# Reconsidering the Relationship between Air Pollution and Deprivation

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## Abstract

**:**

## 1. Introduction

#### A More Pluralistic Theoretical Framework

## 2. Materials and Methods

#### 2.1. Analytical Approach

_{i}is air pollution concentration for Datazone i (e.g., PM

_{2.5}) while x

_{i}

^{T}contains linear and quadratic terms of Income deprivation at Datazone i (centered on the annual mean) and γ is a 2 by 1 vector of regression coefficients, assumed constant across the region; higher-order polynomials were tested but did not add sufficiently to justify the additional complexity. β

_{0}is the intercept, and ε

_{i}residuals assumed to follow a normal distribution.

#### 2.2. Data

_{10}, PM

_{2.5}, NOx, NO

_{2}, SO

_{2}and ozone are produced for points on a 1 km by 1 km square grid for the whole of the UK. To produce estimates for Datazones, the pollution grids are first overlaid with Datazone boundaries to calculate the areas of grid cells falling into a Datazone, and then the pollution level of that Datazone is calculated as the weighted averages of grid cell values (see Supplementary Material for more information). As the data available at 1 km × 1 km resolution are themselves modeled estimates, interpolated and extrapolated from data from several pollution monitoring stations by the Department for Environment Food & Rural Affairs [45] in the UK, the mean annual pollution estimates are in effect modeled twice. However, these data are to our knowledge still the best available data on local air pollution levels for the UK, and were produced to a standard that allows the UK to meet European air quality monitoring objectives, such as those specified in the 2008 EU Air Quality Directive (2008/50/EC), and the related Air Quality Framework directives (2004/107/EC and 1996/62/EC). City regions were defined using the Scottish Government’s Travel-to-Work Areas (TTWAs). These are functional geographies based on commuting flows, measured by the Census 2001. In the analyses below, we use PM

_{2.5}as the measure of air pollution, but the findings in terms of the spatiotemporal nonlinearities in the relationship between air pollution and deprivation apply to other pollutants such as NO

_{2}and SO

_{2}. Summary statistics on air pollution and deprivation in the study area are provided in Table 1.

_{2.5}concentrations in Scotland are not high on average, but there appears to be an increasing trend since 2009 (Table 1). As the spatial scales at which different theoretical processes underlying the link between deprivation and pollution discussed above operate are likely to be varying, we resort to the fine-grained spatial units Datazones in the whole of Scotland as our primary analysis units. The national-scale analysis with fine-resolution geographies produces opportunities of finding interesting, diverse and statistically reliable functional forms of linkage between deprivation and pollution due to large sample size.

## 3. Results and Discussions

#### 3.1. Explore Relationships without Imposing Functional Form

#### 3.2. Local Spatial Non-Linear Analysis

#### 3.3. Identifying Regions

## 4. Conclusions

## Supplementary Materials

_{2.5}values at 1 km × 1 km grid cells from the Defra (left) and estimated values for Datazones in 2004, Figure S2: The PM

_{2.5}values at 1 km × 1 km grid cells from the Defra (left) and estimated values for Datazones in 2012, Figure S3: Pollution–deprivation relationship for four city-regions in 2006, Figure S4: Pollution–deprivation relationship for four city-regions in 2009, Figure S5: Pollution–deprivation relationship for four city-regions in 2012, Figure S6: Local coefficients for income deprivation (a) and squared income deprivation (b) in Glasgow in 2004, Figure S7: Local coefficients for income deprivation (a) and squared income deprivation (b) in Glasgow in 2012, Table S1: GWR estimation results for Glasgow TTWA—2004 and 2012.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Pollution–deprivation relationship for Scotland during 2004–2012. Note: Median Income Deprivation is the median of scores in each decile.

**Figure 2.**Pollution–deprivation relationship for four city-regions in 2004. Note: Deprivation deciles and associated median scores are defined at the national scale to facilitate comparison. These charts are plotted for 2004. Plots for 2006, 2009 and 2012 are also available as Supplementary Materials, available on request. Note: Median Income Deprivation is the median of scores in each decile.

**Figure 5.**Pollution–deprivation relationships for the clusters in 2004. Note: The dashed lines are the approximate 95% confidence intervals.

**Figure 6.**Pollution–deprivation relationships for the clusters in 2012. Note: The dashed lines are the approximate 95% confidence intervals.

Income Deprivation | Mean | Std. Dev | Lower Quantile | Upper Quantile |

2004 | 0.149 | 0.121 | 0.055 | 0.209 |

2006 | 0.141 | 0.110 | 0.055 | 0.198 |

2009 | 0.154 | 0.113 | 0.060 | 0.210 |

2012 | 0.138 | 0.098 | 0.060 | 0.200 |

Air Pollution (PM2.5 Micrograms/m3 (μg m−3)) | Mean | Std. Dev | Lower Quantile | Upper Quantile |

National | ||||

2004 | 8.630 | 1.542 | 7.422 | 9.607 |

2006 | 7.088 | 1.284 | 6.205 | 7.937 |

2009 | 6.779 | 1.135 | 5.995 | 7.523 |

2012 | 7.557 | 1.087 | 6.888 | 8.236 |

Aberdeen | ||||

2004 | 8.247 | 1.308 | 7.092 | 9.363 |

2006 | 6.523 | 1.024 | 5.630 | 7.338 |

2009 | 6.924 | 1.158 | 6.078 | 7.797 |

2012 | 8.169 | 0.887 | 7.677 | 8.665 |

Dundee | ||||

2004 | 8.404 | 0.750 | 7.785 | 8.981 |

2006 | 7.455 | 1.233 | 6.264 | 8.328 |

2009 | 6.680 | 0.622 | 6.122 | 7.059 |

2012 | 7.609 | 0.448 | 7.325 | 7.921 |

Edinburgh | ||||

2004 | 9.442 | 0.865 | 8.952 | 9.935 |

2006 | 7.716 | 0.765 | 7.122 | 8.271 |

2009 | 7.508 | 0.813 | 7.100 | 7.962 |

2012 | 8.497 | 0.701 | 8.130 | 8.874 |

Glasgow | ||||

2004 | 9.986 | 1.357 | 8.967 | 10.878 |

2006 | 8.321 | 1.069 | 7.507 | 8.946 |

2009 | 7.602 | 0.947 | 6.965 | 8.057 |

2012 | 8.066 | 0.954 | 7.427 | 8.552 |

**Table 2.**Estimation results from second-order polynomial regression models for Scotland and four city-regions during 2004–2012.

Variables | National Scale | Aberdeen | Dundee | Glasgow | Edinburgh | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

2004 | 2006 | 2009 | 2012 | 2004 | 2012 | 2004 | 2012 | 2004 | 2012 | 2004 | 2012 | |

Coefficients/(Std. Err) | Coefficients/(Std. Err) | Coefficients/(Std. Err) | Coefficients/(Std. Err) | Coefficients/(Std. Err) | ||||||||

Intercept | 2.132 * | 1.936 * | 1.892 * | 2.006 * | 2.157 * | 2.118 * | 2.133 * | 2.027 * | 2.283 * | 2.079 * | 2.243 * | 2.139 * |

(−0.003) | (−0.003) | (−0.003) | (−0.002) | (−0.011) | (−0.009) | (−0.006) | (−0.005) | (−0.004) | (−0.004) | (−0.005) | (−0.004) | |

Income deprivation | 0.358 * | 0.448 * | 0.261 * | 0.164 * | 0.74 * | 0.357 * | 0.466 * | 0.113 | 0.433 * | 0.374 * | 0.043 | 0.011 |

(−0.024) | (−0.026) | (−0.024) | (−0.024) | (−0.084) | (−0.079) | (−0.051) | (−0.047) | (−0.035) | (−0.037) | (−0.038) | (−0.038) | |

Squared income deprivation | 0.453 * | 0.435 * | 0.548 * | 0.554 * | −1.159 | −0.128 | −0.988 * | −0.139 | −0.586 * | −0.788 * | −0.058 | −0.246 |

(−0.105) | (−0.126) | (−0.119) | (0.151) | (−0.588) | (−0.886) | (−0.269) | (−0.308) | (−0.12) | (−0.184) | (−0.176) | (−0.332) | |

Adjusted R^{2} | 0.085 | 0.092 | 0.05 | 0.022 | 0.14 | 0.043 | 0.265 | 0.026 | 0.139 | 0.083 | 0.001 | 0.001 |

Sample size | 6505 | 6505 | 6505 | 6505 | 461 | 461 | 265 | 265 | 1398 | 1398 | 772 | 772 |

Variables | Minimum | Lower Quartile (25%) | Median (50%) | Upper Quartile (75%) | Maximum | Non-Stationarity Test (F Statistic) |
---|---|---|---|---|---|---|

2004 | ||||||

Intercept | 1.701 | 2.065 | 2.192 | 2.282 | 2.504 | 516.3 * |

Income deprivation | −0.248 | 0.039 | 0.169 | 0.342 | 1.044 | 11.81 * |

Squared Income Deprivation | −1.884 | −0.721 | −0.239 | 0.240 | 8.324 | 5.87 * |

Adjusted R^{2} | 0.827 | |||||

Residual standard error | 0.075 | |||||

2012 | ||||||

Intercept | 1.663 | 1.968 | 2.047 | 2.123 | 2.262 | 383 * |

Income deprivation | −0.28 | 0.020 | 0.154 | 0.249 | 1.409 | 7.52 * |

Squared Income Deprivation | −5.508 | −1.078 | −0.562 | −0.026 | 14.25 | 5.49 * |

Adjusted R^{2} | 0.791 | |||||

Residual standard error | 0.068 |

Models | RSS | DF | MS | F | p |
---|---|---|---|---|---|

2004 | |||||

OLS (2004) | 194.5 | 6502 | 0.03 | ||

GWR | 35.8 | 6336 | 0.006 | ||

GWR improvement | 158.7 | 165.7 | 0.958 | 169.7 | 0.000 |

2012 | |||||

OLS (2012) | 141.2 | 6502 | 0.022 | ||

GWR | 29.4 | 6332 | 0.005 | ||

GWR improvement | 111.8 | 169.8 | 0.659 | 142.1 | 0.000 |

Clusters | Cluster Summaries | Income Deprivation Summaries | ||||
---|---|---|---|---|---|---|

Income Deprivation | Squared Income Deprivation | Cluster Size | Median | Min | Max | |

2004 | Coefficients | |||||

cluster 1 | 0.19 | −0.48 | 2486 | 0.12 | −0.15 | 0.66 |

cluster 2 | 0.52 | −1.02 | 1377 | 0.08 | −0.15 | 0.46 |

cluster 3 | 0.33 | 2.61 | 308 | 0.10 | −0.14 | 0.19 |

cluster 4 | 0.03 | 0.26 | 2334 | 0.14 | −0.15 | 0.55 |

2012 | Coefficients | |||||

cluster 1 | 0.16 | −0.92 | 3008 | 0.12 | −0.14 | 0.44 |

cluster 2 | 0.41 | −0.95 | 1324 | 0.08 | −0.13 | 0.34 |

cluster 3 | 0.08 | 5.08 | 164 | 0.09 | −0.13 | 0.15 |

cluster 4 | −0.01 | 0.11 | 2009 | 0.14 | −0.14 | 0.51 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bailey, N.; Dong, G.; Minton, J.; Pryce, G.
Reconsidering the Relationship between Air Pollution and Deprivation. *Int. J. Environ. Res. Public Health* **2018**, *15*, 629.
https://doi.org/10.3390/ijerph15040629

**AMA Style**

Bailey N, Dong G, Minton J, Pryce G.
Reconsidering the Relationship between Air Pollution and Deprivation. *International Journal of Environmental Research and Public Health*. 2018; 15(4):629.
https://doi.org/10.3390/ijerph15040629

**Chicago/Turabian Style**

Bailey, Nick, Guanpeng Dong, Jon Minton, and Gwilym Pryce.
2018. "Reconsidering the Relationship between Air Pollution and Deprivation" *International Journal of Environmental Research and Public Health* 15, no. 4: 629.
https://doi.org/10.3390/ijerph15040629