# Examining the Driving Factors of SOM Using a Multi-Scale GWR Model Augmented by Geo-Detector and GWPCA Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Sources and Index Selection

#### 2.3. Methods

#### 2.3.1. Geo-Detector

_{h}and N are the number of samples in stratum h and Shaanxi Province, respectively, ${\sigma}_{h}^{2}$ is the variance of SOM in stratum h, and ${\sigma}^{2}$ is the variance of SOM in Shaanxi Province. For q ∈ [0, 1], a larger q value indicates a higher similarity for the spatial distribution between the driving factor and SOM and a stronger driving force of the factor. Geo-detector analysis was performed with the GD R package [40].

#### 2.3.2. Geographically Weighted Principal Component Analysis (GWPCA)

_{i}, v

_{i}). The GW eigenvalues and GW eigenvectors are provided by the decomposition of the GW variance-covariance matrix that is calculated as follows:

_{score}) was calculated using the following formula:

_{score}is the inputs for GWPCA-GWR and GWPCA-MGWR.

_{i}) ≠ s (x

_{i}+ h)] is an indicator function defined as follows:

#### 2.3.3. Geographically Weighted Regression and Multi-Scale Geographically Weighted Regression (GWR and MGWR)

_{GWPCA-GWR}(u

_{i}, v

_{i}) and GWPC

_{scorej}are dependent and independent variables respectively, β

_{0}(u

_{i}, v

_{i}), β

_{j}(u

_{i}, v

_{i}) and ε(i) are the intercept, the regression coefficient of GWPC

_{scorej}and the residual at location i, respectively; GW regression coefficient adopts weighted least square model:

_{i}, v

_{i}) is a diagonal matrix geographic weight that can be generated using the bi-square kernel function as the GWPCA model.

_{bwj}of the MGWR is based on the local regression and bandwidth variation across parameter surfaces. The sum and bandwidth attributes of the MGWR are the same as those of the GWR. The most commonly used quadratic kernel function and AICc criterion were utilized. The iterative convergence criteria used the score of change (SOC

_{f}): change in the GWR smoother:

## 3. Results and Discussion

#### 3.1. Global Statistics

^{−1}, thus signaling that SOM content was slightly enriched during the past decades compared with 10.7 g·kg

^{−1}in the 1980s [2]. Additionally, the global variation coefficient of SOM content was 49.65%, thus indicating moderate variation intensity.

#### 3.2. Local Statistics

^{−1}) were higher than the background value for Shaanxi Province in the Daba Mountains (DBM), Han River Basin (HRB), and central and southern Qinling Mountains (QLM) where double-cropping systems have been widely emphasized [48]. GW means (<10 g·kg

^{−1}) for the Blown Sand Region (BSR) were lower than the global level. Among these, the lowest GW mean SOM content was less than 8 g·kg

^{−1}, as insufficient precipitation and rapid decomposition resulted in the accumulation of SOM in northern Shaanxi [33,49].

#### 3.3. Geographical Detector

#### 3.4. Geographically Weighted Principal Analysis

#### 3.5. Modeling Comparison

^{2}values (Table 2), thus indicating that a large portion of the variation across SOM can be accounted for by the selected variables in this study. There appeared to be overfitting results with higher R

^{2}and lower AICc and RSS in GWR and MGWR, since the AICc were all too low, and a high local multicollinearity among the dependent variables was observed (Figure 5) [13]. Concurrently, considering their high MAE values, it is obvious the GWR and MGWR models cannot provide a goodness of fit. In contrast, GWPCA-MGWR exhibited the lowest MAE, although its R

^{2}was lower and the AICc and RSS were larger than those of the other models.

^{2}and RSS, the model excellence was ordered as GWR > MGWR > GWPCA > GWPCA-MGWR. GWR and GWPCA-GWR appear to be superior to MGWR and GWPCA-MGWR, respectively, in terms of goodness-of-fit, and this is primarily due to local multicollinearity [12]; For the regression error (MAE) and residual spatial heterogeneity, the model excellence was ordered as GWPCA-MGWR > GWPCA-GWR > MGWR > GWR. Consequently, evidence suggests that multi-collinearity may cause a problem with overfitting for GWR, MGWR, and be problematic for GWPCA-GWR modeling of SOM. GWPCA-MGWR was able to overcome these limitations and provide a more parsimonious yet richer goodness-of-fit model.

#### 3.6. Analysis of Coefficient Spatial Pattern

#### 3.7. Limitations of the Study

## 4. Conclusions

^{2}= 0.83) extracts spatial non-stationary structure information and is less prone to issues of local multicollinearity among auxiliary variables, and can effectively capture spatial scale non-stationary relationships between the target and independent variables. The results from GWPCA-MGWR exhibited the lowest prediction error (MAE = 0.001) and the strongest residual spatial heterogeneity, thus indicating that GWPCA-MGWR is capable of identifying dominant driving factors and providing robust modeling of multi-scale multivariate processes. (3) fourteen driving factors were identified as auxiliary variables using the geo-detectors. GWPCA fully extracts the spatial non-stationary relationships among the auxiliary variables. GWPCA-MGWR revealed that under the current bandwidth, soil nutrients and soil types played a role in SOM spatial variability, and this was followed by human activities and geomorphic types.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Maps of the PTV for GWPC1, GWPC2, GWPC3, and CPTV of the first three GWPCs. GWPC, geographically weighted principal component; PTV, percentages of total variation; CPTV, cumulative percentages of the total variation.

**Figure 4.**Maps of the winning variables (i.e., the variables with the highest loadings) in GWPC1, GWPC2, and GWPC3. a, Climate Factors; b, Soil Nutrient Factors; c, Soil Type Factors; d, Geomorphic Type Factors; e, Human Factors.

Variables | q-Value | VIF | Reference |
---|---|---|---|

STN | 0.74 *** | 3.30 | [53] |

County administrative division | 0.58 *** | 3.08 | [55] |

Annual sunshine hours | 0.42 *** | 15.56 | [56] |

Annual precipitation | 0.37 *** | 12.57 | [49,56] |

Annual mean temperature | 0.35 *** | 6.61 | [57] |

Soil Subtype | 0.34 *** | 13.57 | [6] |

Soil Type | 0.32 *** | 14.63 | [6] |

Geomorphic types | 0.27 *** | 2.04 | [9] |

Cropping system | 0.26 *** | 1.49 | [58,59] |

C/N ratio | 0.25 *** | 1.99 | [60] |

Total Agricultural Machinery Power | 0.23 *** | 2.58 | [37] |

Rate of Compound Fertilizer Application | 0.22 *** | 5.31 | [58] |

pH | 0.22 *** | 2.77 | [2] |

Rate of Fertilizer Application | 0.21 *** | 8.77 | [58] |

AICc | R^{2} | RSS | MAE | |
---|---|---|---|---|

GWR | −8978.85 | 0.97 | 28.81 | 0.09 |

MGWR | −8360.19 | 0.97 | 36.91 | 0.25 |

GWPCA-GWR | −56.67 | 0.87 | 189.51 | 0.04 |

GWPCA-MGWR | 405.87 | 0.83 | 205.79 | 0.001 |

^{2}, Adjusted R

^{2}. RSS, Residual sum of squares.

Model | Nugget | Sill | Nugget/Sill | Range (km) | |
---|---|---|---|---|---|

SOM | Gaussian | 0.08 | 0.91 | 8.84 | 835 |

GWR | Gaussian | 0.004 | 0.02 | 20.90 | 1093 |

MGWR | Gaussian | 0.01 | 0.02 | 59.81 | 980 |

GWPCA-GWR | Gaussian | 0.03 | 0.06 | 47.17 | 835 |

GWPCA-MGWR | Gaussian | 0.04 | 0.08 | 49.50 | 799 |

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**MDPI and ACS Style**

Wang, Q.; Jiang, D.; Gao, Y.; Zhang, Z.; Chang, Q.
Examining the Driving Factors of SOM Using a Multi-Scale GWR Model Augmented by Geo-Detector and GWPCA Analysis. *Agronomy* **2022**, *12*, 1697.
https://doi.org/10.3390/agronomy12071697

**AMA Style**

Wang Q, Jiang D, Gao Y, Zhang Z, Chang Q.
Examining the Driving Factors of SOM Using a Multi-Scale GWR Model Augmented by Geo-Detector and GWPCA Analysis. *Agronomy*. 2022; 12(7):1697.
https://doi.org/10.3390/agronomy12071697

**Chicago/Turabian Style**

Wang, Qi, Danyao Jiang, Yifan Gao, Zijuan Zhang, and Qingrui Chang.
2022. "Examining the Driving Factors of SOM Using a Multi-Scale GWR Model Augmented by Geo-Detector and GWPCA Analysis" *Agronomy* 12, no. 7: 1697.
https://doi.org/10.3390/agronomy12071697