# Analyzing the Driving Factors Causing Urban Expansion in the Peri-Urban Areas Using Logistic Regression: A Case Study of the Greater Cairo Region

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## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Study Area

#### 2.2. Data

## 3. Methodology

#### 3.1. Classification of Satellite Images

#### 3.2. Identifying the Variables of the Logistic Regression Model

^{2}statistics with these factors. This process was carried out for each set of variables to assess their reliability. Finally, the total number of independent (variables) decreased from thirteen to eight factors (variables) (see Table 3).

#### 3.3. Logistic Regression Model (LRM)

_{0}, x

_{1}, x

_{2}…x

_{k}) (representing driving factors of urban expansion); and b is the estimated parameters, b = (b

_{0}, b

_{1}, b

_{2}…b

_{k}) (representing variable coefficients)

_{i}is the predicted value of the urban expansion (dependent variable) for sample $\mathrm{i}$; and y

_{i}is the observed value of the urban expansion (dependent variable) for sample i.

_{ij}is the observed value of the independent variable j for sample i. The rest is the same as for the likelihood function. In solving the above equations, LOGISTICREG uses the Newton–Raephson algorithm.

#### 3.3.1. Calibration of the Logistic Regression Model

#### 3.3.2. Goodness of Fit of the Model

^{2}and Nagelkerke R

^{2}were computed to further test the goodness of fit of the model. The Cox and Snell R

^{2}values and the Nagelkerke R

^{2}values are analogous indicators to the R

^{2}statistics of the linear regression. R

^{2}values closer to 1 indicate the model is closer to certainty. The outputs proved that the eight driving factors are significant enough. Cox and Snell R

^{2}value for the model was 0.76, which refers to a very good fit in the study area and the R

^{2}value was 0.90, which reflects the accuracy of the model (see Table 4).

## 4. Results

#### 4.1. Urban Expansion

#### 4.2. Driving Factors (Independent Variables)

#### 4.3. Multicollinearity Analysis for Independent Variables

#### 4.4. Influence of Driving Forces on Urban Expansion

#### 4.5. Prediction of Urban Expansion

_{1}, X

_{2}, …, X

_{k}) is the probability of the dependent variable Y being 1 given (X

_{1}, X

_{2}, …, X

_{k}), i.e., the probability of a cell being urbanized; Xi is an independent variable representing a driving force of urban expansion; and β

_{i}is the coefficient for variable X

_{i}.

#### 4.6. Model Validation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Year | Population of the PUAs | Total Population of the GCR | Percentage of Total Population (%) |
---|---|---|---|

1996 | 2,857,468 | 13,230,496 | 21.6 |

2007 | 3,942,262 | 16,292,269 | 24.2 |

2017 * | 5,231,400 | 20,500,000 | 25.5 |

Dataset | Source | Date |
---|---|---|

Landsat ETM+ for 2007 and Landsat 8 (OLI/TIRS) for 2017 | U.S. Geological Survey Resolution 30 m | 29 April 2007 1 October 2017 |

Reference image for Landsat images | Google Earth Pro Resolution 60 m | April 2007 and October 2017 |

Shapefiles of roads, regional services, water streams, industrial areas and urban centers | GOPP | Produced in 2009 |

Population density | CAPMAS | 1996, 2007 and 2017 |

Variable | Meaning | Nature of Variable |
---|---|---|

Dependent (Y) | 0: no urban expansion; 1: urban expansion | Dichotomous |

X1 (dist_Rd) | Distance to nearest road | Continuous |

X2 (dist_centrs serv.) | Distance to nearest center of regional services | Continuous |

X3 (dist_wtr str.) | Distance to water streams | Continuous |

X4 (dist_M.Agg.) | Distance to Main Agglomeration | Continuous |

X5 (dist_Indust._Ar) | Distance to Industrial Areas | Continuous |

X6 (dist_Urb_centrs) | Distance to nearest urban center | Continuous |

X7 (Pop._Density) | Population density | Continuous |

X8 (Nmbr_urb_cells3*3) | Number of urban cells within a 3 × 3 cell window | Continuous |

Step | −2 Log(Likelihood) | Cox and Snell R^{2} | Nagelkerke R^{2} |
---|---|---|---|

1 | 1744.354 | 0.76 | 0.90 |

Model | Collinearity Statistics | |
---|---|---|

Tolerance | VIF | |

X1 (dist_Rd) | 0.971 | 1.030 |

X2 (dist_centrs serv.) | 0.620 | 1.613 |

X3 (dist_wtr str.) | 0.908 | 1.101 |

X4 (dist_M.Agg.) | 0.572 | 1.748 |

X5 (dist_Indust._Ar) | 0.759 | 1.318 |

X6 (dist_Urb_centrs) | 0.905 | 1.010 |

X7 (Pop._Density) | 0.933 | 1.072 |

X8 (Nmbr_urb_cells3*3) | 0.978 | 1.023 |

Variable | Coefficient | Standard Error | Sig. | Odds Ratio ^{i} |
---|---|---|---|---|

X1 (dist_Rd) | −0.114 | 0.190 | 0.431 | 0.861 |

X2 (dist_centrs serv.) | −0.000 | 0.000 | 0.129 | 1.000 |

X3 (dist_wtr str.) | −0.000 | 0.000 | 0.281 | 1.000 |

X4 (dist_M.Agg.) | −0.000 | 0.000 | 0.000 | 1.000 |

X5 (dist_Indust._Ar) | −0.000 | 0.000 | 0.000 | 1.000 |

X6 (dist_Urb_centrs) | −0.092 | 0.130 | 0.065 | 1.955 |

X7 (Pop._Density) | 0.540 | 0.000 | 0.851 | 0.110 |

X8 (Nmbr_urb_cells3*3) | 0.096 | 0.035 | 0.007 | 1.909 |

^{i}Odds ratio meaning the ratio of the probability of success to the probability of failure for the variable, which represents the effect of each variable in the urban expansion process.

Reality (Reference Image) | |||
---|---|---|---|

Urban Expansion (1) | No Urban Expansion (0) | ||

Predicted Urban Expansion | Urban Expansion (1) | A (true positive) | B (false positive) |

No Urban Expansion (0) | C (false negative) | D (true negative) |

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**MDPI and ACS Style**

Salem, M.; Tsurusaki, N.; Divigalpitiya, P.
Analyzing the Driving Factors Causing Urban Expansion in the Peri-Urban Areas Using Logistic Regression: A Case Study of the Greater Cairo Region. *Infrastructures* **2019**, *4*, 4.
https://doi.org/10.3390/infrastructures4010004

**AMA Style**

Salem M, Tsurusaki N, Divigalpitiya P.
Analyzing the Driving Factors Causing Urban Expansion in the Peri-Urban Areas Using Logistic Regression: A Case Study of the Greater Cairo Region. *Infrastructures*. 2019; 4(1):4.
https://doi.org/10.3390/infrastructures4010004

**Chicago/Turabian Style**

Salem, Muhammad, Naoki Tsurusaki, and Prasanna Divigalpitiya.
2019. "Analyzing the Driving Factors Causing Urban Expansion in the Peri-Urban Areas Using Logistic Regression: A Case Study of the Greater Cairo Region" *Infrastructures* 4, no. 1: 4.
https://doi.org/10.3390/infrastructures4010004