*2.5. Landslide Susceptibility Assessment*

A binary logistic regression model was used to map the spatial variability of the zones prone to landslides in Coonoor. The spatial variation of the factors causing landslides is shown in Figure 2.

Logistic function f(z) describes the probability of occurrence of a landslide event and is defined as

$$\mathbf{f}(\mathbf{z}) = \frac{e^z}{1 + e^z} = \frac{1}{1 + e^{-z}} \tag{1}$$

and it varies from zero to one. "z" is expressed as the linear combination of predictors i.e., independent variables that cause landslides and respective coefficients. The model is expressed by

$$\mathbf{z} = \mathbf{b}\_0 + \mathbf{b}\_1 \boldsymbol{\chi}\_1 + \mathbf{b}\_2 \boldsymbol{\chi}\_2 + \mathbf{b}\_3 \boldsymbol{\chi}\_3 + \dots \dots \dots + \mathbf{b}\_n \boldsymbol{\chi}\_n \tag{2}$$

b0 represents model coefficient i.e., the intercept or constant; b1 ... ... .bn are coefficients representing the measure of the contribution of predictor variables X1 ... .. ... ... . Xn in causing landslides. The terms b0 to bn are unknown and are determined based on the relationship between the independent variables and landslide conditions and are estimated by the maximum likelihood approach, which is a derivative of the probability distribution of landslides, the dependent variable [34]. The independent variables are spatially represented as thematic layers and illustrate each factor causing a landslide. "z" varies between − ∞ and + ∞ and is an index that allows the user to combine the various independent variables responsible for landslide occurrence. Sample observations are used to fit a multiple logistic regression model. The coefficients b0, b1, b2, b3 ... ... .bn are estimated and used to ascertain landslide probability.

Logistic regression (LR) model is built by (i) selection of independent variables based on its association with landslide occurrence (ii) checking the statistical significance of the selected variables using *p*-value significance test (iii) verifying the lack of inter-dependency

between the selected independent variable using collinearity statistics—tolerance and VIF (iv) modelling landslide probability through logistic regression model and (v) validation through Area Under Curve (AUC) and landslide density function using the validation dataset. In this study, the landslide density function, computed for each class of a thematic layer is used to transform nominal variables into numerical variables, and is used as input variables for determination of the LR model. This helps prevent the creation of a large number of dummy variables. Moreover, it incorporates the knowledge of landslide history into the model. The landslide density function is defined as

$$\text{LDF} = \frac{\frac{\text{Area of Lands!life pixels in a particular class}}{\frac{\text{Total Area of land}}{\text{Area of pixels in a particular class}}}{\frac{\text{Area of pixels in a particular class}}{\text{Total Area}}} \tag{3}$$

Landslides cover nearly 1.1% of the total area, which is many times smaller than the area in which landslides are not present, and hence, it can be considered a rare event [43,44]. The ratio of landslide to non-landslide pixels used for developing the training dataset of the model is based on sensitivity analysis conducted on a different ratio of 1:1, 1:2, 1:2.5 and 1:5 based on various literature [31,44,45]. Seed cells of 100 m radius surrounding a landslide location were considered to extract the independent variable's feature in a landslide affected region. Similarly, random locations not affected by landslides were also selected to represent zones not prone to landslides. The landslide pixels' ratio to nonlandslide pixels was maintained as 1:1, 1:2, 1:2.5 and 1:5 to generate the training dataset. It was observed that the ratio of 1:2.5 performed better consistently in these trials, and hence it was selected for the study. Different random sets of pixels with no landslides were selected to verify the consistency of the results. A binary variable to indicate the absence (0) or presence (1) of the landslide was added to the dataset.
