7 Comparative GIS-Based Assessment …
115
7.7 Multi-variate Logistic Regression Model (LRM)
Considering p independent variables, x 1 , x 2 , …, x p , affecting landslide occurrences,
we define the vector X = (x 1 , x 2 , …, x p ). The independent variables are with values
of 1 (presence) or 0 (absence).
The conditional probability that a landslide occurs is represented by P(y = 1/X).
The logit of the multiple LRM (Hosmer and Lemeshow 2000) is
Logit(y) = b 0 + b 1 x 1 + b 2 x 2 + . . . + b p x p
where b 0 is the constant of the equation, and b 1 , b 2 , …, b p are the coefficients of
variables x 1 , x 2 , …, x p .
The probability P(y = 1/X) can be expressed in the LRM:
P
y =
1
X
=
1
1 + e
−(b 0 +b 1x 1 + b 2x 2 + ......+b px p )
where “e” is the constant 2.718.
Higher the value of coefficient, higher will be the weightage.
7.8 Landslide Susceptibility Index Classification
For the differentiation of different susceptibility class, susceptibility index classification was done using R studio. Both the landslide and non-landslide points were taken
for the landslide susceptibility index classification. The susceptibility index having
25% of landslide was classified as low susceptibility, 25–50% as medium susceptibility, 50–75% as high susceptibility, and 75–100% as very high susceptibility (Lee
and Pradhan 2007).
7.9 Landslide Susceptibility Model Validation
and Comparison
It is very important to check the efficiency or the validation of the landslide susceptibility model. In this study, Receiver Operating Characteristic (ROC) index has been
used for the validation of the model (Pontius and Schneider 2001). A good fit model
has Area Under Curve (AUC) values that range from 0.5 to 1, while values below
0.5 represent a random fit (Youssef et al. 2016). The ROC of SIM and LRM using
30% (n = 18) of landslides were obtained to check the accuracy and reliability of
the model.
115
7.7 Multi-variate Logistic Regression Model (LRM)
Considering p independent variables, x 1 , x 2 , …, x p , affecting landslide occurrences,
we define the vector X = (x 1 , x 2 , …, x p ). The independent variables are with values
of 1 (presence) or 0 (absence).
The conditional probability that a landslide occurs is represented by P(y = 1/X).
The logit of the multiple LRM (Hosmer and Lemeshow 2000) is
Logit(y) = b 0 + b 1 x 1 + b 2 x 2 + . . . + b p x p
where b 0 is the constant of the equation, and b 1 , b 2 , …, b p are the coefficients of
variables x 1 , x 2 , …, x p .
The probability P(y = 1/X) can be expressed in the LRM:
P
y =
1
X
=
1
1 + e
−(b 0 +b 1x 1 + b 2x 2 + ......+b px p )
where “e” is the constant 2.718.
Higher the value of coefficient, higher will be the weightage.
7.8 Landslide Susceptibility Index Classification
For the differentiation of different susceptibility class, susceptibility index classification was done using R studio. Both the landslide and non-landslide points were taken
for the landslide susceptibility index classification. The susceptibility index having
25% of landslide was classified as low susceptibility, 25–50% as medium susceptibility, 50–75% as high susceptibility, and 75–100% as very high susceptibility (Lee
and Pradhan 2007).
7.9 Landslide Susceptibility Model Validation
and Comparison
It is very important to check the efficiency or the validation of the landslide susceptibility model. In this study, Receiver Operating Characteristic (ROC) index has been
used for the validation of the model (Pontius and Schneider 2001). A good fit model
has Area Under Curve (AUC) values that range from 0.5 to 1, while values below
0.5 represent a random fit (Youssef et al. 2016). The ROC of SIM and LRM using
30% (n = 18) of landslides were obtained to check the accuracy and reliability of
the model.