Geoscience Reference
In-Depth Information
Logistic regression allows the prediction of discrete variables
by a mix of continuous and discrete predictors. It addresses the
same questions that multiple regression does but with no distri-
butional assumptions on the predictors (the predictors do not
have to be normally distributed, linearly related or have equal
variance in each group).
Suppose Y denotes the crop yield over a certain period of time
and it has two levels, namely, high yield (Y = 1) and low yield
(Y = 0). Further, let there be p climatic explanatory variables
such as rainfall, maximum temperature, minimum temperature,
relative humidity, atmospheric pressure and so on over that spec-
ified period of time. Suppose, π
i
denotes the probability that the
ith observation of the dependent variable takes the value 1, that
is, Yi
i
= 1, for i = 1, 2, …, n. Then, the simple logistic regression
model that best describes the situations can be expressed as
π
i
=
P(Y |X
=
=
x,..., Xx)
=
i
1i
1i
pi
pi
(4.5)
= +
=+
−
e(1e)
1/(1
z
z
e)
z
where
z
+
Here, all other symbols have
their usual meaning as defined earlier. The parameters can be
estimated by fitting the logistic regression. Based on the fitted
value, one can predict the different levels of crop yield.
=
ββ β
x
+
+
x
0
1
1i
p i
time series
approach
Climate is a very heterogeneous factor. The global economy
witnessed a major setback time due to various natural phenom-
ena such as drought, flood, tsunami and so on. All these are the
outcomes of climate change. These natural phenomena directly
or indirectly affect the yield of various crops over the years.
So the alternative approach for studying the impact of climate
change is to use time series modelling by considering the yield
of the present year as the dependent variable and lagged vari-
able as explanatory variables. The simplest of these kinds are
autoregressive (AR) models, moving average (MA) models,
autoregressive moving average (ARMA) models and autore-
gressive integrated moving average (ARIMA) models. The fol-
lowing is a brief description related to these models.
Suppose Y
t
is a discrete time series variable that takes differ-
ent values over a period of time. Then the corresponding pth-
order AR model, that is, AR (p) model, is defined as
AR (p): Y
=+ +
ββ β
Y
Y
++Y
β
+
ε
(4.6)
t
0
1t
−
1
2
t2
−
pt
−
p
t
