Developing a Hybrid Model to Enhance the Robustness of Interpretability for Landslide Susceptibility Assessment

Abstract

Landslide is one of the most damaging natural hazards, causing extensive damage to the infrastructure and threatening human life. Although advances have been made in landslide susceptibility assessment by objective explainable machine learning, the interpretability robustness of traditional single landslide susceptibility model is still low. The proposed interpretable hybrid model in this study overcomes these challenges and aims to enhance the stability of landslide susceptibility interpretability. The model integrates three base machine learning models—LightGBM, XGBoost, and Random Forest—using a heterogeneous category strategy, thereby enhancing the robustness of model interpretability. The hybrid model is interpreted using SHAP (Shapley Additive Explanations) values, which quantify feature contributions. A 10-fold cross-validation with the coefficient of variation (CV) metric reveals that the hybrid model outperforms individual base models in terms of interpretive robustness, yielding a lower CV value of 0.175 compared to 0.208 for LightGBM, 0.240 for XGBoost, and 0.207 for the Random Forest model. Although predictive accuracy remains comparable to the baseline models, the hybrid model provides more stable and reliable interpretability results for landslide susceptibility. It identifies the slope, elevation, and LS factor as the three most important factors for landslide susceptibility in Xi’an city. Furthermore, the quantitative nonlinear relationships between these predisposing factors and susceptibility were identified, providing empowering knowledge for the landslides risk prevention and urban planning in the regions vulnerable to landslides.

1. Introduction

Landslides, which involve the downward movement of rock, soil, and organic material due to gravity, are considered one of the most destructive geohazards [1]. They are among the most dangerous natural disasters, often causing significant damage to infrastructure such as homes, roads, and bridges, and posing severe risks to human life [2]. According to the United Nations Development Program, landslides rank as the second-most frequent geological hazard worldwide, leading to substantial economic losses each year [3]. The World Health Organization (WHO) reports that between 1998 and 2017, landslides affected over 4.8 million people and resulted in more than 18,000 fatalities [2]. Unfortunately, global warming is expected to increase the frequency and intensity of extreme rainfall events, thereby raising the number of people exposed to landslide hazards [4]. The prevailing view is that the most effective approach to minimizing landslide risk lies in the reliable monitoring, assessment, and identification of landslide-prone areas [3]. Landslide susceptibility refers to the likelihood of a landslide occurring under specific topographical and environmental conditions. Understanding this susceptibility is crucial for identifying areas at risk of landslides and is an effective non-engineering method for mitigating landslide-related disasters [5,6].

At present, the models for predicting landslide susceptibility mainly include three types: physically based models, statistical models, and machine learning models [7]. The physically based models is a mechanism-oriented technology, such as the infinite slope stability model [5]. Although physical models can provide reasonably accurate results, the materially intensive nature of their input parameters has limited the applicability of physically based models to smaller spatial extents [8,9]. Landslide susceptibility refers to the likelihood of a landslide occurring of a certain magnitude in a region and is traditionally estimated based on statistical methods that quantify the empirical relationships between environmental conditioning factors and the historical location of landslides [10]. Using these relationships, we can infer patterns of susceptibility in other areas with similar characteristics. Statistical models can be more economical compared to physically based models, thus allowing for wider regional deployment [11]. However, these statistical methods, such as frequency ratio (FR) and the Weights of Evidence (WoE), are generally assumption-driven and could not appropriately describe the nonlinear relationships between the factors with susceptibility, and often requiring intricate combinations of input parameters [12,13]. These machine learning algorithms allow models to describe the nonlinear relationships between predictive variables and landslides, as mentioned above, resulting in better predictive performance [14]. The popular machine learning methods used in landslide susceptibility models include the support vector machine [15], artificial neural networks [16], the Random Forests (RF) [17]. Moreover, several ensemble learning models and deep learning techniques, including Gradient Boosting Decision Trees (GBDT) [18], AdaBoost [19], and Convolutional Neural Networks [20], have also been leveraged for susceptibility prediction.

Predicting landslides is necessary for disaster prevention. Machine learning model processes are expected to be optimized to allow for effective early warning and forecasting of disasters. Nevertheless, models based on machine learning are usually considered to be a “black box” and cannot explain how terms affect susceptibility [21]. To overcome this, there is an increasing research focus on the fundamental techniques of machine learning interpretability [22], also known as Explainable Artificial Intelligence (XAI). The most popular method regarding this case is Shapley Additive Explanations (SHAP), which is based on game theory; it can assign each feature a quantifiable influence and this method can therefore offer detailed explanation in local and global level about a model prediction [23]. Although SHAP has been successfully used to quantify relationships between factors and outcomes prediction of landslide susceptibility as shown by Zhang et al. and Pradhan et al. [24,25], little focus has been placed on the robustness of these explanations. However, the interpretation yielded by the SHAP method is not stable under parameterization and input deviation in the model [26]. Consequently, there is growing concern in the field to make model explanations more robust. Recently, Bommer et al. introduced a framework for evaluating XAI methods to assist the selection of appropriate XAI techniques to specific research objectives [27]. However, they did not specifically argue that those choices explain better than the explanatory model they were inserted into the context but simply that there are other choices. Recent studies have shown that there are ensemble explanatory outcomes when different machine learning models are used together. Thus, it results in more robust and reliable model interpretations compared to interpretations based on a single model [28]. Motivated by this, developing an interpretable hybrid model can be a promising direction to improve the robustness of landslide susceptibility interpretations.

This study addresses the issue of poor robustness in landslide susceptibility explanations using traditional single models by proposing an interpretable hybrid model to bridge this gap. We introduce an effective and manageable heterogeneous category strategy to integrate three base machine learning models: LightGBM, XGBoost, and the Random Forest (RF) model. The objectives of this study are (1) to conduct a comparative robustness analysis of different landslide susceptibility models based on SHAP, (2) to develop a hybrid model using the heterogeneous category strategy to enhance the robustness of model explanations, and (3) to quantify the nonlinear relationships between landslide susceptibility and influencing factors in Xi’an using the developed hybrid model.

2. Materials

2.1. Study Area

Xi’an is the capital of Shaanxi Province. The city lies between 108°50′ E to 109°10′ E longitude and 33°30′ N to 34°30′ N latitude (Figure 1). Xi’an experiences a continental monsoon climate, with four distinct seasons. The city is intersected by eight rivers, including the Jingjiang, Changjiang, Juehe, and Weihe rivers, the latter being the primary source of drinking water [29]. The altitude within the city varies from 336 m to 3748 m, with the southern region being mountainous and the northern region predominantly flat. The annual precipitation ranges from 500 to 700 mm [30], with the average annual temperature recorded at 14.08 °C. January temperatures hover near the freezing point, while July sees an average of 27.0 °C. The lithology is primarily composed of silty clay, loess, sand, and gravel. These materials have a complex origin, predominantly derived from alluvial, diluvial, and aeolian depositional processes [31]. Most rainfall occurs between July and October, a period during which the southern mountainous areas are prone to geological hazards [32]. Despite these challenges, Xi’an is home to a wealth of historical and cultural heritage, with numerous ancient relics, tombs, and traditional structures, including the Terracotta Army, the Han Dynasty Chang’an City, and the Tang Dynasty Daming Palace. [33]. The threat of landslide hazards to both historical sites and urban development underscores the need for comprehensive landslide susceptibility assessments and analysis of driving factors within the region.

2.2. Data

2.2.1. Landslide Inventory

A landslide inventory serves as the foundation for assessing landslide susceptibility and plays a crucial role in the accurate evaluation and efficient management of landslide risks [22]. For this study, the landslide inventory data were acquired from the Resource and Environmental Science Data Platform (https://www.resdc.cn/, accessed on 3 February 2024), and the accuracy of the landslide information has been verified [34]. This dataset records the spatial distribution of landslide geohazards across China from 1949 to 2011 [35]. In the study area, 347 landslide points were detected. An equal number of points, which were not associated with landslides, were randomly selected within the study area. In the machine learning model, for landslide points (i.e., positive samples), the value was set to 1, while for non-landslide points (i.e., negative samples), the value was set to 1. Finally, we correctly combined the 70% positive and negative samples into a training dataset (243 landslide points and 243 non-landslide points) and the remaining 30% as the validation dataset (104 landslide points and 104 non-landslide points).

2.2.2. Landslide Conditioning Factors

Landslides are influenced by factors such as topography, geology, hydrology, meteorological conditions, vegetation cover, and human activities. Fifteen conditioning factors were selected for use in landslide susceptibility modeling, as presented in Figure 2 and listed in

Table 1. The data source used in this study.

Factors	Data	Source of Data	Time	Resolution
AR	Annual spatially interpolated dataset of meteorological elements in China	Resource and Environmental Science Data Platform (https://www.resdc.cn/) (accessed on 3 February 2024)	1960–2020	1 km
Elevation	Digital Elevation Model (DEM)	Shuttle Radar Topography Mission (SRTM, https://www.earthdata.nasa.gov/sensors/srtm) (accessed on 13 February 2024)	2000	90 m
CI
LS
PLC
PRC
Slope
RSP
TWI
Aspect
Lithology	Lithology	China Geological Survey (https://www.cgs.gov.cn/) (accessed on 13 February 2024)	/	1:10,000
NDVI	MOD13A1	(https://lpdaac.usgs.gov/products/mod13a1v006/) (accessed on 15 February 2024)	2020	500 m
Land use	CLCD	https://zenodo.org/records/5816591#.ZAWM3BVBy5c (accessed on 21 February 2024)	2020	30 m
DR	River	HydroSHEDS (https://www.hydrosheds.org/) (accessed on 18 February 2024)	2013	/
Soil	Soil	National Earth System Science Data Center (accessed on 25 February 2024)	/	1:1,000,000

Average annual rainfall (AR), Convergence Index (CI), profile curvature (PRC), LS factor (LS), Normalized Difference Vegetation Index (NDVI), plan curvature (PLC), relative slope position (RSP), distance to river (DR), Topographic Wetness Index (TWI).

. These factors include the following: meteorological conditions represented by average annual rainfall (AR); topography represented by elevation, LS factor (LS), convergence index (CI), plan curvature (PLC), relative slope position (RSP), profile curvature (PRC), and slope; geological categories represented by lithology; human activities represented by land use; hydrological conditions represented by the Topographic Wetness Index (TWI) and distance to river (DR); and vegetation cover represented by the Normalized Difference Vegetation Index (NDVI) and soil. These factors are frequently employed in landslide susceptibility predictions with in-depth information provided in the studies of Guo and Sharma et al. [36,37]. Since the original spatial resolution of the DEM data was 90 m × 90 m, each factor was converted to the same resolution to retain original data accuracy as much as possible [38].

3. Methodology

Figure 3 illustrates the framework developed to improve robustness of the interpretability of landslide susceptibility modeling. Firstly, 15 conditioning factors were chosen based on domain expertise and their spatial relevance. The feature selection followed using Pearson correlation analysis and the Information Gain Ratio (IGR) to mitigate multicollinearity and preserve the most informative variables. Three machine learning models—LightGBM, XGBoost, and Random Forest—were trained independently and then combined using a heterogeneous ensemble approach, weighted by each model’s Area Under the Curve (AUC), to create a hybrid model. To facilitate the interpretable analysis, Shapley Additive Explanations (SHAP) were applied to quantify the contribution of each feature. Lastly, a 10-fold cross-validation scheme was applied, and the coefficient of variation (CV) was used to evaluate the consistency of feature importance rankings across different folds.

3.1. Feature Selection Methods

3.1.1. Pearson Correlation Analysis

Usually, a Pearson correlation analysis should be performed before building a machine learning-based landslide susceptibility model to reduce multicollinearity [39] by removing the strongly correlated conditioning factors. Its linear correlation scale is based on the Pearson correlation coefficient among two variables (X, Y) in the statistics [40]. The Pearson correlation coefficient ranges from +1 to −1, with +1 representing a perfect positive linear correlation, 0 indicating no linear correlation, and −1 signifying a perfect negative linear correlation. To minimize multicollinearity and redundancy, we ensured that the pairwise correlation coefficients among conditioning factors did not exceed 0.8. The Pearson correlation coefficient formula is as follows:

$$r={\displaystyle \frac{1}{n-1}}{\displaystyle {\sum }_{i=1}^n(\frac{X_i-\overline{X}}{{\sigma }_x})}({\displaystyle \frac{Y_i-\overline{Y}}{{\sigma }_y}}),$$

(1)

where t, n denotes the number of samples, X_i and Y_i refer to the individual data points indexed by i, and $X$ and $\overline{Y}$ represent the means of the samples. σ_x and σ_y correspond to the standard deviations of the respective samples.

3.1.2. Information Gain Rate

Given the different types of landslides and their varying responses to factors, it is crucial to identify and eliminate factors that exhibit low or no predictive value during the modeling process [41]. The Information Gain Ratio (IGR) is widely employed for selecting significant landslide factors. In the IGR approach, landslide driving factors with a large information gain value indicate that they have strong predictive ability [42]. Higher IGR for a factor can also be calculated on the previous study by Quinlan et al. [43].

3.2. Baseline Machine Learning Models

3.2.1. LightGBM Model

The LightGBM (Light Gradient Boosting Machine) algorithm, introduced by Microsoft, is an enhanced Gradient Boosting Decision Tree (GBDT) model [44]. Because of its superior accuracy, shorter execution time, and less memory exploit, it has been extensively applied in forecasting landslide susceptibility [45]. This algorithm minimizes the errors of continuous, factor-based decision trees to the largest extent. The specific features that greatly enhance learning efficiency include leaf-wise growth strategy and histogram-based node splitting [46]. LightGBM’s basic learner is a decision tree, which can be denoted as [47]

$$y=f(x)={\displaystyle \sum _{i=1}^T{\alpha }_i·h_i(x)}$$

(2)

where y represents the predicted value, x denotes the input features, T is the total number of trees, $\alpha$_i is the weight of the ith tree, and h_i(x) refers to the prediction made by the ith tree.

3.2.2. XGBoost Model

XGBoost, introduced by Chen and Guestrin et al. [48], offers a scalable and efficient framework that integrates multiple decision trees to generate robust predictions, even in the presence of noisy and complex data [49]. Additionally, it employs a more regularized model formulation to mitigate overfitting, leading to improved performance [50]. This makes XGBoost particularly promising for applications in landslide hazard mapping and assessment. The general formulation for XGBoost prediction can be represented as

$$Y={\displaystyle \sum _{k=1}^k{f}_k(X)}$$

(3)

where Y is the predicted output, X represents the input features, K is the number of trees, and f_k(X) is the prediction from the kth tree.

3.2.3. Random Forest Model

Random Forest (RF) is a robust ensemble learning method that can be used for classification, regression tasks [51]. It can also be seen as a collection of random Decision Trees (DT). Typically, ensemble models outperform individual models, which is why multiple independently trained Decision Trees are combined to form the Random Forest [52]. RF constructs a large number of decision trees during the modeling process. The final classifier is derived by aggregating the outputs of these trees through majority voting [53]. This method has been successfully applied to landslide susceptibility modeling, demonstrating strong performance.

The optimization of parameter of al the models was performed by the Baysean optimization algorithm [54].

3.3. Construction of Interpretable Hybrid Model

3.3.1. Heterogeneous Category Strategy

To integrate the performance predictions of multiple models, ensemble modeling methods are widely adopted, and the resulting hybrid models typically offer better classification than individual models [55]. One such ensemble method, known as heterogeneous category, is used to assign performance weights to models, overcoming the drawbacks of simple averaging [56]. This method improves the weighted averaging approach based on the AUC (area under the curve) values and has been applied in disaster susceptibility modeling [12]. The ensemble method is created using the following formula:

$$EM={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n(AU{C}_i·M_i)}}{{\displaystyle {\sum }_{i=1}^{n}AU{C}_i}}}$$

(4)

where EM represents the resulting ensemble model and AUC_i is the AUC value of the ith single model (M_i).

3.3.2. Shapley Additive Explanations

The practical advantage of applying machine learning in decision-making processes lies in the ability of machine learning models to enhance the accuracy of landslide predictions. Additionally, these models can be explained through interpretability techniques [57]. Recently, Shapley Additive Explanations (SHAP) have emerged as an effective method for interpreting the modeling processes of machine learning and deep learning models [58]. Additionally, SHAP facilitates the evaluation of factor interactions through the computation of boosted Shapley values, which provides global performance insights while preserving local accuracy [59]. The Shapley value is mathematically defined as

$${\varphi }_j(\nu )={\displaystyle \sum _{S\subseteq \left\{1,\dots ,p\right\}\left\{j\right\}}\frac{\left|S\right|!\left(p-\left|S\right|-1\right)!}{p!}}\left({\nu }_x\left(S\cup \left\{j\right\}\right)-{\nu }_x(S)\right),$$

(5)

where S represents a subset of the p features used by the model, x refers to the feature value vector of the instance under analysis, and v_x(S) denotes the prediction generated for the feature values in the subset S. Importantly, the interpretation of the hybrid model is grounded in a heterogeneous category strategy, which facilitates the creation of an interpretable hybrid model. The final SHAP values are obtained by aggregating the SHAP values of the three models, weighted in accordance with the heterogeneous category strategy.

3.4. The Evaluation for Model Performance and Interpretive Robustness

Model performance is evaluated using various statistical metrics, including the area under the receiver operating characteristic curve (AUC), accuracy, F1 score, recall, and precision. The AUC measures the model’s ability to distinguish between landslide and non-landslide areas. Accuracy indicates the overall correctness of predictions. Precision reflects the proportion of correctly predicted landslide instances among all predicted positives, while recall measures the proportion of actual landslides correctly identified. The F1 score, as the harmonic mean of precision and recall, provides a balanced measure of model performance in imbalanced datasets [60]. These allow the evaluation of the result of the model in relation to the test samples and the predicted value of true positive and false positive [61]. In particular, they are determined as

$$AUC={\displaystyle \frac{{\displaystyle \sum TP}+{\displaystyle \sum TN}}{P+N}}$$

(6)

$$Accuracy=(TP+TN)/N$$

(7)

$$\mathrm{Re}call=TP/\left(TP+FN\right)$$

(8)

$$F1=\left(2\times {\displaystyle \frac{TP}{TP+FP}}\times {\displaystyle \frac{TP}{TP+FN}}\right)/\left({\displaystyle \frac{TP}{TP+FP}}+{\displaystyle \frac{TP}{TP+FN}}\right)$$

(9)

$$\mathrm{Pr}ecison=TP/(TP+FP)$$

(10)

where P denotes the locations where landslides occur, while N refers to areas without landslides. True positives (TP) and true negatives (TN) represent correctly predicted landslide and no-landslide locations, respectively. False negatives (FN) and false positives (FP) refer to incorrectly predicted landslide and no-landslide locations. N represents the total number of samples.

To evaluate the robustness of model interpretation, this study employs the coefficient of variation (CV) to quantify the variability in factor rankings across 10-fold cross-validation runs. The CV is a statistical metric used to evaluate the level of variation in each indicator within a system. A higher CV indicates greater variability, suggesting lower interpretive robustness of the model. The CV is calculated as follows:

$$\sigma ={\displaystyle \frac{1}{k}}{\displaystyle \sum _{i=1}^k{r}_i}$$

(11)

$$\mu =\sqrt{{\displaystyle \frac{1}{k}}{{\displaystyle \sum _{i=1}^k(r_i-\mu )}}^2}$$

(12)

$$CV={\displaystyle \frac{\sigma }{\mu }}$$

(13)

where CV is the coefficient of variation, $\sigma$ is the mean value, $\mu$ is the standard deviation of the rankings of a given factor r_i, and k is the number of folds.

Furthermore, McNemar’s chi-squared tests was employed to examine the statistical significance of differences between model outputs [62].

4. Results

4.1. Feature Selection

To reduce potential redundancy among predictive variables and improve both model efficiency and performance, we employed the information gain ratio (IGR) and Pearson correlation coefficients for optimal feature selection. Figure 4a shows the contributions of each factor according to their IGR values, with 12 out of 15 factors exhibiting IGR values greater than zero. Aspect, soil, and DR showed IGR values of zero, indicating a negligible influence on landslide occurrence in the study area. Consequently, these three factors were excluded from further analysis. Furthermore, as shown in Figure 4b, the pairwise correlation coefficients among the remaining 12 landslide conditioning factors were all below 0.8, with a maximum value of 0.79, indicating low multicollinearity and minimal redundant information. Accordingly, 12 factors were retained for the development of subsequent machine learning models.

4.2. Interpretive Robustness and Model Performance

The hybrid model is developed to enhance interpretability robustness while ensuring that predictive accuracy remains competitive. To this end, the coefficient of variation (CV) was used to quantify the robustness of feature rankings based on SHAP values under 10-fold cross-validation. A lower CV indicates greater consistency across folds. As shown in Figure 5, the proposed hybrid model demonstrates the highest robustness, with the lowest CV value of 0.175 (Figure 5d), whereas the three baseline models exhibit CVs exceeding 0.2, suggesting weaker consistency in their explanations. The boxplots further support this observation: only a single outlier is observed for the hybrid model, in contrast to multiple fluctuations in the baseline models, indicating that the hybrid model provides more reliable feature rankings. In terms of model accuracy (

Table 2. Performance metrics of the four models.

Models	AUC	Accuracy	Precision	Recalls	F1 scores
LightGBM	0.86	0.78	0.77	0.88	0.82
XGBoost	0.87	0.79	0.79	0.83	0.81
Random Forest	0.86	0.78	0.77	0.86	0.81
Hybrid	0.87	0.8	0.79	0.87	0.83

), five commonly used evaluation metrics were employed. While the hybrid model does not significantly outperform the baseline models, it maintains a comparable and stable level of accuracy. These findings suggest that the improved interpretability of the hybrid model is achieved without compromising predictive performance, supporting its practical applicability.

Table 3. McNemar’s test results comparing landslide susceptibility outputs across different models.

Models	LightGBM	XGBoost	Random Forest	Hybrid
LightGBM	0	**	**	**
XGBoost	8573.9	0	**	**
Random Forest	12,033.8	736.6	0	**
Hybrid	7757.3	1283.1	3921.1	0

Notes: ** represents the statistical significance p < 0.05.

presents the results of McNemar’s chi-squared tests [62] applied to the susceptibility maps, organized in a symmetric matrix format. The analysis reveals statistically significant differences among the susceptibility outputs of different models, with all p-values below 0.05. This indicates that, despite similar overall model accuracies, the spatial patterns of susceptibility differ considerably, underscoring the necessity of ensemble modeling.

4.3. Landslide Susceptibility Mapping

Landslide susceptibility mapping is the direct output of the models and serves as a critical component of susceptibility assessment. It is therefore essential to validate the spatial patterns of susceptibility generated by the proposed hybrid model. Figure 6 presents the spatial distributions of landslide susceptibility in Xi’an, as predicted by the three baseline models and the hybrid model, while

Table 4. The area percentage of landslide susceptibility classes, and the frequency ratio (FR) predicted by different models (unit: %).

Susceptibility	LightGBM		XGBoost		Random Forest		Hybrid
	P/%	FR	P/%	FR	P/%	FR	P/%	FR
Very low	49.38	0.01	51.08	0.01	35.17	0.00	42.72	0.01
Low	17.13	0.17	13.38	0.15	23.46	0.02	20.44	0.07
Medium	10.19	0.42	11.23	0.49	14.65	0.57	11.79	0.47
High	11.24	1.92	11.98	1.56	14.99	1.67	12.72	1.61
Very high	12.06	5.85	12.33	5.84	11.73	5.63	12.33	5.96

Frequency ratio was derived as the ratio between the proportion of landslide occurrences and the proportion of the corresponding area.

summarizes the proportional areas assigned to each susceptibility class. It is worth noting that the natural breaks (Jenks) method was used to classify landslide susceptibility into discrete levels. As shown in Figure 6, the hybrid model produces a spatial pattern that is consistent with those of the baseline models and aligns well with the observed distribution of historical landslides, demonstrating its reliable predictive capability. Further insights from Table 3 reveal that, although the area proportions of susceptibility classes predicted by the hybrid model are generally comparable to those of the baseline models, some differences remain. Specifically, the hybrid model’s estimates for each susceptibility level tend to fall between those of the three baseline models. This intermediate positioning suggests improved generalization and reduced uncertainty of the hybrid model, relative to individual models.

4.4. Interpretation of Landslide Susceptibility

4.4.1. Global Interpretation

Determining the operational direction of each driving factor (Figure 7) and assessing their contributions (Figure 8) are crucial for understanding the landslide formation mechanisms in the study area. However, the explanatory outcomes may differ across models, making it necessary to explore these discrepancies and demonstrate the advantages of the hybrid model. As shown in Figure 7, the operational direction of each factor is similar across the three baseline models. For instance, slope and susceptibility exhibit a generally positive relationship, while elevation and susceptibility show an inverse correlation. However, Figure 8 reveals notable differences in factor rankings across the three baseline models. Specifically, although the LightGBM and XGBoost models agree on the three most important factors, discrepancies emerge from the fourth position onwards. This divergence is more pronounced in comparison to the RF model. For instance, both LightGBM and XGBoost identify slope as the most significant factor, while RF ranks elevation as the most influential. This discrepancy can even change further with different training iterations (Figure 5). Therefore, a more stable hybrid model is valuable, as it mitigates the uncertainty inherent in the interpretation of individual models. As shown in Figure 8d, the hybrid model combines results from all three base models, and the contribution of each factor (indicated by bar length) lies between the contributions of the baseline models. Additionally, the operational direction of each factor in the hybrid model remains consistent with that in the original baseline models. These findings demonstrate that the hybrid model reduces uncertainty in factor interpretation and provides more reliable explanatory results.

4.4.2. Marginal Effects of Driving Factors

Using the hybrid model, we applied SHAP values to interpret how the six most significant factors influence landslide susceptibility in the study area, as shown in Figure 9. The factors, including slope, elevation, LS, RSP, NDVI, and TWI, were found to have the greatest impact on landslide susceptibility. Notably, the relationships between these factors and susceptibility are nonlinear, with clear threshold effects that highlight the marginal contributions of each factor. Specifically, for slope, the threshold was identified at 5.9° and 39.6°. Susceptibility increases when slope lies between these two values, while it decreases when the slope is either below 5.9° or above 39.6°. Similarly, elevation promotes susceptibility between 490 m and 1375 m, but inhibits it above 1375 m or below 490 m. For LS, susceptibility is enhanced when the value is between 5.0 and 29.6, with a suppression occurring outside this range. RSP also exhibits a similar pattern: susceptibility increases between 0.012 and 0.185 but decreases outside this range. NDVI shows susceptibility enhancement between 0.53 and 0.64, with inhibition outside these values. Finally, TWI enhances susceptibility between 5.92 and 8.56 but reduces it outside this range. These threshold effects clearly demonstrate the complex, marginal contributions of each factor to landslide susceptibility. By using the hybrid model, we are able to quantitatively describe these nonlinear relationships and better understand the marginal effects of each factor.

5. Discussion

5.1. The Advances of the Hybrid Model

This study addresses the challenge of improving the interpretability and robustness of landslide susceptibility assessments, which remains a critical issue in geohazard prediction (e.g., [28,63]). Recent studies have highlighted the strengths and limitations of commonly used machine learning models, such as LightGBM, XGBoost, and Random Forest (RF), in providing accurate susceptibility predictions [64]. However, these models often exhibit inconsistencies in feature importance rankings and variation in model explanations, which can undermine their reliability in real-world applications [65,66]. This study presents a hybrid model that enhances the robustness of interpretability for landslide susceptibility predictions by integrating multiple models, providing a more robust explanation of landslide susceptibility. The hybrid model offers notable advantages over traditional models. In terms of interpretability, it demonstrates greater robustness in feature rankings across folds, as evidenced by the lower coefficient of variation (CV) values (Figure 5). This robustness is essential for ensuring reliable, consistent outputs in susceptibility assessments, where fluctuations in factor importance can lead to different predictive results. Previous studies have emphasized the importance of stable, interpretable models in geohazard prediction, yet single models often fail to provide such consistency [67]. The hybrid model alleviates this limitation effectively, offering a more dependable solution for understanding and explaining landslide susceptibility. Regarding predictive performance, although the hybrid model does not significantly outperform the individual models (Table 2), it maintains comparable accuracy while offering superior robustness. This aligns with the original intention of the EBM model proposed by CA et al., which integrates gradient boosting techniques with decision trees to provide both direct interpretability and competitive accuracy [68]. In contrast to this study, the hybrid model we propose employs a more accessible integration strategy that combines multiple base models and their explanatory results, offering greater scalability. In summary, the hybrid model retains high accuracy while reducing variability in the interpretation of results, which is a key advantage over standalone models.

5.2. Interpretability of Driving Factors

The interpretation of driving factors influencing landslide susceptibility is a critical aspect of hazard assessment, as understanding these factors can lead to more accurate risk predictions and informed decision-making [69]. This study makes an important contribution by identifying and quantifying the nonlinear relationships between key factors like slope, elevation, and topographic wetness index (TWI) with landslide susceptibility. Consistent with the study by Wang et al., elevation and slope emerged as the most influential factors associated with landslide occurrence [70]. While the correlation between elevation and landslides may seem ambiguous, it could be attributed to the concentration of logging roads within certain elevation bands, which alters terrain stability and land use patterns. In addition, the study finds that slope increases susceptibility within a range of 5.9° to 39.6°, beyond which it begins to decrease. These results align with those of Liu et al., who identified a high incidence of landslides within the slope range of 2.95° to 68.19° [71]. Similarly, elevation shows a peak susceptibility between 490 m and 1375 m, with susceptibility dropping outside of this range. These findings push forward the field’s understanding by demonstrating that the relationship between landslide susceptibility and driving factors is far from simple linearity. In the context of the existing literature, this work moves beyond the traditional emphasis on identifying which factors are important (e.g., slope, elevation, rainfall) and begins to delve deeper into how these factors interact with each other in a nonlinear fashion. Previous studies have often highlighted slope as a key factor in landslide susceptibility assessments (e.g., [72,73,74]), but without clearly defining the specific range of slope values that lead to increased risk. By incorporating these threshold effects generated by interpretable machine learning models into the analysis, this study adds valuable detail to the ongoing research into landslide susceptibility.

5.3. Implication and Limitation

This study’s identification of threshold effects and nonlinear relationships in landslide susceptibility has significant implications for Xi’an, a city with rich cultural heritage and growing infrastructure [75]. By identifying critical thresholds for factors like slope (5.9° to 39.6°) and elevation (490 m to 1375 m), urban planners can make informed decisions about land use in landslide-prone areas, minimizing risks to both modern infrastructure and ancient landmarks such as the city walls and Terracotta Army. The study’s focus on multi-factor interactions is crucial for Xi’an’s long-term development, balancing urbanization with the preservation of cultural sites. These insights can help guide sustainable development and enhance the city’s resilience to landslides, ensuring both growth and heritage preservation. The proposed hybrid model demonstrates strong potential for application across diverse geographic environments. Its flexible design enables the incorporation of region-specific conditioning factors, allowing it to adapt to varying environmental, climatic, and urban conditions. Moreover, the model can be implemented entirely using Python 3.9, enhancing its accessibility and facilitating broader adoption in both academic and practical settings.

Several limitations are inevitably present in this study. The interpretable hybrid model proposed is based on three popular base machine learning models. However, the integration of deep learning models such as CNN, LSTM, and transformer, among others, warrants further development. The strategy used in this study, heterogeneous category, effectively integrates the models in a simple manner, but a comparison with other strategies, such as stacking and bagging, in terms of model interpretability deserves further exploration. In addition, differentiating landslide types in future driver analyses would significantly enhance the robustness and interpretability of the results. Despite these limitations, we emphasize the contribution of the proposed interpretable hybrid model in improving the robustness of model explanations.

6. Conclusions

This study proposes an interpretable hybrid model to improve the robustness of model interpretability for landslide susceptibility assessments. The model adopts a heterogeneous category strategy, integrating three machine learning models (LightGBM, XGBoost, and Random Forest) along with their SHAP, achieving a comprehensive interpretation of multiple models. The conclusions are as follows:

(1)

The hybrid model demonstrates superior robustness, with a coefficient variation (CV) value of 0.175, significantly lower than the CV values exceeding 0.2 for the baseline models. This indicates more reliable feature rankings across folds.

(2)

Although the hybrid model does not drastically outperform the individual models, it maintains competitive predictive accuracy, with an AUC of 0.87, accuracy of 0.80, precision of 0.79, recall of 0.87, and F1 score of 0.83. This highlights its effectiveness in providing stable and consistent results for landslide susceptibility mapping.

(3)

The study identifies critical threshold values for factors like slope (5.9° to 39.6°) and elevation (490 m to 1375 m), which demonstrate nonlinear relationships with landslide susceptibility. These insights contribute to a more nuanced understanding of the factors influencing landslide occurrence.

By integrating multiple models, the hybrid approach minimizes uncertainties in factor interpretation, offering more stable and dependable results compared to individual models, particularly in terms of understanding factor interactions. Despite these strengths, the integration of deep learning models, such as CNN, LSTM, and transformer, remains a promising direction for future research to further improve the robustness and generalization capabilities of the model.