# A Combined Method for Preparation of Landslide Susceptibility Map in Izmir (Turkije)
## 3 Materials and Methods
### Statistical Analysis  
#### 3.3.1 Logistic Regression (LR)  
Landslide researchers have used various techniques in the production of LSMs due to data and model deficiencies [100]. Multivariate statistical analysis is one of these. LR is one of the most used multivariate statistical analysis techniques. LR allows evaluation of the multivariate regression relationship in landslide susceptibility studies. The advantage of LR is that the variables can be continuous, discrete or any combination of the two [9]. The purpose of LR in this context is to find the most appropriate relationship between the existence of landslides and a set of independent parameters such as slope angle and lithology [101]. For LR studies, the dependent variable should be entered as 0 or 1 so that the model applies correctly to landslide probability analysis. Fuzzy logic can be used to normalize these data between 0 and 1 [40]. The LR algorithm applies maximum probability estimation after converting the dependent variable into a logic variable representing the natural logarithm of the dependent or non-dependent probabilities [92; 102]. LR is based on the logistic function given by Equations (1) and (2) [103],  
\[P=\frac{1}{1+e^{-Z}} \tag{1}\]  
In this equation, \(P\) is assumed to be the estimated value of landslide occurrence varying between 0 and 1, while \(Z\) is assumed to be a linear combination of the factors causing the landslide and the factors  
\[X_{i}\ (i\ \text{(i: 1,2,3, }\ldots\,n).Z=B_{0}+B_{1\times 1}+B_{2\times 2}+ \ldots\.\.+B_{n}X_{n} \tag{2}\]  
where B\({}_{0}\) is the prediction for the intersection and B\({}_{1}\); B\({}_{2}\); \(\ldots\.\); B\({}_{n}\) are estimates for coefficients associated with independent variables. The value Z is found by using the second equation; the value is found after it is replaced in Equation (1) and the landslide probability value (P) is found. In the analysis, Idrisi software [104] geospatial monitoring and modeling system was used to establish the relationship between the area in which landslides occurred(landslide inventory) and the factors that caused the landslides (slope, slope orientation, lithology, etc.).  
The equation for landslide occurrence estimation with LR is given below (Equation (3)).  
\[Z=-12.8124+5.379812^{*}\text{asp}+0.220848^{*}\text{curve}+0.751963^{*}\text{ dod}-0.197740^{*}\text{elv}-0.720106^{*}\text{land}+3.754381^{*}\text{lith}+0.956580^{ *}\text{slope}+0.738011^{*}\text{spi}-0.197984^{*}\text{dfs} \tag{3}\]  
In this equation, \"asp\" is slope aspect, \"curve\" is curvature, \"dod\" is density of discontinuity, \"elv\" is elevation, \"land\" is land use, \"lith\" is lithology, \"slope\" is slope angle, \"spi\" is stream power index and \"dfs\" is distance from stream.  
A summary of the basic statistics of the LR model obtained using Idrisi software [97] Logistic reg tools is given in Table 2. Of the values included in these statistics, a pseudo-R\({}^{2}\) equal to 1 indicates perfect fit, while 0 indicates no relevance. The pseudo-R\({}^{2}\) value shows how well the logit model fits the dataset. A pseudo-R\({}^{2}\) greater than 0.2 shows a relatively good fit [105]. In this study, the pseudo-R\({}^{2}\) value was calculated as 0.1607 (Table 2). In addition, a value of 0.8499 was obtained for the relative operating characteristic (ROC), which can be considered a sign of good correlation between the independent and dependent variables.