Chapter 3METHODS

3.0 Data

3.1 Overview and Goals

The primary goal of this section is to explore different methods in which populations of

urban spaces can be visualized in new ways at various scales. The historical growth of Chicago

has created a landscape in which a system of boundaries exists that is commonly used in

cartographic representations of the city. This boundary system limits the understanding into the

complexity of the urban space and the micro-processes of human settlement in Chicago.

Traditional choropleth and dot density techniques rely on the established boundary units and

represent Chicago’s population in a simplified and typically uninformative way. With

experimentation in the methodological approach to the problem of urban population distribution,

maps and visualizations can be made to better characterize the phenomenon of people in space.

The following methods are investigated in the remainder of this chapter to construct different

visualizations from the available data:

1. Section 3.2 will explore the vertical residential environment of Chicago and

create a new measurement to describe the living spaces of Chicago- the

measurement of personal space.

2. Section 3.3 will look at the rationale for and the methodological of comparing

demographic profiles as a measure to better understand the significance of the

personal space measurement.

3. Section 3.4 will consider different exploratory spatial statistic models to describe

the geographic distribution of different classifications of living space across the

city of Chicago.

4. Section 3.5 will construct a method to visualize the individual person in the

landscape of the urban environment.

5. Section 3.6 will investigate an alternative approach to visualize the intensity of

people and spaces without the use of traditional boundary units.

3.2 Personal Space Model

3.2.1 Vertical Space Problem

The origin for the following methods is derived from the second research question of this

thesis- in what ways does the vertical extent of neighborhoods obscure our understanding of

spaciousness and crowdedness for urban residents. Chicago is considered the to be the birthplace

of the skyscraper and boast the tallest building in the United States, the Willis Tower- a 110

story, 1454 foot structure in the Loop (Fountain, 2001). The history of skyscrapers in the

redevelopment of post fire Chicago began in 1885 with the completion of the Home Insurance

Building, the first steel-framed skyscraper in the world. Originally constructed with a height of

138 feet, the building was later expanded to a height of 180 feet before being demolished in

1931. Historically, Chicago has played a prominent role in the development of the skyscraper and

at various times in the history of skyscraper development has boasted the world’s tallest building

(Daniel & Grant, 2005).

Louis Sullivan, an urban designer and architect in Chicago recognized that the skyscraper

would represent a new form of architecture in the post fire landscape of Chicago (Kaufman,

1969). Sullivan discarded conventions and designed buildings that emphasized their vertical

nature before adequate technology existed to construct the design. Materials and technologies

were invented in order to realize the Sullivan vision for the new urban space. This new form of

architecture, with an emphasis on the vertical space, became known as the Chicago School of

Design (Kaufman, 1969).

Through the 20th century, Chicago went through two distinct phases of high-

rise construction- a first boom, from the early 1920s to the mid-1930s, and a second boom from

the early 1960s until the present. The spatial distribution of the high rise buildings are mostly

concentrated in the Loop and along the Magnificent Mile in Chicago's Near North

Side community area (Kaufman, 1969). There are 2,265 high-rises (over 150 feet) structures in

the city of Chicago and 903, about 40%, are zoned for residential use.

With the amount of vertical residential space in Chicago available, the traditional

representations of spaciousness and crowdedness within the boundary units of community area

or census block as characterized by population density are inadequate measurements. The

measurement of population density will not account for the vertical structure of modern urban

residential patterns and could confuse places of high density and places of crowded living

conditions. The aim of this method is to create a new measurement which can account for the

vertical spaces within buildings and reconstruct the idea of population density into one of

personal space.

3.2.2 Model of Vertical Space

The first step in the personal space model is a binary dasymetric approach is used to

separate residential and non-residential structures throughout the city. This method will take the

building footprints for every building in Chicago and eliminates the non-residential structures

based on urban zoning codes attached to each building. The binary approach in this context

deems single-family and multi-family residential structures as suitable for living and places of

business, industry, and other buildings as unsuitable, filtering or masking out the areas deemed

unsuitable (Maantay et al., 2007). A complication with this approach is mix use buildings where

commercial and residential reside in the same structure. Structures such as these are common in

the recently gentrified areas of the city, along major artillery roads, and along natural features

such as parks and waterfronts (Grant, 2002).

Mixed-use development is the zoning of a building or a set of buildings to have more

than more than a singular purpose- not solely residential or commercial space- rather a mixture

of many uses. Mix use developments are created to spatially cluster employment, housing,

commercial, and recreational activities together in a centralized urban space (Duaney, 2002).

Mix use buildings and New Urbanism communities are developed to help eliminate some of the

strain on the local transportation network. A collection of similar mixed buildings, or a New

Urban District, is preferably spatially close to a public transit node (Grant, 2002). Mix use

buildings are often the result of gentrified post industrial urban areas or as part of a planned town

center. In specific zoning terms, mix use development refers to some combination of residential,

industrial, office, commercial, and institutional land uses (Duaney, 2002). In the mix use

building pictured below, small-scale commercial uses fill the street level and residential the

upper two floors. This type of structure is common in the redeveloped spaces of Chicago and

adds a level of uncertainty to the personal space model.

Figure 10-Mix Use Building, Lincoln Park Chicago

This binary dasymetric approach will begin to counteract the generalizations and

arbitrary boundaries of neighborhoods and census zones by assigning only specific buildings as

suitable for living. Mix use buildings, in this step, are considered as suitable for inhabitance by

residents. Later in the model mix use buildings will be divided so that 40% of the space will be

assigned to non residential and 60% to residential. A limitation of the binary approach is that it

assumes homogenous residential space in the buildings distributed across Chicago, and the

model will assign a singular value to the space. This method will only deem a building as

suitable to be included in the residential density formula, and does not account for variation

within buildings. This variable, whether the building is suitable or unsuitable for residential, is

named residential buildings.

Following this, an areal interpolation approach is used to allow for the transformation of

a source data set into a target data set (Mennis 2003). This method is used to aggregate

population values from the different zones to the target layers. In this case, the target layer is the

summation of residential floor space within the lowest level of census measurement, the census

block. This method takes the data within the specified zones from the source data- population

data summarized- and aggregates this into the appropriate zones of the target data set.

Specifically, this method will assign the population of each census block into the buildings

deemed residential in the binary method. The summation of the livable area for each building is

calculated with the product of the residential buildings classification, the area of the building

footprint, and the number of stories for that building. A total livable space is calculated for each

building, represented with a variable livable space. In the case of mix use buildings, 40% of the

livable space will be assigned to non residential and 60% to residential, following the model

used in development simulation experiments (Waddell, 2003). The population of the census

block is assigned to the building based on what percentage of the cumulative livable space

within the census block is the livable space of that building. For example, if one building

accounted for 25% of the cumulative livable space of a census block, 25% of that blocks raw

population numbers would be allocated to that specific building. Areal weighting is a simple

interpolation method which will allocate the summarized population data according to the

proportional area of the zones in the target data (Langford, 2003).

Personal Space=∑(residential buildings∗building footprint∗number of stories )

census block populaiton¿

¿

Each person within the block will be allocated a percentage of the total residential floor

space within the boundary of the population data. The areal interpolation will again rely on the

assumption that population is distributed uniformly within the target zones (Maantay, 2007), that

the residential patterns within the building are homogenous. Obviously this is not true, but the

level of measurement is constrained by the census data- in other words, the lowest level of

census information, the census block, controls the scale of the project. The buildings can be

mapped as a percentage of the total but individual building variation within the block cannot be

achieved with this approach.

This research is concerned with creating the most accurate and precise representation the

population of the urban environment possible with census data- a detailed illustration of where

and how people live. While having the before mentioned limitations, the use of a dasymetric

technique will expose the limitations of the cartographic technique of choropleth mapping and

the conceptual limitations of urban population density mapping. Moving beyond population

density in the traditional sense, the amount of residential living square footage allotted to each

person is calculated with this – a measurement that can be described as personal space. The

personal space measurement will show not how many people live in an area, but how people live

within that area, how populations are distributed across the built environment of the modern

urban space. A bivariate choropleth design will allow for the spaces in the city where density and

crowdedness are confused to be illustrated.

3.2.3 Bivariate Legend

The bivariate legend allows for spatial comparisons and for the emergence of spatial

patterns in the differences between the traditional population density measurement and the

personal space measurement at the city scale. Using a bivariate map illustrates the correlation

between the traditional measurement and the new measurement, revealing areas of Chicago that

are misrepresented by the traditional population density measurement. This legend is created by

plotting the population density of every census block aggregated to every building within that

census block on the x-axis and dividing that range into three quantiles. This will give each of the

three classifications the same number of observations, essentially creating a high population

density, medium population density, and low population density classification. The range of

personal space is plotted on the y-axis and also divided into three quantiles. This creates a high

personal space, medium personal space, and low personal space classification. The two

classifications are combined together on a three by three grid and symbolized using diverging

color schemes. The diverging color scheme in the bivariate legend of personal space and

population density is applied to every building in Chicago and begin to illustrate where there is

an interesting interaction between the two measurements.

The critical areas of this legend are the four corners- the green, purple, orange, and pink

classifications. The green classification symbolizes places that have a high density and a high

amount of personal space. A high population density suggests that there are many people living

on the planar surface within the boundary unit of the census block. High personal space would

suggest that the people living within this boundary unit are living in residential spaces that are

above average in terms of amount of space per person. The green classification of buildings

suggests that the traditional measurement of population density is insufficient in characterizing

the lived experience of crowdedness or spaciousness in the living space of the built environment.

Likewise, the pink classification illustrates buildings in low population density blocks where the

amount of personal space is below average. Again, this classification illustrates a space where

the traditional measurement has failed to characterize the experience of crowdedness or

spaciousness in the living space of the built environment. The purple classification shows areas

where the population density is high and personal space is low. The orange classifications show

areas where population density is low and personal space is high. The muted colors that form the

cross in the middle signify the spaces in the city that are average in population density or

personal space.

The design of the bivariate legend is done so to illustrate the spaces where the traditional

measurement of population density either adequately captures or fails to characterize the living

spaces of Chicago in terms of the experience of crowdedness or spaciousness of personal

residential space. The personal space metric and population density of the surrounding census

block can be measured in each building in the city. Moving from the building level to the scale

of the entire city, the representation of the bivariate space metric at each building becomes

obsolete. Rather, the most appropriate measure is to summarize the average amount of personal

space per census block and, combined with the census block population density, display the

bivariate choropleth map for the extent of Chicago. This method will essentially break down the

census data to allocate the amount of residential space per person and then reconstructs it at the

census block level for representation. The bivariate metric can be utilized all the way out to the

community area level for a very broad overview of the spatial structure of this interaction. The

allocation of this data to the community level, however, will rely on the boundaries that the

measure itself is attempting to deconstruct and ultimately provides little insight.

3.3 Demographic Profiles of Chicago

A primary purpose of the personal space measurement to is to evaluate the residential

spaces in Chicago and gain a better understanding of how people are distributed across different

spatial environments. In order to better understand this distinction and to explore the implications

of the new measure, this section will examine how demographic distributions change when the

definition of the space is changed. Demographic profiles of neighborhoods or classifications of

neighborhoods are commonly used measures to evaluate the social environment of a space. The

evaluation of the members of a contained micro-environment, such as a bounded neighborhood,

allows for the conceptualization of the socio-economic influences and the socio-cultural features

of a space (Wen et al, 2003). The use of census data to show that a certain percentage of a space

is of one group and another percentage, a different group, is an essential element of the

organizational framework of population analysis. This section will explore this concept and show

the differences in racial classifications when the measurement population density is changed to

personal space

“Obtaining racial data would seem to be a straightforward process: the census asks a question; statisticians, demographers, and other properly trained professionals tabulate the responses (Nobles, 2000).

This process however is not as basic as it would initially appear. In the Census form,

respondents are given the choice to select multiple racial categories from the following list of

options: ‘White’, ‘Black or African American’, ‘American Indian or Alaska Native’, ‘Asian’,

‘Native Hawaiian or Other Pacific Islander’, and ‘Other’ (US Census Bureau, 2011). The Census

forms list two ethnicities, ‘Hispanic or Latino’ and ‘Non-Hispanic or Latino.’ The Census

Bureau defines ‘Hispanic or Latino’ as "a person of Cuban, Mexican, Puerto Rican, South or

Central American or other Spanish culture or origin regardless of race” (US Census Bureau,

2011). For this research, I have divided the racial or ethnic self identification into five categories

for analysis and representation: White, Black, Hispanic, Asian, and Other.

To illustrate the differences in the changes in demographics as the value of personal

space is changed; the comparison of high density spaces will be made with the high density, high

space classification- green- and the high density, low space classification- purple. Similarly, the

low density spaces will be contrasted with the low density, high space areas- the orange

classification- and the low density, low space areas- pink. The comparison of the different spaces

will show both percent of total population for the different classifications as well as raw

population numbers. The demographic profiles are collected from the census block

measurement.

3.4 Spatial Structure of Chicago

3.4.1 Spatial Statistics Goals and Overview

The goal of this section is to employ spatial statistic tools and concepts in an exploratory

manner to investigate the distribution of different classified census blocks on the bivariate map

of Chicago. This section is exploratory in nature in that, rather than using spatial statistics to

make concrete or absolute claims about the urban space and the people that inhabit them, the

techniques are being used a tool to begin to understand how different classified areas operate in

space and where would be the most apt place to focus qualitative and quantitative analysis will

be in the future.

The dataset for this section is a point pattern dataset from the city of Chicago that has

16,885 point features representing the centroids of each census block in the city of Chicago. The

points are classified into nine classes based on a bivariate legend explained above- traditional

population density measurement on the ‘y’ axis and personal space measurement on the ‘x’ axis.

The main areas of interest in the analysis are the points that are classified in the four

corners of the legend, the areas that represent the combinations of highs and lows in the

classification- in this case the green, pink, purple, and orange classifications. The green

represents areas of high population density and high amounts of personal space. The purple is

low population density and high personal space. The orange classification is high density, low

space and the pink low in both categories. The 16,885 point dataset for the entire city of Chicago

required sampling for the nearest neighbor analysis. Nearest neighbor analysis works well up to

3,000 points; beyond 3,000 the measurement starts to break down and does not return consistent

variables (Bailey & Gartrell, 1995).

3.4.2 CSR Model

The first test will be testing whether each of the four corners of the bivariate

classification, the four areas of interest, differ in their distribution across the city space from

complete spatial randomness. This will indicate whether the spaces of interest from the bivariate

model show a pattern of clustering beyond what would be expected from a random point pattern.

The first step in this process is to calculate the nearest neighbor calculation on each of the four

areas of interest. The null hypothesis for this experiment is that the spatial distribution of the

classified census blocks is not clustered and is completely spatially random in location within the

city boundary of Chicago. The next step is to simulate a completely spatially random dataset of

3000 points within the city of Chicago with n=39 simulations and calculate the nearest neighbor

of each simulated point for each simulation. This is done to create a distribution of nearest

neighbor results equaling a 95% confidence intervals (Bailey & Gartrell, 1995). This allows for

a distribution for what a complete spatially random pattern would look like which can be

compared to the each classification in an fhat-h plot. This will allow for the comparison of the

different classified point patterns to determine if they are spatially not randomly across the space

of Chicago.

3.4.3 Thomas Model

After determining whether or not the dataset is completely spatially random, the next

logical step is to formally test whether the four point patterns compare to a cluster model. Using

the Thomas cluster model, this test will determine if certain areas of interest are significantly

more clustered than the background population of Chicago census blocks. The purpose of this

experiment is to determine if any of the point patterns are significantly more clustered than a

fairly strong simulated cluster model using a Thomas cluster model with the size and intensity of

the cluster based on a sampling of all the blocks in the city. This approach this will illustrate the

areas that are especially clustered while at the same time taking into account that the point

pattern is derived from census blocks and an artifact of the census structure will be a gridded

pattern. The null hypothesis is that there will be no clustering above what is expected from the

background distribution of census blocks. By using the Thomas cluster model with a radius and

intensity of cluster simulations based on the structure and natural clustering of census blocks, the

gridded structure of the city can be accounted for and classifications that exceed expected

clustering can be observed. The first step is to simulate a Thomas model dataset of 3000 points

within the city of Chicago with n=39 simulations and calculate the nearest neighbor of each

simulated point for each simulation. The intensity of the cluster is calculated using the rate of

clustering from all the census blocks in a community area. This represents the natural clustering

of the city’s census block structure. The radius of the cluster is average length of a community

area centroid to its boundary. The cluster model with the intensity and radius of the cluster set at

this level is designed to replicate the underlying population of census blocks in Chicago. The

model creates 39 simulations to create a distribution of nearest neighbor results at 95%

confidence intervals.

3.4.4 Interaction Model

The next test is an interaction model on all the area of interest point patterns against the

other area of interest point patterns to determine if certain classifications attract or repeal other

classifications. This analysis is performed multi-directionally to determine if one point pattern

holds more weight in the repulsion or attraction interaction. This test will be performed

specifically on the green, pink, purple, and orange classifications against each other in both

directions. Not all of the sets of points have the same number of observations. The following list

shows the number of points each classification has: Green-1,238, Pink- 1,211, Orange- 2,826,

and Purple-2,853. To alleviate any problems that may arise from different size samples, each

classification has been randomly sampled to equal 1,211 observations. The interactions of point

patterns will explain whether one event, the green classification for example, has a direct impact

on the spatial structure a second event, the purple classification for instance. Both events occur in

the same space, the city boundary area of Chicago, but it is unclear whether or not there is an

association between the two.

The null hypothesis is that all couplets of events will be independent of each other and

not show significant signs of attraction or repulsion. For this test, there are two variables, event I

and event J. The interaction method will test to see if the probability that the distance from a

randomly selected object in event I is closer to which of the two point patterns. This is repeated

for every point in the target event. For example, if testing the interaction of the green

classification to the purple classification, each point in green is selected and a nearest neighbor

analysis run to determine if the nearest point is of the green or the purple classification. This will

determine whether the spatial distribution of the purple classification has a direct influence on

the spatial distribution of the green classification.

With the use of exploratory data analysis- the complete spatial randomness model, the

Thomas cluster model, and the interaction model- the spatial structure of how the different

classifications are distributed across Chicago can begin the be explored. Exploratory spatial

statistics are a starting point for beginning to think about what types of social and historical

processes in Chicago are driving the spatial interaction of different lived experiences in different

built environments.

3.5 Dot Density Methods

There are four main considerations when making a dot density map that must be

considered in order to intelligently design the map with implying a misleading spatial

distribution of the phenomena. One must consider the aggregated boundary units, the size of the

dots, the observations per dot, and the location of the dots (Slocum et al, 2009). To understand as

precisely as possible the residential patterns in the urban space, these considerations need to be

narrowed in scope as much as possible. Dots should be placed in the smallest areal unit, the

residential building, to increase the precession of the placement of the individual. Each dot

should represent one person to increase the accuracy of the representation of the individual. To

observe the most accurate map of how people occupy the urban space, the boundaries need to

removed and the individuals represented in space alone.

When making a dot density map, the smaller the polygon the dots are randomly placed

within the more accurate their location will be to the location of the entity being mapped

(Slocum et al, 2009). Ancillary information, in this case, the buildings zoned residential and the

vertical extent of those buildings are used to as the target layer which dots will be placed in. The

population of each individual building is determined by using a Poisson distribution based on the

expected population of each building. The expected population for each building is derived by

calculating the expected amount of space per person from the total population of the census

block into the amount of cumulative personal space measured in the census block. The personal

space measurement will create a measurement that quantifies the amount of residential space in

each building per person, the inverse of that will be the amount of expected people per building.

From the expected intensity, the Poisson distribution allocates individuals into the building to be

represented in a dot density map. This is done under the assumption that all buildings in the

census block are not homogenous both in terms of numbers and in terms of racial breakdown.

The Poisson method, in this case, will account for variation within the buildings and not give

every building in the census block individuals based on the common value of average personal

space.

The dot density method for this series of maps will represent each individual in the city

with a singular dot confined to the building the Poisson distribution estimates that individual to

live. The dots will use a symbology in which the hue of the dot will represent one of the five

census race categories- White, Black, Hispanic, Asian, or Other. The use of chorodots will allow

for the representation of different attributes while maintaining similar size and spatial locations

across all observations (MacEachren, 1990). The chorodot technique will allow for the

representation of different groups of individual people filling the space, both the planar and the

vertical spaces, of the built environment around them. The infrastructure of the urban space

provides a spatial structure of individual residential behavior that operates not on the boundaries

of neighborhoods or census blocks, but rather on the functionality of the residential environment.

The representation of this phenomenon, individuals of different races confined to the buildings

the model predicts them to live in will provide valuable insight into the settlement patterns across

Chicago.

3.6 Intensity Methods

The final methods are designed to use the distribution of people allocated to specific

buildings to create two new maps that show the intensity of people and the intensity of space

without the use of any administrative boundaries. Both maps are made with a kernel density

function to create, first a representation of the population of Chicago with the boundary units

removed, and second, a representation of the degree of crowdedness in Chicago. This map is

designed to model these two population features without relying on boundaries or arbitrary

geographies to determine the areas of classification.

The population intensity map shows the distribution of people across the planar surface

of the city. While this method does not account for the vertical space of buildings, it does use the

personal space measurement as a derivative to create the estimation of how many people live in

each building. The kernel intensity method is designed so that the estimated population value for

each residential structure in the city is accounted for. The kernel radius is a function of that

intensity of the population in each building. The assumption behind this is that the more people

in each building, the more communal space they will occupy and draw resources from when

outside the residential structure. The kernel size function is designed so the population of the

building does not have a huge impact of the kernel size, but does alter it slightly to account for

this allocation of communal space- an indication of the perceived experience of crowdedness of

the space surrounding residential structure. The kernel size is designed so that a single family

home with few residents will have an impact of intensity to match that of roughly a size of a yard

while the most populated structure in the city will have a kernel size of about half a city block.

By having the size of the kernel as a function of building population, the population of each

residential structure will have an impact on the micro-scale population intensity in the immediate

area around the building, but the intensity of the total building population will be the driving

force behind the population intensity map. This map shows the areas of high and low intensity of

populations without the use of any administrative boundaries, but fails to account for the amount

of space each person has. This map is represented using a traditional heat map index with colors

ranging from blue for low intensity to red for high intensity.

The second map, the space intensity map, also employs a kernel density method with a

constant kernel size of 100 feet in diameter. The range of personal space is normalized on a scale

of 0-1 so that the density function will show the distribution of the personal spaces and not the

larger numbers of square feet per person. This method is designed not to calculate the intensity

of the number of people each building has, but to calculate the intensity of the space each person

has. The space intensity map is representing the relative crowdedness or spaciousness of each

building in the city without relying on administrative boundary enumerations. This map is

represented using a heat map index with colors ranging from blue for low intensity of

crowdedness to red for high intensity of crowdedness.

Both the population intensity map and the space intensity map are exported into the

Google Earth interface for seamless viewing and interactivity at multiple scales. By using the

format of an interactive virtual globe, it is immediately noticeable how the intensity of

population and space change based on the built environment and vertical dimension of buildings.

Another useful feature of the Google Earth interactive display is the addition of a three

dimensional model to show the vertical extent of the built environment. In a map of population

or crowdedness with boundaries, the spaces that are non-residential would have the same value

as those places where people live. There is no population that lives on a golf course. A park is

not a spacious or crowded living space. Using this method shows a clear difference in how the

spatial structure of the city changes the intensity of people and spaces without generalizations

and the use of boundaries.

3.7 Summary

The methods section of this thesis employs a variety of techniques in attempts to better

describe and represent the phenomenon of modern urban residential life. The main focus with

this method is working towards the deconstruction of the employment of boundaries in

cartographic representations of urban space. The vertical space is a feature of urban residential

structure that has not been accounted for with the traditional measurements of density and the

representations of density with standard choropleth and dot density approaches. The personal

space index and the bivariate legend are methods to model this vertical space as an active

residential environment. The exploratory spatial statistic models are attempts to discover patterns

across the space of Chicago of the personal space classifications. A fine scale dot density

approach to allocate individuals and demographic characteristics of the individuals to the

building level at a level of representation where each dot equals one person was performed to

explore the microstructure of the built environment in Chicago. A kernel density approach was

taken to represent the intensity of population and the intensity of crowdedness at various scales

across the city without the use of boundaries. The maps created with the methods illustrated in

this section have been placed in the virtual globe environment of Google Earth for seamless user

interaction. The virtual globe environment allows for results to be observed at various scales set

against the context of areal imagery of the city.