# Global and Local Modeling of Land Use Change in the Border Cities of Laredo, Texas, USA and Nuevo Laredo, Tamaulipas, Mexico: A Comparative Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Collection

## 3. Methods

#### 3.1. Data Sampling and Multicollinearity Detection

#### 3.2. Global Logistic Regression

#### 3.3. Logistic GWR

_{i}) = log

_{e}(P

_{i}|1 − P

_{i}) = β

_{0}+ β

_{1}x

_{1}

_{i}+ β

_{2}x

_{2}

_{i}+ … + β

_{m}χ

_{mi}+ ε

_{i}

## 4. Results and Discussion

#### 4.1. Logistic Regression Analysis

#### 4.2. Diagnostics of Logistic GWR

#### 4.3. Results of Logistic GWR and Spatial Non-Stationarity Relationship

#### 4.4. Methodological Implications

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Spatial and temporal patterns of urban growth during 1985–2000 and 2000–2014, Laredo–Nuevo Laredo.

**Figure 3.**Site specific factors considered for urban growth: (

**a**) slope, (

**b**) elevation, and (

**c**) population density.

**Figure 4.**Spatial distribution of transportation network and industrial sites used as proximity factors.

**Figure 6.**The location of the systematic random sample points for the time periods 1985–2000 and 2000–2014, respectively.

**Figure 7.**Logistic GWR results: estimated coefficient (

**a**) and T-statistic surfaces (

**b**): slope, 2000–2014.

**Figure 8.**Logistic GWR results of the estimated coefficient: distance to the airports (

**a**) and distance to the industrial sites (

**b**), 2000–2014.

**Figure 9.**Logistic GWR results of the estimated coefficient (

**a**,

**c**) and T-statistic surfaces: density of existing urban clusters (

**b**,

**d**), 1985–2000 and 2000–2014.

**Figure 10.**Logistic GWR results: estimated coefficient of density of the highway and major roads, 1985–2000 (

**a**) and 2000–2014 (

**b**).

Description | Units | Date | Nuevo Laredo | Laredo | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Standard Deviation | Minimum | Maximum | Mean | Standard Deviation | Minimum | Maximum | ||||

Site specific variables | |||||||||||

Elevation | Elevation of one specific pixel of 30 m*30 m | Meter | 1985–2000 | 136.07 | 15.46 | 0.00 | 161.00 | 145.00 | 23.23 | 0.00 | 214.10 |

2000–2014 | 136.42 | 15.73 | 0.00 | 161.00 | 146.34 | 23.05 | 0.00 | 214.10 | |||

Slope | The tangent of angle of surface to horizontal level | Degree | 1985–2000 | 2.14 | 1.79 | 0.00 | 21.00 | 3.28 | 2.85 | 0.00 | 27.00 |

2000–2014 | 2.12 | 1.66 | 0.00 | 15.00 | 3.36 | 2.90 | 0.00 | 35.00 | |||

Population_Den | Population density | 100 per km^{2} | 1985–2000 | 44.23 | 2.84 | 0.00 | 203.94 | 6.45 | 10.33 | 0.00 | 47.28 |

X | The x coordinate of the sampling points | Meter | 1985–2000 | 446.13 | 2.16 | 439.83 | 452.64 | 451.37 | 6.26 | 426.18 | 467.13 |

2000–2015 | 445.90 | 2.19 | 439.83 | 452.64 | 451.67 | 0.15 | 426.18 | 467.13 | |||

Y | The y coordinate of the sampling points | Meter | 1985–2000 | 3037.30 | 5.17 | 3027.63 | 3047.16 | 3047.85 | 9.60 | 3027.21 | 3069.00 |

2000–2014 | 3037.08 | 5.29 | 3027.63 | 3047.16 | 3047.89 | 0.23 | 3027.21 | 3069.00 | |||

Proximity variables | |||||||||||

Dis_Airports | Euclidean distance to airports for corresponding city | Meter | 1985–2000 | 4586.30 | 2483.27 | 0.00 | 10,375.80 | 8360.25 | 6545.40 | 30.00 | 34,463.10 |

2000–2014 | 4494.75 | 2568.53 | 0.00 | 10,375.80 | 8344.00 | 6837.42 | 30.00 | 34,463.10 | |||

Dis_RailWay | Euclidean distance Rio Grande River | Meter | 1985–2000 | 3629.59 | 2505.45 | 0.00 | 10,276.20 | 4677.72 | 5469.29 | 0.00 | 28,156.50 |

2000–2014 | 3827.82 | 2515.42 | 0.00 | 10,276.20 | 7569.95 | 124.65 | 123.69 | 28,308.40 | |||

Dis_River | Euclidean distance to railway for corresponding city | Meter | 1985–2000 | 3862.33 | 1986.91 | 0.00 | 8136.20 | 3841.45 | 3153.67 | 0.00 | 14,466.00 |

2000–2014 | 4078.45 | 1964.62 | 0.00 | 8136.20 | 58.53 | 0.00 | 0.00 | 10,001.50 | |||

Dis_Bridges | The Euclidean distance to the four international bridges | Meter | 1985–2000 | 7477.92 | 3191.26 | 234.31 | 15,221.50 | 11,197.01 | 6401.62 | 189.74 | 36,039.00 |

2000–2014 | 7830.80 | 3177.56 | 152.97 | 15,221.50 | 11,397.82 | 10,488.55 | 768.38 | 36,039.00 | |||

Dis_Industries | Euclidean distance to manufacturing plants for corresponding city | Meter | 1985–2000 | 2606.09 | 1850.80 | 0.00 | 7804.67 | 4745.85 | 5330.43 | 0.00 | 28,422.70 |

2000–2014 | 2700.33 | 1853.14 | 0.00 | 7804.67 | 2919.22 | 1738.06 | 0.00 | 14,704.90 | |||

Dis_HigMajWay | Euclidean distance to highway and major roads for corresponding city | Meter | 1985–2000 | 846.15 | 651.70 | 0.00 | 4412.35 | 734.07 | 713.07 | 0.00 | 4804.59 |

2000–2014 | 842.58 | 701.68 | 1.16 | 4105.09 | 499.56 | 331.34 | 0.00 | 3569.96 | |||

Dis_UrbanClust | Euclidean distance to urban clusters for corresponding city | Meter | 1985–2000 | 429.63 | 484.97 | 0.00 | 3519.73 | 561.60 | 640.98 | 0.00 | 4639.05 |

2000–2014 | 146.21 | 154.20 | 30.00 | 953.42 | 139.58 | 3.52 | 30.00 | 1073.31 | |||

Density variables | |||||||||||

Den_HigMajWay | The number of pixels of highway and major roads within 5*5 neighbors | N/A | 1985–2000 | 0.36 | 1.47 | 0.00 | 12.00 | 0.86 | 2.51 | 0.00 | 18.00 |

2000–2014 | 0.43 | 1.60 | 0.00 | 12.00 | 0.75 | 0.06 | 0.00 | 22.00 | |||

De_Industries | The number of pixels of industrial pixels within 5*5 neighbors | N/A | 1985–2000 | 0.24 | 2.01 | 0.00 | 25.00 | 0.35 | 2.59 | 0.00 | 25.00 |

2000–2014 | 0.49 | 3.07 | 0.00 | 25.00 | 1.74 | 0.00 | 0.00 | 25.00 | |||

Den_UrbanClust150 | The number of pixels of built-up land within 5*5 neighbors | N/A | 1985–2000 | 1.06 | 3.17 | 0.00 | 22.00 | 1.02 | 2.98 | 0.00 | 25.00 |

2000–2014 | 2.98 | 4.84 | 0.00 | 22.00 | 2.91 | 0.12 | 0.00 | 24.00 |

**Table 2.**Global logistic regression results for the probability of conversion from non-urban to urban.

Independent Variables | 1985–2000 | 2000–2014 | ||||
---|---|---|---|---|---|---|

β | S.E. | Odds Ratio | β | S.E. | Odds Ratio | |

Site specific variables | ||||||

Elevation | 0.001 | 0.003 | 1.001 | --- | --- | --- |

Slope | −0.101 | 0.026 | 0.904 | −0.041 ^{(*)} | 0.024 | 0.96 |

Proximity variables | ||||||

Dis_Airports | 0.000 ^{(***)} | 0.000 | 1.000 | −0.092 ^{(***)} | 0.014 | 0.913 |

Dis_RailWay | 0.000 ^{(***)} | 0.000 | 1.000 | --- | --- | --- |

Dis_River | --- | --- | --- | 0.000 | 0.000 | 1.000 |

Dis_Industries | --- | --- | --- | −0.067 ^{(*)} | 0.029 | 0.936 |

Dis_HigMajWay | −0.001 ^{(***)} | 0.000 | 0.999 | --- | --- | --- |

Density variables | ||||||

Den_HigMajWay | 0.090 | 0.024 | 1.094 | 0.075 ^{(***)} | 0.019 | 1.078 |

Den_Industries | 0.030 ^{(***)} | 0.019 | 1.031 | 0.046 ^{(***)} | 0.01 | 1.047 |

Den_UrbanClust150 | 0.172 ^{(**)} | 0.021 | 1.187 | 0.132 ^{(***)} | 0.011 | 1.142 |

Sample size | 2556 | 2486 | ||||

−2 Log likelihood | 2433.055 | 2369.868 | ||||

Cox and Snell | 0.197 | 0.162 | ||||

Nagelkerke | 0.286 | 0.239 | ||||

PCP | 77.5 | 78 |

^{(*)}: significance at 0.05 level;

^{(**)}: significance at 0.01 level;

^{(***)}: significance at 0.001 level. PCP: the percentage correctly predicted with cut value 0.5. ---: the variable was not included in regression analysis due to multicollinearity.

**Table 3.**Diagnostic information of logistic geographically weighted regression (GWR) during 2000–2014.

Logistic GWR Result | ||||
---|---|---|---|---|

β | Lower Quartile β | Median β | Upper Quartile β | |

Slope | −0.041 | −0.051 | −0.035 | −0.027 |

Dis_Airports | −0.092 | −0.135 | −0.079 | −0.037 |

Dis_River | 0.000 | 0.000 | 0.000 | 0.000 |

Dis_Industries | −0.067 | −0.114 | −0.095 | −0.081 |

Den_UrbanClust150 | 0.132 | 0.109 | 0.131 | 0.148 |

Den_Industries | 0.046 | 0.012 | 0.028 | 0.045 |

Den_HigMajWay | 0.075 | 0.052 | 0.060 | 0.066 |

Constant | −0.883 | −1.020 | −0.800 | −0.552 |

Comparison of logistic GWR and global logistic regression | ||||

Global logistic regression | Logistic GWR | |||

−2 Log likelihood | 2369.868 | 2265.202 | ||

Global AIC | 2385.868 | 2307.967 | ||

PCP | 78.0 | 78.6 |

© 2020 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**

Zhao, C.; Jensen, J.L.R.; Weaver, R.
Global and Local Modeling of Land Use Change in the Border Cities of Laredo, Texas, USA and Nuevo Laredo, Tamaulipas, Mexico: A Comparative Analysis. *Land* **2020**, *9*, 347.
https://doi.org/10.3390/land9100347

**AMA Style**

Zhao C, Jensen JLR, Weaver R.
Global and Local Modeling of Land Use Change in the Border Cities of Laredo, Texas, USA and Nuevo Laredo, Tamaulipas, Mexico: A Comparative Analysis. *Land*. 2020; 9(10):347.
https://doi.org/10.3390/land9100347

**Chicago/Turabian Style**

Zhao, Chunhong, Jennifer L.R. Jensen, and Russell Weaver.
2020. "Global and Local Modeling of Land Use Change in the Border Cities of Laredo, Texas, USA and Nuevo Laredo, Tamaulipas, Mexico: A Comparative Analysis" *Land* 9, no. 10: 347.
https://doi.org/10.3390/land9100347