Dissertation Project 1: Regressions of Slopes for Boston
Michael Shields
8/30/2020
Running Regression on Extracted Slopes (via Random Effects)
Project 1 argues that gentrification is only one form of neighborhood change (contingent on a rapid increase in a neighborhood’s socioeconomic status). Therefore, to understand gentrification, it needs to be stripped of all its politically-charged attributes. I argue that gentrification - at its most rudimentary form - is a rapid increase in socioeconomic status. All other indicators normally touted to be a part of gentrification (i.e. displacement, increase in white residents, higher rents, positive changes to the built infrastructure [investment from public and private entities], etc.) become secondary attributes that are “testable.”
This project began with the construction of a neighborhood-level uniform measure of socioeconomic status (SES) using a reflective factor analysis (Read more here: https://rpubs.com/mshields417/diss_project1_sesBOS). The factor loadings were extracted to create a series of SES scores per city census tract over a five-year period of 2014 to 2018 (thus for each year between 2014 through 2018, a single city census tract had a unique SES score).
A mixed-effects model was used to extract the “random effects” coefficients (i.e. the slopes) of each census tract’s SES score during the five-year period. These slopes represent the individual trajectories of each of the tract’s SES scores during the five-year period. The range in SES slopes for each Boston census tract are summarized below (a summary of the slopes are also z-scored for easier interpretation).
## ses_slope zSESslope
## Min. :-10011 Min. :-2.0205
## 1st Qu.: -2838 1st Qu.:-0.5727
## Median : -1177 Median :-0.2376
## Mean : 0 Mean : 0.0000
## 3rd Qu.: 1759 3rd Qu.: 0.3550
## Max. : 34018 Max. : 6.8658
Extracting Slopes for Dependent Variables of Gentrification
For the purpose of testing “neighborhood change” attributes that have colloquially and qualitatively been attributed to gentrification, the extracted SES slopes will be used as an independent variable among individual regression models. The dependent variable will be the various neighborhood-change-attributes traditionally aligned with gentrification theories, like: Increased Rent, Increases in Non-Hispanic White residents, Decreases in Residents of Color, Increases in Young Professionals, etc.
As with SES, a series of mixed effects models were used to extract the random effects of each census tract for each dependent variable. For example, each tract had an individual percentage of Non-Hispanic White residents that altered from 2014 to 2018. Thus, a mixed effects model using a beta regression (ideal for working with continuous dependent variables that ranges from 0 to 1) was used to extract estimated slopes per tract of the percent of Non-Hispanic White residents.
Different mixed effects regression models were used based on the structure and normality of each variable. A summarized list of each variable, the type of mixed effects regression used, and a summary of its slopes are listed below.
| X | Variable | Minimum | First.Quarter | Median | Mean | Third.Quarter | Maximum | Range | MLM.Regression.Type |
|---|---|---|---|---|---|---|---|---|---|
| 1 | SES | -1.001100e+04 | -2838.0000000 | -1.17700e+03 | 0.0000e+00 | 1.759000e+03 | 3.401800e+04 | 4.402900e+04 | Normal |
| 2 | Total Population | -2.032200e+02 | -61.1800000 | -1.29700e+01 | 0.0000e+00 | 4.352000e+01 | 3.887800e+02 | 5.920000e+02 | Normal |
| 3 | Total Housing | -5.996814e+01 | -17.6501600 | -7.55449e+00 | -1.0000e-05 | 5.849750e+00 | 3.057869e+02 | 3.657550e+02 | Normal |
| 4 | Percent White (NH) | -1.939800e-01 | -0.0615408 | 1.74460e-03 | -9.1000e-06 | 4.885810e-02 | 3.148346e-01 | 5.088146e-01 | Transformed Beta |
| 5 | Percent Black (NH) | -3.763903e-01 | -0.0570647 | 1.06020e-03 | -1.5630e-04 | 5.799450e-02 | 2.762030e-01 | 6.525933e-01 | Transformed Beta |
| 6 | Percent Asian (NH) | -3.926980e-01 | -0.0920749 | -5.51890e-03 | -5.9510e-04 | 9.243560e-02 | 5.886431e-01 | 9.813411e-01 | Transformed Beta |
| 7 | Percent Latinx | -2.288410e-01 | -0.0630120 | -1.35910e-02 | -4.8900e-04 | 4.784800e-02 | 4.135860e-01 | 6.424270e-01 | Beta |
| 8 | Percent Under 18 Yrs | -1.480335e-01 | -0.0368392 | -9.70300e-04 | -6.8000e-06 | 2.976530e-02 | 1.960980e-01 | 3.441316e-01 | Beta |
| 9 | Percent Ages 18 to 24 Yrs | -2.185758e-01 | -0.0497491 | -7.69200e-04 | 1.2970e-04 | 5.699670e-02 | 2.119986e-01 | 4.305744e-01 | Beta |
| 10 | Percent Ages 25 to 34 Yrs | -1.400377e-01 | -0.0430244 | -3.89120e-03 | -5.1300e-05 | 3.109180e-02 | 2.459311e-01 | 3.859687e-01 | Beta |
| 11 | Percent Ages 35 to 44 Yrs | -1.570723e-01 | -0.0325411 | 5.23410e-03 | -4.9400e-05 | 3.428420e-02 | 1.347638e-01 | 2.918361e-01 | Beta |
| 12 | Percent Ages 45 to 59 Yrs | -1.282455e-01 | -0.0359207 | 3.86000e-04 | -1.5900e-05 | 3.320380e-02 | 2.063646e-01 | 3.346101e-01 | Beta |
| 13 | Percent Ages 60 to 74 Yrs | -1.520092e-01 | -0.0493157 | 1.01918e-02 | -5.8100e-05 | 3.763460e-02 | 2.075364e-01 | 3.595456e-01 | Beta |
| 14 | Percent Ages 75 Yrs and Up | -2.813344e-01 | -0.0564323 | 2.83520e-03 | -1.0210e-04 | 5.920970e-02 | 2.572005e-01 | 5.385349e-01 | Beta |
| 15 | Percent on Public Assistance | -2.880872e-01 | -0.0627065 | 1.31418e-02 | 1.9810e-04 | 6.165540e-02 | 2.454371e-01 | 5.335243e-01 | Transformed Beta |
| 16 | Percent of Households in Poverty | -1.918466e-01 | -0.0433578 | 4.74440e-03 | 1.6140e-04 | 5.065010e-02 | 1.927195e-01 | 3.845661e-01 | Beta |
| 17 | Percent of Family Households | -1.767203e-01 | -0.0312378 | -2.30490e-03 | -1.8000e-06 | 3.305840e-02 | 1.737769e-01 | 3.504972e-01 | Beta |
| 18 | Percent of Same-Sex Households | -7.512903e-01 | -0.1768855 | 7.58349e-02 | -6.8130e-04 | 8.012240e-02 | 6.085124e-01 | 1.359803e+00 | Transformed Beta |
| 19 | Percent of Renters | -2.126181e-01 | -0.0376984 | -1.77020e-03 | 5.3400e-05 | 3.868070e-02 | 1.958976e-01 | 4.085157e-01 | Transformed Beta |
| 20 | Median Gross Rent | -1.020733e+02 | -27.3221800 | 3.33582e+00 | -7.0000e-05 | 2.332887e+01 | 1.552462e+02 | 2.573195e+02 | Normal |
| 21 | Median Gross Rent (Adjusted) | -1.015903e+02 | -28.2893900 | 1.91646e+00 | 3.0000e-05 | 2.416680e+01 | 1.418668e+02 | 2.434571e+02 | Normal |
| 22 | Percent of Parcels with at Least One Building Permit |
-1.871740e-02 | -0.0053631 | -2.90520e-03 | 8.2800e-05 | 3.334500e-03 | 2.760900e-02 | 4.632640e-02 | Beta |
| 23 | Percent of Parcels with at Least One New Construction Permit |
-3.735700e-02 | -0.0125510 | -2.65800e-03 | 1.9930e-03 | 9.286000e-03 | 1.062050e-01 | 1.435620e-01 | Transformed Beta (non-convergence) |
| 24 | Percent of Parcels with at Least One Renovation/Addition Permit |
-2.197090e-02 | -0.0058417 | -3.04540e-03 | 1.1090e-04 | 4.312700e-03 | 2.836370e-02 | 5.033460e-02 | Beta (non-convergence) |
| 25 | Percent of Parcels with at Least One Demolition Permit |
-4.272880e-02 | -0.0052756 | 4.61000e-05 | 9.2900e-05 | 4.040100e-03 | 5.708150e-02 | 9.981030e-02 | Transformed Beta |
| 26 | Median Home Value (Adjusted) | -1.919410e+05 | 25780.0000000 | 3.10160e+04 | 4.0669e+04 | 3.848900e+04 | 1.158511e+06 | 1.350452e+06 | Normal |
Seeing Correlations Between Slopes
Before conducting the regressions (or using the econometric technique of “Seemingly Unrelated Regressions”), I ran a simple Pearson’s correlation tabulation to understand the relationship each slope-variable has with the slope of SES. Surprisingly, it seems that only built environment changes - like changes in building permits (especially, New Construction and Renovation/Additions) along with Housing and Rent have the strongest positive relationships with SES change. Negative correlations include the number of persons on some form of public assistance, Asian residents, residents aged 60 to 74, and demolition permits.
A correlation matrix is shown below to display the relationships.
Closer Examination of Variable-Slope Relationships
It is somewhat surprising that some slope-variables did not correlate with the change in SES - considering all that is observed about gentrification in major U.S. cities. To further understand why some variables did not correlate, individual scatter plots were made with neighborhoods detailed. Understanding the reality of change (i.e. which neighborhoods saw rapid SES rise but minimal to no changes in another variable) may elude to other mediating effects or unconsidered phenomenon.