2.5.1. Multicollinearity Analysis

Collinearity among the selected independent variables profoundly affects the model performance [39,46]. Tolerance and variance inflation factor (VIF) is used to measure multicollinearity in selected variables. Tolerance values less than 0.2 indicate marginal multicollinearity among selected independent variables, while tolerance less than 0.1 advocates multicollinearity to a grea<sup>t</sup> extent. Similarly, a variable with VIF greater than 2 indicates serious multicollinearity [44,47]. All the variables selected have a tolerance greater than 0.2 and VIF less than two, which indicates that the variables are not unduly correlated with each other (Table 2). Hence, all the selected variables were used to build the model.



Statistical Package for Social Sciences (SPSS) was used to build the logistic regression model. The logistic regression method based on the forward likelihood ratio was selected to assess the effect of the predictor variables of landslide occurrences. The statistical significance of the chosen variable was evaluated using the χ2 score. The Wald χ2 score's significance level for a predictor variable to enter the model was set at 0.1. The training sets were evaluated based on the χ2 value of Hosmer–Lemeshow, Nagelkerke R2, and Cox and Snell R2.

### 2.5.2. Landslide Susceptibility Map and Validation

The model was trained using the landslides that occurred between 1992 and 2009. The pixel size of the raster dataset used for the landslide model was 30 m × 30 m. The

total area of Coonoor region was represented with 255,700 pixels and the landslide data used for training the model consisted of 7859 pixels. Random selection of landslide and non-landslide pixels was adopted to build the logistic regression model. Validation of the model was carried out using the landslides that happened between the years 2010–2018. The coefficients calculated using the logistic regression model are assigned as weights for the thematic layer. The weighted thematic layers are combined in a GIS environment. The landslide probability is determined from the logistic function "z". The spatial distribution of landslide probability represents the landslide susceptibility of the region. Hence, the spatial variation of probability is reclassified into five categories: very low, low, moderate, high, and very high, using quantile classification to represent landslide susceptibility. The landslide susceptibility map is validated using the landslide density index and area under the curve (AUC) to envisage the prediction and success rate of the landslide model built. Cumulative landslide percentage and area were plotted, and the area under these curves was calculated using both the training dataset and validation dataset of landslides. These represent the prediction and success rate of the model developed.
