversity Index (Tract) 0.017221 0.000107* 0.000262* 1.879304
Median Household Income (BG) 0.000004 0.000740* 0.002166* 2.173575
Median Household Income (Tract) 0.000014 0.000005* 0.000005* 4.840523
Owner-Occupied Housing Units (BG) 0.054556 0.054649 0.303144 1.185458
Owner-Occupied Housing Units (Tract) -0.018501 0.732632 0.796711 2.119452
Renter Occupied Housing Units (BG) 0.716471 0.000000* 0.000000* 2.78653
Renter Occupied Housing Units (Tract) 0.636554 0.000001* 0.000001* 4.435324
Vacant Housing Units (BG) 0.088075 0.06783 0.166905 1.518525
Vacant Housing Units (Tract) 0.206148 0.036685* 0.104551 2.384923
Household Income ˂ $15,000 (BG) 0.081308 0.009277* 0.034546* 1.661251
Household Income ˂ $15,000 (Tract) 0.342867 0.005780* 0.002463* 5.926499
Household Income ≥ $200,000 (BG) 0.012074 0.627874 0.699758 1.399957
Household Income ≥ $200,000 (Tract) -0.138725 0.011745* 0.015300* 2.377661
Male Population (BG) 1.105138 0.000000* 0.000003* 6.370187
Male Population (Tract) 0.931577 0.001237* 0.004860* 8.088657
Female Population (BG) -1.464225 0.000000* 0.000000* 5.372064
Female Population (Tract) -1.281492 0.000001* 0.000068* 7.210129

The generalized linear regression tool provided output feature classes of the standardized
residuals for the model at the census block group and census tract scales. The standardized
residuals show where the model is over- and under-predicting the dependent variable based on
the observed values. Residuals compare the observed values to the predicted values on a linear
prediction line (Figure 12). Observed values less than the predicted values result in over-
prediction, observed values more than the prediction line result in under-prediction. The census

49

block group and census tract models show both types of predictions (Figures 15 and 16). The
over- and under-predictions also suggest that key variables are missing in the study area that
would help to explain property crime occurrence. Missing could be commercial areas, business
centers, tourist spots, recreation or nightlife areas, police departments.

Figure 15 GLR census block group standardized residuals
When comparing the standardized residuals for the census block groups and census
tracts, the results were different. The most significant difference was in the southwest. For the
census block groups (Figure 15), the standardized residuals are below the mean, and for the
census tracts, they are above the mean (Figure 16). Differences in standardized residuals for the
census tracts and census block groups in the same locations in the study area suggest the
regression analysis susceptibility to the MAUP scale effect.

50

Figure 16 GLR census tract standardized residuals
The census block group GLR residuals present more of a heterogeneous pattern than the
more homogenous census tracts. Although the regression models used the same datasets and
variables, they produced different results due to the different scales of analysis. The MAUP
causes the differences. One of the MAUP effects is that variables become more correlated as the
aggregation level increases. When comparing the two GLR residual maps, the standardized
residuals for the census tracts present a more homogenous pattern than the census block groups,
and the increased correlation of the variables can explain this result. The patterns of the residuals
also indicate that the variable relationships may not stationary throughout the study area.

51

Chapter 5 Discussion and Conclusions
As introduced in Chapter 1, the MAUP will be a problem when using data that has been
aggregated to aerial units or partitioned to zones. These are two ways the MAUP presents itself,
as the MAUP scale effect and the MAUP zone effect. The zone effect emerges when data is
processed on the same scale, but the delineation of the data changes. The scale effect, which this
thesis focused on, occurs when data is aggregated to aerial units that have different scales. The
selection level for aggregation impacts the visualization of the data. Data depicted using census
tracts versus census block groups or counties versus states can present very different results
when using the same underlying data. The goal of this study was not to show how the
aggregation of data at different scales changes how information is visualized. The goal was to
take the issue of the MAUP one step further and evaluate the scale effects of the MAUP on
statistical analysis of property crime occurrence in San Francisco, California. The research
question, which asked whether the optimized hot spot analysis and generalized linear regression
results were different at the census block group and census tract scales due to the MAUP, was
confirmed.
The findings of this study are similar to the findings of prior studies. For example,
Fotheringham and Wong (1991) found that the aggregation of data causes a smoothing effect and
results in a decrease in the variation evident in the data. The smoothing effect is more than likely
what happened to the property crime as the scale of aggregation was increased from the census
block group to the census tract. As the scale of aggregation increased, the local relationships and
dynamics of the data were lost, leading to higher data heterogeneity.
The MAUP scale effects resulted in optimized hot spot analysis results that were different
at the census block group and census tract scales. At the census block group scale, there were hot

52

spots and cold spots present that were not present at the census tract scale. The MAUP scale
effect on optimized hot spot analysis is due to the change in the counts of the features and how
distances are calculated for feature neighbors. The fixed distance band determines the optimal
scale of analysis, and this study used. When the average nearest neighbors changed because of
the change of scale, the distance to significant peaks in data clusters also changed. When data is
aggregated to different boundaries, the weighted values also change because the value for each
feature is compared proportionally to the sum of all features. If the value is more than the sum,
the process at that location is not considered random, and that feature is given a statistically
significant z-score. The effects of the weighted features and distance band thresholds for the
Getis-Ord Gi* statistic were seen in the results of the optimized hot spot analysis.
The weight of each feature, based on the sum of the crime points, had the biggest effect
on the MAUP. As aggregation increased from census block groups to census tracts, and the
crime counts in local neighborhoods were combined, the variances decreased, causing low
counts to increase or high counts to decrease. The changes resulted in the smoothing effect in the
data due to aggregation described by Fotheringham and Wong (1991). As a result of the
smoothing effect, the cold spot present at the census block group, disappeared at the census tract
scale, and the hot spot areas decreased in terms of the geographic extent. For the census block
groups, 17% of the features were considered statistically significant, and for the census tracts,
8.3% of the features were considered statistically significant. The statistically significant hot and
cold spot areas decreased by 2.5 square miles for the census tracts. These findings are similar to
those in McKay (2018). McKay conducted hot spot analysis of crime in Strathclyde at two
different scales: output areas and data zones. The data zones are nested within the output areas.

53

The hot spot analysis had more areas that were colds spots at the data zone scale, and a large
statistically significant hot spot appeared that was not present at the data zone scale.
The MAUP effects on hot spot analysis, depend on the data, scale, weight or count of
each feature, and the number of neighbors each feature has, which is determined by the distance
band threshold. The appearance or disappearance of statistically significant hot or cold spots can
occur as the scale increases or decreases. The cluster analyses highlight anomalies in the data are
present. If those anomalies change with scale, as demonstrated by the property crime in this
study, efforts to addresses property crime, such as implementing safety measures, may not be
effective. It is important to note that cluster analyses may also be affected by the study area
shape and size. For example, in this study, the coastline and removed census tracts (Golden Gate
Park and Presidio) were physical barriers and impacted how the fixed distance band and
neighbors were calculated.
Statistical analysis sensitivity to the MAUP was also seen in the regression analysis
results. The exploratory regression was used to determine the final selection of the variables for
the GLR model. Once the final selection of variables was determined, exploratory regression was
conducted again, to evaluate the significance of the variables as predictors of property crime
occurrence at each scale. The results were not consistent at the two aggregation scales. The
variables significance as predictors of property crime changed. Changes were seen in the
significance percentage and rank between the variables at the census block group and census
tract scales. The positive and negative linear relationships of some of the variables to property
crime also changed with scale.
Scale changes were also seen in the model coefficients, which indicate the strength and
relationship of each variable to property crime, and the variable coefficient probabilities, which

54

indicate whether a coefficient is statistically significant in the final GLR models. The three
variables that had coefficients change from positive at one scale to negative at another scale were
the unemployment rate, the number of owner-occupied housing units, and household income ≥
$200,000. Statistical significance changes in the coefficient probabilities were seen for the
household income ≥ $200,000 and the number of vacant housing units. The GLR models
adjusted R
2
values also changed. These values are an indicator of the model performance. The
adjusted R
2
value was higher for the census tracts (51%) than census block groups (47%). The
increased adjusted R
2
squared values confirmed earlier studies which found that correlations
among variables strengthen as data is aggregated due to the MAUP (Gehlke and Biel, 1934;
Openshaw and Taylor, 1979; Wong, 2009; Fotheringham and Wong, 1991; Cheng and
Fotheringham, 2013; Saib et al. 2014).
The MAUP will always be a factor when data is aggregated to different scales or zones
and should always be considered in spatial analysis. Therefore, a spatial analysis should be
conducted at multiple scales if the data is available to do so. Decisions or assumptions made
based on the analytical results using aggregated data could be wrong. This is the risk of not
analyzing data at multiple scales to determine the presence and severity of the MAUP.
The concepts and methods used in this study provide a framework for evaluating the
MAUP effects, even if researchers use different data and tools. Although in many GIS core
curricula, the MAUP is regarded as a core concept, many professionals and researchers often fail
to consider it in their analysis. One of the aims of this study is to raise awareness of the MAUP
among people who conduct spatial analysis.

55

5.1. Limitations and Recommendations
5.1.1. Assessing Model Significance to Property Crime in San Francisco
If evaluating the model significance to property crime in San Francisco, the variables
used for the regression models in this study explain approximately 50 % of property crime
occurrence. Due to this, a further avenue of research could be identifying and using variables that
are specific to just the routine activity theory or the social disorganization theory. In addition,
crime theory models often combine two or more variables to create a new variable. For example,
combining two variables to create a variable measuring disadvantage or poverty in an area. This
study did not generate combined variables, which is another possible reason why the model only
explains about half of the property crime occurrence in San Francisco.
5.1.2. Future Work and Avenues for Research
One avenue for future research would be to evaluate the same outcome using GWR. A
local form of regression, such as GWR, may lessen the effect of the MAUP. Global regression
models assume that the relationships are the same over the whole study area, where, GWR takes
into consideration that the relationships may vary over space and calculates regression models
for each feature. OLS is a global form of regression and assumes the relationships are static and
consistent over space and uses a single equation for the study area. GWR would result in a better
model because it reflects Tobler’s First Law of Geography. However, Cheng and Fotheringham
(2013) confirmed that the MAUP is still present in the results of GWR, but less so compared to
OLS.
The second avenue for future research would be to conduct bivariate correlation analysis
to test the model variables at each scale. Bivariate correlation analysis is used to model the
relationships between the dependent and independent variables, and well as the relationships of

56

independent variables to each other. Bivariate correlation analysis models relationships that are
nonlinear, whereas the GLR and exploratory regression analysis use ordinary least squares,
which assumes that the relationships are linear. The regression residuals patterns from the GLR
in this study indicate that variable relationships to property crime may not be linear or standard
over the study area. Bivariate correlation analysis can assist in exploring spatial autocorrelation
and non-stationarity between the variables.
The third avenue for research is adding variables that may contribute to crime besides
sociodemographic factors. A possible reason the model explains about 50% of the variability of
property crime, could be that the model did not consider some key variables. Examples of key
variables could be missing spatial features like stores, police stations, tourism and nightlife
attractions and business districts. In addition to the missing spatial features, another analysis
could be done to explore the property crime analysis not in just space, but in time. There are
certain times of day where areas or people within those areas may make opportune targets.
The fourth avenue for future research is to conduct regression and cluster analysis by
using normalized and non-normalized data. Pietrzak (2014) and Louvet et al. (2015) explored the
impact of the MAUP in such a manner. They suggest that normalized data is less susceptible to
the scale effects of the MAUP. The cluster analysis performed in this study used only property
crime counts. Therefore, evaluating the MAUP scale effects on the results of the cluster analysis
by comparing cases of normalized (i.e., counts per unit acre or 1,000 residents) and non-
normalized data (counts) might yield better results.
5.2. Final Thoughts
This study is relevant to assessing property crime and the MAUP scale effects. The
MAUP is a well-known issue in the spatial sciences; however, non-GIS professionals, crime

57

analysts, and government officials may not be familiar with the matter. This study highlights
how the MAUP applies to multiple disciplines, increases MAUP awareness, and provides a
framework that can be replicated in other studies.
Crime analysts and public stakeholders in San Francisco, and other cities, can use the
methods in this study when addressing and implementing safety measures to mitigate crime. As
seen with the analyses in this study, identifying areas with significant property crime occurrence
and what factors explain the phenomenon are affected by the MAUP scale effects. Therefore,
analyzing crime at multiple scales should also be considered because areas of interest are subject
to change as the scale changes.
Stakeholders must understand assessments of causative crime attractors fluctuate with
scale due to the MAUP. For example, the unemployment rate variable was negatively related to
property crime at the census block group scale and positively related at the census tract scale.
Why was the unemployment rate contributary to property crime at the census tract scale but not
at the census block group scale? The household income ≥ $200,000 variable was positively
related to crime at the census block group scale and negatively related at the census tract scale.
Are households with higher incomes only targets for property crime in areas that are not
surrounded by areas with higher household incomes? The owner-occupied housing units variable
was negative at the census tract scale, and positive at the census block group scale. These results
lead to different assumptions and subsequent questions at each scale. Analysts and researchers
conducting spatial analyses examining socio-demographic phenomena such as crime must
closely scrutinize resultant data in terms of the MAUP.

58

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Bolstad, Paul. 2016. GIS Fundamentals: A First Text on Geographic Information Systems
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Cahill, Meagan, and Gordon Mulligan. 2007. “Using Geographically Weighted Regression to
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Appendix A Optimized Hot Spot Analysis Results Windows

63

Abstract (if available)

Abstract The Modifiable Areal Unit Problem (MAUP) is a phenomenon that occurs when data is arbitrarily aggregated or partitioned to spatial boundaries or units. This phenomenon occurs in most, if not all, spatial analysis efforts. The MAUP effects on analytical results cannot be predicted. The MAUP can cause analysis results, especially statistical results, to vary depending on the scale, aggregation, or partition used for analysis. This fact implies that inferences made based upon the results may not exist if the scale, aggregation unit, or partition change. Yet, in most spatial analysis efforts, there is no consideration of the MAUP. This study explored the MAUP scale effects on the results of optimized hot spot analysis and generalized linear regression analysis by using sociodemographic data and 2017 property crime incidents data in San Francisco, California. A comparative study was conducted at the census block group and census tract scales. The results suggested the presence of the MAUP in the statistical analyses. This thesis provides a framework for geospatial analysts to evaluate the MAUP. It also serves to highlight how the MAUP is present with commonly used analytical methods and data. The results of this research contribute to the body of literature regarding the MAUP effects on cluster and regression analysis.

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Asset Metadata

Creator Zahrani, Benecia (author)

Core Title Evaluating the MAUP scale effects on property crime in San Francisco, California

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 07/23/2020

Defense Date 05/14/2020

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

Tag cluster analysis,data aggregation,MAUP,Modifiable Areal Unit Problem,OAI-PMH Harvest,regression analysis,scale effects,spatial analysis,spatial partitioning,spatial statistics

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Oda, Katsuhiko (committee chair), Fleming, Steven (committee member), Wilson, John (committee member)

Creator Email benecia.zahrani@gmail.com,zahrani@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-343163

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Legacy Identifier etd-ZahraniBen-8732.pdf

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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...

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