danmelton.net

Spatial Modeling of Tolerance

As Florida’s research argues, the more gays, artists and foreign-born immigrants in a region, the more tolerant that region is perceived. However, does residential matching or just consumption characterize this relationship? The following are my hypotheses:

Hypothesis (1): Creatives will locate to regions with larger diverse subgroup populations (Florida).

Hypothesis (2): Creatives will locate to these neighborhoods where diverse groups spatially locate (Florida).

Hypothesis (3): There will be a residential spatial mismatch between Creative Class and Diversity (Melton).

To test these hypotheses, I use group concentration measures. A plethora of research exists on measuring residential concentrations, though the literature mostly concerns segregation. Dissimilarity, isolation and exposure indices are the most popular, at least in use, of segregation studies. I propose using two methods, one based on a location quotient similar to Florida. The other is the standardized spatial GINI index proposed by Dawkins (2004). Location quotients measure group proportions controlling for the larger base population. Using census tracts as a proxy for neighborhoods, I create a location quotient for each variable (bohemians, same-sex partnered households, foreign-born immigrants, and Creative Class occupations) at the tract level. Formula 1 below displays the location quotient:

(1) LQ = (Tract Diverse Population/City Diverse Population)/(Tract Population/ City Population)

Location quotients utilize a ratio method that (1) considers the proportion of the group that locates to an area (i.e. neighborhood) from the entire region (i.e. metropolitan area) and (2) relates that to the population that located to the area compared to the entire population for the region. If a location quotient exceeds one, then the minority population is much more likely to live in the region than the base population. After some initial testing, I consider a tract concentrated if its location quotient exceeds three. I chose this number after running simulations at location quotients at half intervals from one to five. After three, the number of tracts drops dramatically.

I also look at whether or not these populations live together. Tracts with a location quotient above one for each group are considered in this analysis. As the formula shows, this method enables a comparative analysis of tracts. Most research considers a census tract concentrated if the minority population exceeds a certain percentage threshold. When considering population dynamics and critical mass, I find this to be a misleading approach. For instance, assume two tracts in different cities where the population percent of gays in both tracts is 40%. Can we conclude that the two gay populations and the visual evidence of the community would be the same between the two tracts? Or can we conclude that the gays in both census tracts will be able to support the same level of gay-focused bars, organizations and political movements? No, if the two census tracts have differing population bases (500 gays/2k population base versus 200/800 base), then the critical mass difference between the two tracts can make all the difference.

The second method employs spatial measures including the standardized spatial gini, exposure and isolation indices. Exposure measures the amount of residential exposure of group x to group y. Formula 2 displays the exposure calculation:

(2) Exposure = ?[(Tract Creative population/City Creative population)/(Tract Diverse population/Tract population)]

Isolation measures the average tendency or degree of a group to be concentrated. Formula 3 displays the isolation calculation, where X refers to the population of interest, such as creatives.

(3) Isolation = ?[(Tract X population/City X population)*(Tract X population/Tract population)]

The final measure is the standardized spatial GINI technique developed by Dawkins which measures both concentration and unevenness. Using GIS methods, it overcomes a number of difficulties generally associated with concentration indices, including the ‘checkerboard problem’ and the transfer issue (see ibid.). To calculate the standardized spatial Gini, the process requires geospatial software and matrix calculations. I use GeoDa and a Php/Mysql combination (see the appendix for program code). The standardized spatial Gini is composed of two parts, a spatial Gini (Gs) and a Gini computation (Go). First, compute a segregation ratio for each tract. In this case, each tract is assigned a ‘segregation’ score denoted by Di/Ci. Second, all tracts within the region are ranked in a decreasing order by this segregation score and entered into formula 4.

(4) Go = [ C1, C2, … Cn,]? G [ D1, D2, … Dn,]
Where:
Ci = Neighborhood’s share of the region’s creatives (Ci/(?Cn), ranked by decreasing values of Di/Ci.
Di = Neighborhood’s share of the region’s diversity (Di/(?Dn), ranked by decreasing values of Di/Ci.
[ C1, C2, … Cn,]? = row vector
[ D1, D2, … Dn,] = column vector

The middle G denotes the G-matrix, an n x n matrix with zeroes along the determinant, -1 in the upper triangle and 1 in the lower (Silber 1989). Formula 5 shows the G-matrix.

(5) G =

To obtain the spatial Gini, tracts must be re-ranked accounting for spatial relations with their neighbors. Formula 6 displays the spatial gini:

(6) Gs = [ C1r, C2r, … Cnr,]? G [ D1r, D2r, … Dnr,]
Where:
Cir = Neighborhood’s share of the region’s creatives (Ci/(?Cn), re-ranked by decreasing values of Di/Ci.
Dir = Neighborhood’s share of the region’s creatives (Di/(?Dn), re-ranked by decreasing values of Di/Ci.

Unlike Dawkins who uses a nearest neighbor approach, I rely on a contiguity analysis that averages values for bordering neighbors. For instance, assume a city with three tracts (i), equal populations and the following values for diversity (D) and creatives (C): [ i(D,C)…A(40, 25), B(5,25), C(5, 100) ]. With these values, we can compute each tract’s proportion of the region’s diverse or creative population: [ i(D,C)…A(.8, .16), B(.1,.16), C(.1, .66) ] and a segregation ratio [ A(1.6), B(.2), C(.05) ]. With these values, we can rerank the tracts and fill in the formula as Go = [ .66, .16, .16 ]? G [ .1, .1, .8 ].

Now assume that A borders B and B borders C. Averaging the data of neighbors and replacing the original values with our new spatially-based values, we obtain: [ A(22.5,25), B(16.7,50), C(5,41.67) ]. Again, the proportion computation yields: [A(.45, .167), B(.334,.33), C(.1,.83) ]. We can also refigure our segregation ratio and reorder our tracts: [C(.12), B(.33), A(.9)] . In this example, the tracts did not change positions, even though values are different. Plugging our new values into formula 6, we arrive at Gs = [ .66, .16, .16 ]? G [ .1, .1, .8 ]. The standardized spatial gini is then:

Gst = Gs/Go = [ .66, .16, .16 ]? G [ .1, .1, .8 ] / [ .66, .16, .16 ]? G [ .1, .1, .8 ]=.674/.674=1

Since the Go and Gs are the same, segregation in this city is driven entirely by the concentration into two poles, tract a and tract c. However, had the population of both been spread out more evenly, Gst would have been close to zero. Gst ranges from –1 to 1. Values approaching 1 indicate concentration (high isolation, low exposure) and those approaching 0 suggest evenness (high exposure, low isolation). Negative values suggest that tracts are so uneven that a large number of tracts are spatially reranked. High negative values indicate very high unevenness due to concentrated clusters. This corresponds to a city where there are dense pockets of diversity spread through out the region.

Turn to Figure 10, which duplicates Figure 9, but with segregation measures added. Included in the graph are the isolation, exposure, GINI and standardized GINI measures. Moving from left to right, percentage of the US group population that lives in the region increases, along with the creativity score and perception of tolerance. If concentrated enclaves are predictors of population size, creativity and tolerance, then we should see the following relationships among the segregation measures:

1. Isolation and GINI measures will be upward sloping. This indicates that as the population size increases, it is more inclined to concentrate to particular community centers or enclaves.

2. Exposure scores will increase as population and creativity index increase. Even though the community becomes more concentrated, the larger subgroup populations will increase as will the chance that creatives will rub shoulders with diversity.

3. The standardized spatial GINI will be downward sloping, approaching –1 as population and creativity score increase. If the concentration of the community increases as the group population and city size increase, we should see a larger percentage of the GINI attributed to spatiality.

For this paper, I use census tracts to approximate neighborhoods in 313 metropolitan statistical areas where data is available. All data is from the US Census 2000 summary 3 file. I combined this data with Tiger map files made available through the census website, merging census tract maps with those for central cities, PMSAs and MSAs. I use this data set over newer sources to stay consistent with Florida’s research methods. For Bohemians, I use Florida’s definition of bohemian that typifies this class of workers by occupation. Florida uses PUMS data to determine classification.

However, I use census data from the summary 3 file which includes sports players. A lower classification level is not available to the public. This data only considers people who are employed in an artist-related profession; it does not consider people who work as hobbyist artists. For gays, I use the unmarried same-sex partner data for both male and female. Same-sex partnered households should not be construed as a direct measure of overall gays and lesbians. The 2000 Census only measures gays and lesbians that check a box indicating unmarried partner; research shows that these households are on average more educated, have higher incomes and are mostly white. Also, bisexual and transgender persons are not explicitly included, but may be represented in the same-sex partnered data. This measure is only a proxy and should be taken with caution in interpreting both mine and Florida’s results. For foreign-born immigrants, I count all persons who were born outside of the United States and indicated a foreign status on the Census. Finally, I also include the Creative Class as specified by Florida. Unlike Florida, I do not include the bohemian artists in the Creative Class measure, since they are a driver of tolerance. For a class breakdown by occupation, turn to the appendix.

For the purposes of comparison, I present the results grouped by creativity ranking (Florida 2002). I cluster the creativity index score, which is derived by taking the reverse ranking of each of the four indices. Those include the Milken Tech-Pole rating for 1999 (technology), patents per capita in 1999 (innovation), the location quotient of same-sex partnered households (diversity) and the location quotient of Creative Class workers (talent). The scores presented here differ slightly from Florida’s original results as I use a larger number of metropolitan areas, resulting in potentially higher scores.