Table 1 Joint Hotspot Category
Area Poor
Food Scarcity
Unemployment Response Variable
Category Score
A Yes 3
Yes 2 Yes1
6 B
Yes 3 Yes 2
No 0 5
C Yes 3
No 0 Yes 1
4 D
No 0 Yes 2
Yes 1 3
E Yes 3
No 0 No 0
3 F
No 0 Yes2
No 0 2
G No 0
No 0 Yes 1
1 H
No 0 No 0
No 0 To determine the importance between poverty, unemployment, and food
security we will use the MDGs criteria: poverty reduction as target number one will be given a score of three, reducing the proportion of people who suffer from
hunger as the second target will be given a score of two, and in cooperation with developing countries, develop and implement strategies for decent and productive
work for youth as the 16
th
target will be given a score of one UN 2000. Based on the addition of these scores we will develop a final category of multiciriteria
hotspots shown in Table 1. These categories will be used as a response variable for ordinal logistic regression model. These methods will be used to identify the
factors that are of significant influence towards poverty, unemployment, and food scarcity hotspots.
2.12. Ordinal Logistic Regression
Logistic regression extends categorical data analysis to data sets with binary response and one or more continuous factors Freeman, 1987. Ordinal logistic
regression perform logistic regression on an ordinal response variable. One way to use category ordering forms logit of cumulative probabilities for ordinal response
Y with c categories, x are explanatory variables. The cumulative probability for each category can be formulated as:
| x
F x
j Y
P
j
= ≤
...
1
x x
j
π π
+ +
=
where
x
j
π
is the response probability of the j
th
category of explanatory variable x. Cumulative logits for each category j are defined as
− =
1 ln
x F
x F
x L
j j
j
; where 1
,..., 2
, 1
− =
c j
A model that simultaneously uses all cumulative logits can be written as
\
] _
\
` a b] Each cumulative logit has its own intercept. The
_
\
` are increasing in j, since
| x
j Y
P ≤
increases in j when x is fixed, and the logit is an increasing function of this probability Agresti 2002.
b] and _
\
` are the maximum likelihood estimators for each
_
c
and b
d
. These estimators represent the change in logits cumulative for each j category, if the other explanatory variables do not influence
ˆ x L
j
. The interpretation of the
b] is the change in logit cumulative for each j category, in other hand, odds ratio will change equal to exp
b] for each change of explanatory variables x Agresti 2002.
The estimate value for |
x j
Y P
≤ can be derived with inverse
transformation of logit cumulative function, the result will be shown below. e f g hi
j kl _
\
` a b
d
mn a kl _
\
` a b
d
mno345p5 h q r s
tp e f g hi
j a 5uv
_
\
` b
d
m o8 wt G4 G e f g hi
j a 5uv
x
] o
2.13. Testing the Model Significance
Likelihood ratio test of the overall model is used to assess parameter
i
β
with
hypothesis:
H :
...
1
= =
=
p
β β
H
1
: at least there is one
p i
i
,..., 2
, 1
; =
≠
β , where i is the number of
explanatory variables.
The likelihood-ratio test uses G statistic, which is G = -2 lnL L
k
where L is likelihood function without variables and L
k
is likelihood function with variables Hosmer Lemeshow 2000. If H
is true, the G statistic will follow chi-square distribution with p degree of freedom and H
will be rejected if value of G X
2 p,
α
or p-value
α
. A Wald test is used to test the statistical significance of each coefficient
i
β
in the model. Hypothesis are H
:
=
i
β
H
1
:
p i
i
,..., 1
; =
≠
β
where i is the number of explanatory variables. A Wald test calculates a W statistic, which is formulated as
ˆ ˆ
ˆ i
i
SE W
i
β β
β
=
Reject null hypothesis if |W| Z
α
2
or p-value
α
Hosmer Lemeshow 2000.
2.14. Assumption of Logistic Regression
