# Landslide Susceptibility Mapping for the Muchuan County (China): A Comparison Between Bivariate Statistical Models (WoE, EBF, and IoE) and Their Ensembles with Logistic Regression

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geological and Geomorphological Setting

^{2}. The attitude of the study area ranges from 290 to 1866 m above the sea level. The annual rainfall is 1332 mm and it mainly concentrate from June to September. Geologically, the study area located in the Muchuan–Mabian arcuate fold belt of southwest of Yangtze para-platform where folds are developed more than faults. The study area is covered by various types of lithological units such as mudstone, sandstone, siltstone, and coal measure strata (Table 1).

## 3. Materials and Methods

#### 3.1. Landslide Conditioning Factors

#### 3.2. Preparation of Training and Validation Datasets

#### 3.3. Weight of Evidence

_{i}is the weight contrast of ${W}_{i}^{+}$ and ${W}_{i}^{-}$.

#### 3.4. Evidential Belief Function

_{i}is the degree of belief of ith conditioning factor. Dis

_{i}is the degree of disbelief of ith factor. Similarly, Unc

_{i}means the degree of uncertainty of ith factor. Pls shows the upper limits of probability. Oppositely, Dis shows the lower limits of probability.

#### 3.5. Index of Entropy

_{ij}is the probability density of class i of factor j. H

_{jmax}and H

_{j}are the entropy values of factor j. S

_{j}is the amount of classes factor j. I

_{j}is the information coefficient factor j. W

_{j}is the weight for the parameter as a whole.

#### 3.6. Logistic Regression

_{i}(i = 1,2,3,…,n) is the coefficient, and x

_{i}(i = 1,2,3,…,n) is the independent variable.

## 4. Results and Analysis

#### 4.1. Multicollinearity Analysis

_{i}is the negative correlation coefficient of the ith independent variable that makes regression analysis on other independent variables.

#### 4.2. Generating Landslide Susceptibility Maps

#### 4.3. Model Validation and Comparison

## 5. Discussions

^{+}and W

^{-}produced by WoE model are a pair of weight parameters that named positive weight and negative weight. A positive weight means it may promote the occurrence of landslide, while negative weight means the opposite. The parameter of Bel generated by EBF model can be regard as the symbol that indicates the relationship between landslide and landslide conditioning factor. The parameter of W

_{j}generated by IoE model represents the importance of each factor. It can be seen from the Table 3 that slope angle has the highest weight (0.229) which means it is the most important factor, followed by land use (0.207), soil (0.194), altitude (0.190), lithology (0.141), TWI (0.08), distance to roads (0.062), slope aspect (0.051), NDVI (0.037), distance to rivers (0.022), plan curvature (0.009), and profile curvature (0.004). In addition, it is obvious to find that Bel and W

^{+}show the same results.

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Landslide conditioning factors: (

**a**) Altitude; (

**b**) plan curvature; (

**c**) profile curvature; (

**d**) slope angle; (

**e**) slope aspect; (

**f**) distance to roads; (

**g**) distance to rivers; (

**h**) topographic wetness index (TWI); (

**i**) normalized different vegetation index (NDVI); (

**j**) land use; (

**k**) soil; (

**l**) lithology.

**Figure 3.**Landslide susceptibility maps: (

**a**) EBF model; (

**b**) WoE model; (

**c**) IoE model; (

**d**) EBF-LR model; (

**e**) WoE-LR model; (

**f**) IoE-LR model.

Group | Lithology | Geologic Ages |
---|---|---|

A | Brick red massive allochemical rock, sandstone sandwiched mudstone and siltstone Brick red thin-thick layer silty fine-grained arkose, mudstone Brick red massive allochemical rock, sandstone sandwiched mudstone and siltstone | Cretaceous |

B | Grayish-purple arkose, siltstone sandwiched mud shale and coquina Bright red mudstone, sandwiched with the same color sandstone and siltstone Grayish-purple arkose, siltstone sandwiched mud shale and coquina | Jurassic |

C | Yellow-gray feldspar-quartz sandstone interbedded with purple-red mudstone | Jurassic |

D | Magenta mudstone, quartz sandstone, and siltstone sandwiched biosparite and marl | Jurassic |

E | Gray sandstone, siltstone, and mudstone Grayish-yellow debris-feldspar, siltstone, mudstone, and coal | Triassic |

F | Yellow-gray medium-thick dolomite sandwiched limestone, gypsum salt, and salt-soluble breccia | Triassic |

G | Limestone, dolomite, and shale | Triassic |

H | Yellow-green siltstone sandwiched with mudstone and coal | Permian |

I | The upper part is limestone and dolomite and the lower part is shale sandwiched siltstone | Permian |

J | Grayish-green dense amygdaloidal basalt sandwiched picrite, tuff sand mudstone, shed coal and siliceous rock | Permian |

**Table 2.**Analysis. WOE: weight of evidence; EBF: evidence belief function; IoE: index of entropy; TOL: tolerance; VIF: variance inflation factor.

Number | Factors | WOE | EBF | IoE | |||
---|---|---|---|---|---|---|---|

TOL | VIF | TOL | VIF | TOL | VIF | ||

1 | Slope aspect | 0.921 | 1.086 | 0.922 | 1.085 | 0.924 | 1.083 |

2 | Altitude | 0.835 | 1.197 | 0.659 | 1.517 | 0.659 | 1.517 |

3 | Land use | 0.861 | 1.162 | 0.830 | 1.206 | 0.828 | 1.208 |

4 | Lithology | 0.691 | 1.447 | 0.577 | 1.733 | 0.577 | 1.732 |

5 | NDVI | 0.980 | 1.020 | 0.953 | 1.050 | 0.954 | 1.048 |

6 | Plan curvature | 0.898 | 1.114 | 0.894 | 1.118 | 0.905 | 1.105 |

7 | Profile curvature | 0.912 | 1.097 | 0.896 | 1.116 | 0.929 | 1.076 |

8 | Distance to rivers | 0.981 | 1.020 | 0.969 | 1.032 | 0.973 | 1.028 |

9 | Distance to roads | 0.764 | 1.309 | 0.706 | 1.416 | 0.707 | 1.414 |

10 | Slope angle | 0.869 | 1.151 | 0.802 | 1.247 | 0.818 | 1.222 |

11 | Soil | 0.798 | 1.253 | 0.717 | 1.394 | 0.723 | 1.384 |

12 | TWI | 0.916 | 1.091 | 0.860 | 1.163 | 0.863 | 1.158 |

**Table 3.**Between landslides and conditioning factors using WoE, EBF, and IoE models. Bel: belief; Dis: the degree of disbelief: Unc: the degree of uncertainly; Pls: the degree of plausibility.

Factors | Class | No. of Landslide | No. of Pixels in Domain | W^{+} | W^{-} | C | Bel | Dis | Unc | Pls | W_{j} |
---|---|---|---|---|---|---|---|---|---|---|---|

Altitude (m) | 290–500 | 42 | 727325 | 0.035 | −0.009 | 0.044 | 0.270 | 0.125 | 0.605 | 0.875 | 0.190 |

500–700 | 110 | 1330115 | 0.394 | −0.352 | 0.746 | 0.387 | 0.089 | 0.524 | 0.911 | ||

700–900 | 38 | 640772 | 0.061 | −0.014 | 0.076 | 0.277 | 0.125 | 0.598 | 0.875 | ||

900–1,100 | 5 | 354758 | −1.375 | 0.081 | −1.456 | 0.066 | 0.137 | 0.797 | 0.863 | ||

1,100–1,300 | 0 | 246634 | 0.000 | 0.073 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

1,300–1,500 | 0 | 144601 | 0.000 | 0.042 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

1,500–1,700 | 0 | 50150 | 0.000 | 0.014 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

1,700–1,866 | 0 | 2344 | 0.000 | 0.001 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Plan curvature | −26.54–−3.17 | 6 | 125417 | −0.153 | 0.005 | −0.159 | 0.165 | 0.199 | 0.636 | 0.801 | 0.009 |

−3.17–−1.10 | 39 | 592578 | 0.166 | −0.037 | 0.203 | 0.228 | 0.191 | 0.582 | 0.809 | ||

−1.10–0.56 | 75 | 1660025 | −0.211 | 0.158 | −0.369 | 0.156 | 0.232 | 0.612 | 0.768 | ||

0.56–2.62 | 62 | 909888 | 0.200 | −0.081 | 0.282 | 0.236 | 0.182 | 0.582 | 0.818 | ||

2.62–26.21 | 13 | 208791 | 0.110 | −0.007 | 0.118 | 0.215 | 0.196 | 0.588 | 0.804 | ||

Profile curvature | −34.72–−4.17 | 9 | 170680 | −0.056 | 0.003 | −0.059 | 0.199 | 0.201 | 0.600 | 0.799 | 0.004 |

−4.17–−1.39 | 43 | 777064 | −0.008 | 0.002 | −0.010 | 0.209 | 0.201 | 0.590 | 0.799 | ||

−1.39–0.88 | 76 | 1299477 | 0.048 | −0.029 | 0.077 | 0.221 | 0.195 | 0.585 | 0.805 | ||

0.88–3.66 | 57 | 1012294 | 0.010 | −0.004 | 0.014 | 0.212 | 0.200 | 0.588 | 0.800 | ||

3.66–29.66 | 10 | 237184 | −0.280 | 0.018 | −0.297 | 0.159 | 0.204 | 0.637 | 0.796 | ||

Slope angle (°) | 0–10 | 0 | 738575 | 0.000 | 0.237 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.229 |

10-20 | 84 | 1233686 | 0.200 | −0.128 | 0.328 | 0.168 | 0.110 | 0.722 | 0.890 | ||

20-30 | 63 | 836797 | 0.300 | −0.117 | 0.417 | 0.185 | 0.111 | 0.703 | 0.889 | ||

30-40 | 29 | 433617 | 0.182 | −0.029 | 0.210 | 0.165 | 0.122 | 0.714 | 0.878 | ||

40-50 | 11 | 186715 | 0.055 | −0.003 | 0.058 | 0.145 | 0.125 | 0.730 | 0.875 | ||

50-60 | 8 | 58411 | 0.899 | −0.025 | 0.924 | 0.337 | 0.122 | 0.541 | 0.878 | ||

60-70 | 0 | 8690 | 0.000 | 0.002 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

70–77.14 | 0 | 208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Slope aspect | Flat | 0 | 1192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.051 |

North | 28 | 508458 | −0.013 | 0.002 | −0.015 | 0.124 | 0.111 | 0.764 | 0.889 | ||

Northeast | 33 | 489376 | 0.190 | −0.035 | 0.225 | 0.152 | 0.107 | 0.741 | 0.893 | ||

East | 26 | 507513 | −0.085 | 0.014 | −0.099 | 0.115 | 0.113 | 0.772 | 0.887 | ||

Southeast | 20 | 402282 | −0.115 | 0.014 | −0.129 | 0.112 | 0.113 | 0.775 | 0.887 | ||

South | 24 | 393289 | 0.090 | −0.012 | 0.102 | 0.138 | 0.110 | 0.753 | 0.890 | ||

Southwest | 16 | 351360 | −0.203 | 0.020 | −0.223 | 0.103 | 0.113 | 0.784 | 0.887 | ||

West | 20 | 414052 | −0.144 | 0.018 | −0.162 | 0.109 | 0.113 | 0.778 | 0.887 | ||

Northwest | 28 | 429177 | 0.157 | −0.024 | 0.181 | 0.147 | 0.108 | 0.744 | 0.892 | ||

Distance to roads (m) | 0–500 | 69 | 827671 | 0.402 | −0.167 | 0.569 | 0.271 | 0.167 | 0.562 | 0.833 | 0.062 |

500–1,000 | 48 | 611007 | 0.343 | −0.091 | 0.433 | 0.255 | 0.180 | 0.564 | 0.820 | ||

1,000–1,500 | 36 | 493759 | 0.268 | −0.052 | 0.320 | 0.237 | 0.188 | 0.575 | 0.812 | ||

1,500–2,000 | 20 | 366762 | −0.022 | 0.003 | −0.025 | 0.177 | 0.198 | 0.625 | 0.802 | ||

> 2,000 | 22 | 1197500 | −1.110 | 0.300 | −1.410 | 0.060 | 0.267 | 0.674 | 0.733 | ||

Distance to rivers (m) | 0–200 | 57 | 1032619 | −0.010 | 0.004 | −0.014 | 0.208 | 0.201 | 0.591 | 0.799 | 0.022 |

200–400 | 69 | 844083 | 0.382 | −0.160 | 0.543 | 0.308 | 0.171 | 0.521 | 0.829 | ||

400–600 | 29 | 700716 | −0.298 | 0.063 | −0.361 | 0.156 | 0.213 | 0.630 | 0.787 | ||

600–800 | 22 | 496233 | −0.229 | 0.033 | −0.263 | 0.167 | 0.207 | 0.626 | 0.793 | ||

> 800 | 18 | 423048 | −0.271 | 0.032 | −0.303 | 0.160 | 0.207 | 0.633 | 0.793 | ||

TWI | 0.35–1.63 | 104 | 1318729 | 0.347 | −0.289 | 0.635 | 0.401 | 0.152 | 0.447 | 0.848 | 0.080 |

1.63–2.41 | 66 | 1221212 | −0.031 | 0.016 | −0.048 | 0.275 | 0.206 | 0.519 | 0.794 | ||

2.41–3.36 | 20 | 653109 | −0.599 | 0.099 | −0.698 | 0.156 | 0.224 | 0.621 | 0.776 | ||

3.36–4.81 | 4 | 243618 | −1.223 | 0.051 | −1.274 | 0.083 | 0.213 | 0.703 | 0.787 | ||

4.81–14.58 | 1 | 60031 | −1.208 | 0.012 | −1.221 | 0.085 | 0.205 | 0.710 | 0.795 | ||

NDVI | -0.13–0.13 | 2 | 110968 | −1.130 | 0.022 | −1.151 | 0.077 | 0.206 | 0.717 | 0.794 | 0.037 |

0.13–0.24 | 15 | 350282 | −0.264 | 0.026 | −0.290 | 0.184 | 0.206 | 0.610 | 0.794 | ||

0.24–0.30 | 41 | 864378 | −0.162 | 0.048 | −0.210 | 0.204 | 0.211 | 0.585 | 0.789 | ||

0.30–0.37 | 87 | 1306577 | 0.177 | −0.123 | 0.300 | 0.286 | 0.178 | 0.536 | 0.822 | ||

0.37–0.58 | 50 | 864494 | 0.036 | −0.012 | 0.049 | 0.249 | 0.199 | 0.553 | 0.801 | ||

Land use | Farm land | 140 | 1951094 | 0.252 | −0.449 | 0.701 | 0.421 | 0.108 | 0.471 | 0.892 | 0.207 |

Forest land | 54 | 1459960 | −0.411 | 0.216 | −0.627 | 0.217 | 0.210 | 0.572 | 0.790 | ||

Grass land | 0 | 42187 | 0.000 | 0.012 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Water | 0 | 25016 | 0.000 | 0.007 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Residential areas | 1 | 16239 | 0.099 | 0.000 | 0.100 | 0.362 | 0.169 | 0.469 | 0.831 | ||

Bare land | 0 | 2203 | 0.000 | 0.001 | 0.000 | 0.000 | 0.170 | 0.830 | 0.830 | ||

Soil | Type 1 | 31 | 440582 | 0.232 | −0.038 | 0.271 | 0.188 | 0.096 | 0.716 | 0.904 | 0.194 |

Type 2 | 12 | 208103 | 0.033 | −0.002 | 0.036 | 0.154 | 0.099 | 0.747 | 0.901 | ||

Type 3 | 4 | 96481 | −0.296 | 0.007 | −0.304 | 0.111 | 0.100 | 0.789 | 0.900 | ||

Type 4 | 9 | 147720 | 0.088 | −0.004 | 0.093 | 0.163 | 0.099 | 0.738 | 0.901 | ||

Type 5 | 1 | 41304 | −0.834 | 0.007 | −0.841 | 0.065 | 0.100 | 0.835 | 0.900 | ||

Type 6 | 0 | 3783 | 0.000 | 0.001 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Type 7 | 0 | 27855 | 0.000 | 0.008 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Type 8 | 54 | 1441599 | −0.398 | 0.207 | −0.605 | 0.100 | 0.123 | 0.777 | 0.877 | ||

Type 9 | 0 | 68835 | 0.000 | 0.020 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

Type 10 | 84 | 1020437 | 0.389 | −0.218 | 0.608 | 0.220 | 0.080 | 0.700 | 0.920 | ||

Lithology | A | 26 | 396261 | 0.163 | −0.023 | 0.185 | 0.159 | 0.098 | 0.743 | 0.902 | 0.141 |

B | 43 | 424981 | 0.596 | −0.120 | 0.715 | 0.245 | 0.089 | 0.666 | 0.911 | ||

C | 59 | 765703 | 0.323 | −0.113 | 0.437 | 0.186 | 0.089 | 0.724 | 0.911 | ||

D | 17 | 252004 | 0.190 | −0.016 | 0.207 | 0.163 | 0.099 | 0.738 | 0.901 | ||

E | 38 | 686719 | −0.008 | 0.002 | −0.010 | 0.134 | 0.100 | 0.766 | 0.900 | ||

F | 1 | 267436 | −2.702 | 0.074 | −2.777 | 0.009 | 0.108 | 0.883 | 0.892 | ||

G | 10 | 467170 | −0.958 | 0.091 | −1.048 | 0.052 | 0.110 | 0.839 | 0.890 | ||

H | 0 | 97599 | 0.000 | 0.028 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | ||

I | 1 | 46018 | −0.942 | 0.008 | −0.951 | 0.053 | 0.101 | 0.846 | 0.899 | ||

J | 0 | 92808 | 0.000 | 0.027 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 |

Landslide Conditioning Factors | WoE-LR | EBF-LR | IoE-LR |
---|---|---|---|

Slope aspect | 0.780 | 6.477 | 15.569 |

Altitude | 1.016 | 8.123 | 11.110 |

Land use | 0.271 | 1.560 | 2.973 |

Lithology | 0.484 | 3.951 | 3.567 |

NDVI | 0.720 | 2.710 | 17.231 |

Plan curvature | 0.628 | 4.169 | 82.950 |

Profile curvature | 2.878 | 22.826 | 1239.456 |

Distance to rivers | 1.045 | 5.298 | 52.206 |

Distance to roads | 0.467 | 2.634 | 7.665 |

Slope angle | 3.995 | 20.993 | 12.357 |

Soil | 0.204 | 2.520 | 2.100 |

TWI | 0.774 | 3.204 | 11.377 |

Slope aspect | −1.856 | −17.300 | −17.304 |

Model | M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 |
---|---|---|---|---|---|---|---|---|

Z | −12.651 | −12.968 | −14.119 | −15.345 | −13.752 | −15.018 | −15.077 | −16.006 |

Asymp. Sig. (2-tailed) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Model | M9 | M10 | M11 | M12 | M13 | M14 | M15 | |

Z | −14.900 | −10.849 | −12.203 | −10.313 | −2.577 | −4.809 | −3.680 | |

Asymp. Sig. (2-tailed) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Variables | AUC | SE | 95% CI |
---|---|---|---|

EBF model | 0.791 | 0.0226 | 0.747 to 0.830 |

WoE model | 0.753 | 0.0243 | 0.707 to 0.795 |

IoE model | 0.778 | 0.0233 | 0.734 to 0.819 |

EBF-LR model | 0.826 | 0.0207 | 0.784 to 0.862 |

WoE-LR model | 0.792 | 0.0226 | 0.748 to 0.831 |

IoE-LR model | 0.825 | 0.0208 | 0.784 to 0.861 |

© 2019 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**

Li, R.; Wang, N.
Landslide Susceptibility Mapping for the Muchuan County (China): A Comparison Between Bivariate Statistical Models (WoE, EBF, and IoE) and Their Ensembles with Logistic Regression. *Symmetry* **2019**, *11*, 762.
https://doi.org/10.3390/sym11060762

**AMA Style**

Li R, Wang N.
Landslide Susceptibility Mapping for the Muchuan County (China): A Comparison Between Bivariate Statistical Models (WoE, EBF, and IoE) and Their Ensembles with Logistic Regression. *Symmetry*. 2019; 11(6):762.
https://doi.org/10.3390/sym11060762

**Chicago/Turabian Style**

Li, Renwei, and Nianqin Wang.
2019. "Landslide Susceptibility Mapping for the Muchuan County (China): A Comparison Between Bivariate Statistical Models (WoE, EBF, and IoE) and Their Ensembles with Logistic Regression" *Symmetry* 11, no. 6: 762.
https://doi.org/10.3390/sym11060762