Spatial Regression Approach in Determining Factors Affecting Percentage of Human Trafficking Victims inWest Java.

SPATIAL REGRESSION APPROACH IN DETERMINING FACTORS
AFFECTING PERCENTAGE OF HUMAN TRAFFICKING VICTIMS
IN WEST JAVA

DANIA SIREGAR

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
2013

SUMMARY
Spatial Regression Approach in Determining Factors Affecting
Percentage of Human Trafficking Victims in West Java. Supervised by
ASEP SAEFUDDIN and ANANG KURNIA.
DANIA SIREGAR.

The spatial dimension plays a key role in many social phenomenons such as poverty,
pollution, disease, crime and others. Social phenomenon in certain areas is influenced by the
social phenomenon in other locations. One of the interesting social phenomenons that will

be studied in this research is human trafficking in West Java. The aims of this study are
to identify the spatial effects on percentage of human trafficking victims, and to determine
the factors which affected percentage of human trafficking victims in West Java in 2010.
The existence of spatial relationship information between district/municipality led to need
to accommodate the spatial variability in the model, so that the model used were spatial
regression models. Based on the analysis, spatial effect influential significantly the percentage
of human trafficking victims. The hotspot for human trafficking victims were Cimahi
Municipality, Bandung Municipality and Bandung District. The best model to accommodate
spatial effect in this study was General Spatial Model (GSM) with AIC-value=-361.46
and R2a=71.34%. Based on GSM obtained the indepen-dent variables or factors which

significantly affected percentage of human trafficking victims in West Java in 2010 for
α=0.05 as follows: the average of population with divorce status, the average of population
with local migrant status, and the average of population with maximum education in Junior
High School.

Key words: Spatial regression models, GSM, human trafficking, hotpsot.

SPATIAL REGRESSION APPROACH IN DETERMINING FACTORS
AFFECTING PERCENTAGE OF HUMAN TRAFFICKING VICTIMS

IN WEST JAVA

DANIA SIREGAR

Minithesis
as one of requirements to obtain
Bachelor's Degree of Statistics (with honors)
at Department of Statistics

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
2013

Title of Minithesis : Spatial Regression Approach in Determining Factors Affecting

Percentage of Human Trafficking Victims in West Java.
Name
NIM

: Dania Siregar
: G14080015

Approved

Advisor I,

Advisor II,

Prof. Dr. Ir. Asep Saefuddin, M.Sc
NIP. 195703161981031004

Dr. Anang Kurnia
NIP. 197308241997021001

Known
Head of Department of Statistics
Faculty of Mathematics and Natural Sciences
Bogor Agricultural University

Dr. Ir. Hari Wijayanto, M.Si.
NIP. 196504211990021001

Date of Graduation:

ACKNOWLEDGEMENTS
Alhamdulillah, In the name of Allah The Beneficent, The Merciful praise be to Allah The Lord
of The World. Blessing and salutations be upon the most honorable Muhammad saw. as prophet
and messenger, his family and disciples who follow him in goodness till the day of judgment.
The paper is entitled "Spatial Regression Approach in Determining Factors Affecting
Percentage of Human Trafficking Victims in West Java". It would not have been possible to
complete this paper without the assistance of several individuals. The author would like to thank
profusely to all those who have helped, among others:
1. Prof. Dr. Ir. Asep Saefuddin, M.Sc. and Dr. Anang Kurnia, as advisory committee have
provided guidance, direction, and feedback during the writing of this paper.
2. Dr. Ir. Hari Wijayanto, M.Si. and all teaching staf of Department of Statistics who have
provided knowledge for author carried out study in Bogor Agricultural University.
3. The entire administrative staff and employees of Department of Statistics who always ready
to assisted the author in completing various needs related to the completion of this paper.
4. Mother and father who always give love, affection and trust to the author since childhood till

now.
5. Rona Karunia Siregar, Nadia Itona Siregar, and M. Ihsan Siregar who have provided the
motivation to the author in order to give best.
6. Dr. Ahmad as counselor at Al Iffah Boarding School who has provided much insight about
the meaning and purpose of life.
7. Sekar Sari Utami Wiyaja, her help in scientific discussion regarding spatial regression.
8. All friends in Department of Statistics.
9. All friends in Student’s Advisory Assembly of Bogor Agricultural University (MPM KM
IPB) who taught the author the meaning of brotherhood and team work.
10. All friends in Student’s Parliament of Bogor Agricultural University (DPM KM IPB) who
taught the author the meaning of caring and affection to each other.
11. Ana Widiyawati, Arni Nurwida, Hilda Rafika Wati, Intan Apriliani, Miftachul Jannah, Yulia
Devi Anggorosasi, Baehaki Fajri Ibnu Abbas and M. Tegar Kusmahidayat Konenda as
friends who always complement each other and give encouragement to complete the mandate
of the organization and the mandate of the academic with balanced.
12. All those who have provided support, prayer and motivation in completion this paper.
Hopefully all the kindness rewarded by Allah swt. and this paper can be useful for all those
who read it.

Bogor, January 2013

Dania Siregar

CURRICULUM VITAE
The author named Dania Siregar and was born in Kalianda on February 27, 1991, a
daughter of couple Pandeangan Siregar, S.Pd.SD and Mely Maryati, S.Pd.SD. The author
is second daughter of four children.
In 2002 the author completed her primary school education at SDN 2 Kalianda. The
author continued her studies at SMPN 1 Kalianda and graduated in 2005. In 2008 the
author graduated from SMAN 1 Kalianda and in the same year passed the selection into
the Bogor Agricultural University through the Invitation Selection of Bogor Agricultural
University. The author chose mayor Statistics, Faculty of Mathematics and Natural
Sciences with a minor in Consumer Sciences.

During the study, the author had actived in Student’s Parliament of Bogor Agricultural
University and Student’s Advisory Assembly of Bogor Agricultural University, became assistant
lecturer in experimental design, and had actived helping colleagues and clients in data
analyzes. The author conducted field practice at Research Center for Agriculture of
Biotechnology and Genetic Resources (BB-Biogen) in February-April 2012.

TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................... viii
LIST OF FIGURES .............................................................................................................. viii
LIST OF APPENDIXES ....................................................................................................... viii
INTRODUCTION .................................................................................................................
Background..................................................................................................................
Objective .......................................................................................................................

1
1
1

LITERATURE REVIEW ......................................................................................................
Multiple Regression Analysis ........................................................................................
Spatial Regression Analysis ..........................................................................................
Spatial Effect Test ................................................................................................
Spatial Modeling ..................................................................................................
Spatial Weighting Matrix ....................................................................................
Best Model Selection ...........................................................................................

Spatial Analysis in Human Trafficking .........................................................................

1
1
2
2
4
4
5
5

METHODOLOGY.................................................................................................................
Data ..............................................................................................................................
Methods .........................................................................................................................

6
6
6

RESULTS AND DISCUSSION ............................................................................................

6
Exploring Data ...............................................................................................................
6
Multiple Regression Analysis .......................................................................................... 8
Testing for Spatial Effects ............................................................................................... 9
Spatial Autoregressive Model (SAR) .................................................................... 10
General Spatial Model (GSM) .............................................................................. 10
The Factors which Affected Percentage of Human Trafficking
Victims in West Java ..................................................................................................... 11
CONCLUSIONS AND RECOMMENDATION ...................................................................
Conclusions ...................................................................................................................
Recommendation ...........................................................................................................

11
11
11

REFERENCES ......................................................................................................................

11

APPENDIXES .......................................................................................................................

13

viii

LIST OF TABLES
Page

Distribution of frequency based on percentage interval
of human trafficking victims in West Java.............................................................. 8
2. The results of spatial dependence .............................................................................
9
3. The parameters estimation for SAR ........................................................................
10
4. The parameters estimation for GSM .......................................................................
10
1.

5.

The indicators of goodness model ...............................................................................

11

LIST OF FIGURES
1.
2.
3.
4.
7
5.
6.
7.

Page
Moran’s scatter plot .......................................................................................................
2
Spatial weighting illustration. ........................................................................................
5
Diagram percentage of human trafficking victims in West Java in 2010. ....................
7

The thematic map of percentage interval of human trafficking victims in West Java
Normality plot for multiple regression. .........................................................................
Scatter diagram between residual and fitted value of multiple regression ....................
Moran’s scatter plot .......................................................................................................

8
9
9

LIST OF APPENDIXES
1.
2.
3.
4.
5.
6.
7.
8.

Page
The independent variables ............................................................................................. 14
Descriptive statistics of the independent variables ........................................................ 15
Fitting linear line pattern for the variables no-multicolinearity ..................................... 16
Normality plot for SAR model ...................................................................................... 17
Scatter plot between residual and fitted value for SAR model ..................................... 17
Normality plot for GSM ................................................................................................ 17
Scatter Plot between residual and fitted value for GSM ............................................... 17
Administrative map of West Java Province ................................................................... 18

1

INTRODUCTION
Background
The spatial dimension plays a key role in
many social phenomenons such as poverty,
pollution, disease, crime and others. Social
phenomenon in certain areas is influenced by
the social phenomenon in other locations as
stated in the first law of geography advanced
by W Tobbler cited by Anselin (1988), it is
stated that everything is related to everything
else, but near thing are more related than
distant one. Spatial effects are relatively
common happened between one region to
another. Based on LeSage (1998), two
problems arise when sample data has a
location component: 1) spatial dependence
exists between the observations and 2) spatial
heterogenity occurs in the relationships which
are modeling. The existence of spatial
relations in dependent variable will cause
estimates to be inaccurate because the
assumption of randomness error is violated.
To solve above problems, required a
regression model that incorporates the spatial
relationship between regions into the model.
The existence of spatial relationship
information between regions led to need to
accommodate the spatial variability in the
model, so that the model used is spatial
regression models.
One
of
the
interesting
social
phenomenons to be studied in this research is
human trafficking. Human trafficking for
forced labor or sexual exploitation is believed
to be one of the fastest growing areas of
crime. It becomes the second largest source of
illegal income worldwide after drug
trafficking. Combating human trafficking, or
the use of force, fraud or coercion to transport
persons across international borders or within
countries to exploit them for labor or sex,
become important priority for many
goverments around the world (Belser 2005 ;
Laczko 2005, referenced in Goździak and
Bump 2008). Information of spatial relations
that have been occurred in this case is
assumed based on Sanders (2007) that the
spatial interactions can be also expressed as
an influence of a location on another, without
being explicitly embodied in the form of a
measurable exchange or flow, like life
experience, trafficking trajectories or local
customs.
Based on International Organization for
Migration (US) (2011) in trafficking case
data, Indonesia become top ten countries of
destination where victims were trafficked in

2011. Beside that based on data from the
Criminal Investigation Police Headquarters
of the Republic of Indonesia Agency (ID), in
the period 2005-2009, West Java was on the
top of trafficking cases, followed by West
Kalimantan, East Java, Central Java and West
Nusa Tenggara. Coordinator Minister for
People's Welfare in 2009, Agung Laksono,
said the high incidence of human trafficking
occured because human trafficking had
syndicates and huge resource. In addition, the
perpetrators often move transportation routes
which was lack of supervision. Besides that,
human trafficking was closely associated with
high rates of poverty and unemployment, low
level of education, gender discrimination, and
early marriage and divorce (Jabar … 2009).
This is the background why the author took
the human trafficking cases in West Java to be
analyzed using spatial regression models. The
author hoped that the information from this
research could help decision-makers to craft
effective policies.
Objective
The aims of this study are to identify the
spatial effects on percentage of human
trafficking victims, and to determine the
factors which affected percentage of human
trafficking victims in West Java in 2010 using
spatial regression model.

LITERATURE REVIEW
Multiple Regression Analysis
Multiple regression analysis is an analysis
to evaluate the relationship between response
variables and several explanatory variables.
General multiple regression model, as
follows:

with is the respond variable vector (N 1),
is the matrix of explanatory variables
(N k),
is the vector of regression
coefficients (k 1), is the vector error noautocorrelation (N 1), and N is the number of
observations. Regression parameters expected
by Least Squares Method. Regression
parameter estimators:
̂

The alleged of regression parameters which
have been obtained need to be tested by using
t-test. The aim of t-test is to test the effect of
any explanatory variables one by one to the

3

There are four quadrants reflect in Moran’s
scatter plot:
 Quadrant I (red points) states that have
observations above the mean, where the
average of neighboring states’ observations
is also greater than the mean,
 Quadrant II (green points) states that exhibit
observations below the mean, but the
average of neighboring states’ observations
is above the mean,
 Quadrant III (blue points) states with
observations below the mean, and the
average of neighboring states’ observations
is also below the mean,
 Quadrant IV (purple points) states that have
observations above the mean, and the
average of neighboring states’ observations
is below the mean.
Spatial effect can be divided into two
parts, namely the spatial dependence and
spatial heteroskedasticity. Spatial dependence
occurs due to the dependence of the spatial
data (spatial error correlation). While the
spatial heteroskedasticity due to differences
between one region to another (Random
Region Effect).
1. Testing for spatial dependence
Testing for spatial dependence
performed is to know the type of
dependence in data used. The type of
dependence obtained will be used as the
basis for spatial regression modeling.
Anselin (1988) stated that Lag range
Multiplier test is the test to know whether
in the data used has spatial dependence or
not.
Testing hypotheses and test statistics
using Lagrange Multiplier test involve:
a) Spatial dependence in the dependent
variable/spatial dependence of lag
H0 :ρ = 0 (there are no spatial
dependence of lag)
H1 :ρ ≠ 0 (there
are
spatial
dependence of lag)
the test-statistic:

̂ is mean square error from OLS
method.
tr is operator of matrix trace, namely,
sum of elements diagonal matrix.
Statistic LMlag distributed
. The
decision is to reject H0 if the value of
LMlag>
or p-value < . So the
next process is the formation of the
Spatial
Autoregressive
models
(SAR).
b) Spatial dependence in error
H0 : λ = 0 (there are no spatial
dependence in error)
H1 : λ ≠ 0 (there
are
spatial
dependence in error)
the test-statistic:
LMerr=

c)

[

(

tr

(

̂)

(

̂

)

(

)]

)

-1

(Lag,err)

ε

–

2
2

y

where
T
y
ε

̂)

]+

Ε is the error vector (nx1) from
Ordinary Least Square (OLS), ̂
obtained with OLS method.

ε

2

T

–

y

2
T
T
T

T

T

–

)]

where
D = [

(

(

where
ε is error vector (nx1) from Ordinary
Least Square (OLS)
tr is operator of matrix trace, namely,
sum of elements diagonal matrix.
Statistic LMerr distributed
.
The decision to reject H0 if the value
of LMerr>
or p-value < . So the
next process is the formation of the
Spatial Error Model (SEM).
General Spatial Model (GSM)
H0 :ρ and λ = 0 (there are no spatial
dependence)
H1 :ρ and λ ≠ 0 (there are spatial
dependence)
the test-statistic:

2

LMlag =

[

2

Statistic LM(lag,err) distributed
.
The decision to reject H0 if the value
of LM(lag,err)>
or p-value < . So
the next process is the formation of
the General Spatial Model (Anselin
1988).

4

2. Testing for Spatial Heteroskedasticity
The spatial heteroskedasticity also
need to be tested. The test used to Spatial
heteroskedasticity is Breusch-Pagan test. A
generic
form
of
homoskedasticity
expressed by the following equation:
with …
a set of constants,
the
constant term of the regression and
the regressors. In the case of
homoscedasticity, quite obviously, we
so that,
have:
:
under H0 we have
constant.
Therefore, the hypotheses for testing
homoskedasticity are:
H0:
H1: at least one
if H0 is not rejected, the homoskedasticity
is fulfilled so that E[εi2] = var[εi] = σi2 =
= constant. The Breusch-Pagan (BP) teststatistic expressed by the following
equation:
∑
∑
∑
BP=

distributed
fi=

̂

̂

with

,

̂ =(

̂

), and

̂ =∑
̂ . The decision to reject H0 if
the value of BP>
. Anselin (1988)
referenced in Arbia (2006).
Spatial Modeling
General model of spatial regression
expressed in equation (1) and (2)
y = ρW1y+ Xβ + u
u = λW2u + ε
ε N (0, σ2I)

(1)
(2)

with y(nx1) is the dependent variable vector;
X(n x (k +1)) is the matrix of independent
variables; β((k+1)x1) is the regression coefficient
vector;
ρ is the spatial lag coefficient
parameter of dependent variable; λ is the
coefficient of spatial parameter lag in the
error; u(Nx1) is the error vector in equation (1),
ε(Nx1) is the error vector in equation (2), which
is the normally distributed with zero mean and
variance σ2I; W1 (nxn), W2(nxn) are the weighting
matrix, I(nxn) is the identity matrix, n is the
number of observations / locations (i = 1,2,3,
..., n), k is the number of dependent variables
(k = 1,2,3, ..., l). Error of regression (u) is
assumed to have the effect of random
locations and has a spatial autocorrelation. W1
and W2 are weighting showing the
relationship continguity or function of the
distance between sites and the diagonal is

zero. Anselin (1998) referenced in Lesage
(1998).
In equation (1), when X = 0 it will
became the first order spatial autoregressive
as in equation (3).
y = ρW1y+ ε
ε N (0, σ2I)

(3)

If W2= 0 or λ=0, the equation (1) will
became a model Spatial Autoregressive
Model (SAR) as in equation (4)
y = ρW1y+ Xβ + ε

(4)

If W1= 0 or ρ=0, the equation (1) will
become a model Spatial Error Model (SEM)
as in equation (5)
y = Xβ + λW2u+ ε

(5)

If W1, W2 ≠ 0, λ≠0 ρ≠0, the equation (2), will
become a model Spatial Autoregressive
Moving Average (SARMA) as in equation
(1). The parameters of λ, ρ and β could be
estimated
by
maximum
likelihood.
Hypotheses testing for the significance of the
parameters could be done with the following
Wald test.
Hypotheses:
H0 :
= [λ, ρ, β0 … βk]T = 0
H1 :
≠0
The Wald test-statistics:
Wald =

̂

where
as an estimate of the parameter pth;
var ( ) as a parameter to estimate the
variance pth. The decision to reject H0 if Wald
2
test statistics>ᵡ α,1.
Spatial Weighting Matrix
One important part of regression
modeling is the determination of the spatial
weighting matrix. According to Lesage (1998)
there are alternative ways to define the
presence of a contiguity relationship. They are
Linear Contiguity, Rook contiguity, Bishop
contiguity, Double Linear Contiguity, Double
Rook contiguity and Queen Contiguity. The
guiding principle in selecting a defnition
should be the nature of the problem being
modeled, and perhaps additional non-sample
information that is available. LeSage and Pace
(2011) said that the matrix W provided a
(normalized) structure of connectivity
between the observations and in spatial

6

Sanders (2007) said that conceptual models
concerning the meaning of the chosen
indicators, particularly the link between the
phenomenon being studied (which refers to a
theoretical framework) and the set of data
obtained from its measurements (which refers
to what is observable), given the observation
levels that were chosen. So the causes of
human trafficking in Indonesia base on AED
(2011) including poverty, lack of employment
opportunities, unequal gender roles, and
community and family pressures to employ
children. A cultural acceptance of a young
marrying age for girls often leads to false
marriages or failed marriages; following
which, the girls are sometimes forced into
prostitution.
Children are particularly
vulnerable due to the fact that a quarter of
junior secondary school age students do not
attend school. Though the law provides for
free education, in practice most schools are
not free of charge, and poverty places
education out of reach for many children.
Furthermore, 60 percent of children under 5
years old do not have official birth
certificates, putting them at risk of trafficking.
METHODOLOGY
Data
The data used in this study were
secondary data obtained from Integrated
Service Center forWomen and Children (ID)
(2010), and from website of Center for Data
and Development Analysis of West Java
about Spatial Data of Population and Labor
Force 2010. The variables used in this study
were 17 variables consisting of a dependent
variable and 16 in dependent variables as
follows:
a. Dependent variable (Y) is proportion
between the number of human trafficking
victims and the number of population in
each district/municipality in West Java.
This data was only handled by Integrated
Service Center for Women and Children
(ID) in 2010.
b. Independent variables (X) are the factors
that was suspected causing occurrence of
human trafficking in West Java.
The independent variables could be seen on
Appendix 1.
Methods
The stages of data analysis would be used
as follows:

1.

Exploring
data
using
descriptive
statistics.
2. Selecting independent variables.
Calculating the value of the correlation
between the independent variables and
selected the independent variables were
not multicollinearity where variance
inflation factor (VIF) < 10.
3. Fitting line pattern to determine the
pattern of the relationship of each
independent variable with the dependent
variable.
4. Predicting and testing the parameters of
multiple regression models and testing
the error assumptions.
5. Determining the spatial weighting matrix
W.
6. Testing the spatial auto correlation using
Moran’s Index.
7. Examining the spatial effects, namely
spatial
dependence
and
Spatial
heteroskedasticity. Lagrange Multiplier
test for testing spatial dependence and
Breusch-Pagan test for testing spatial
heteroskedasticity.
8. Predicting and testing the parameters of
spatial regression models.
9. Testing error assumptions of spatial regression models.
10. Choosing the best model by looking at
value of Akaike Information Criterion
(AIC) and adjusted R2.
11. Concluding.

RESULTS AND DISCUSSION
Exploring Data
West Java province consists of 17
districts and 9 municipalities. According to
population cencus result, total population of
West Java in 2010 reached 43 053 732
persons. Further-more, in 2010 the population
growth rate was 1.90 percent, while the
population density was 1 158 persons/km.
Base on data from Integrated Service Center
for Women and Children (ID) in 2010,
Bandung Municipality become the region
which the highest percentage of human
trafficking victims in West Java, reaching
0.0011692%, followed by Bandung District
(0.0011326%),
Sumedang
District
(0.0009144%), Garut District (0.0006239%),
Bandung Barat District (0.0005959%),
Cimahi District (0.0005543%), Sukabumi
District (0.0005125%) and Purwakarta
District (0.0003519%), more information
could be seen in Figure 3.

8

Table 1 Distribution of frequency based on percentage interval of human trafficking victims in
West Java.

1

Interval of human
trafficking victims
(%)
0.000000 – 0.000188

2

0.000189 – 0.000352

3

0.000353 – 0.000624

4

0.000625 – 0.001169

Group

Districts/Municipalities
Bogor, Depok Municipality, Bekasi Municipality , Bekasi,
Karawang, Subang, Indramayu, Cirebon Municipality,
Kuningan, Ciamis, Banjar Municipality, Tasikmalaya
Municipality , Tasikmalaya and Sukabumi Municipality.
Purwakarta, Cianjur, Bogor Municipality , Majalengka,
and Cirebon.
Sukabumi, Cimahi Municipality, Bandung Barat and
Garut.
Bandung Municipality, Bandung, and Sumedang.

the districts/municipalities in surrounding also
had high enough percentage of human
trafficiking victims. Based on the thematic
map, visually proved there were spatial effect
between the district/municipality and other
district/municipality.
The factors thought to influenced the
occurrence of human trafficking in this study
involve of demographic factors, marital status,
poverty, migration and education (Goździak
and Bump 2008) are summarized in 16
independent variables. Based on data in
Appendix 2 could be seen that Bandung
Municipality is municipality with the highest
population density, Subang is district with the
highest for average of population with live
divorce status, Tasikmalaya Municipality is
municipality with the highest percentage of
poverty, Bekasi Municipality is municipality
with the highest average of population with
local migrant status (risen migrant). Risen
migrant is the designation for someone who if
the places of residence at the time when data
collected were different from the places of
residence at the time of the previous five
years, and then Tasikmalaya is district with
the highest for average of population with
maximum education in primary school.
Multiple Regression Analysis
In the early stages, multiple regression
modeling undertaken for all variables.
Furthermore, from this modeling was found
that there were multicollinearity in the
independent variables by looking at the value
of VIF is more than 10. In addition, the
author also tested correlation between the
independent variables to convinced that
variables with VIF0150. This
suggested that residual distributed
normally on α=5%.

Figure 5 Normality plot for multiple
regression

9

2.

Homoskedasticity
Figure 6 is scatter diagram between
residual and fitted value of multiple
regression which have “horizontal
ribbon”. It exhibit that the assumption of
homoskedasticity was fulfilled.

Figure 6 Scatter
diagram
between
residual and the fitted value of
multiple regression.
3.

Independent error
The points in Figure 6 did not have a
pattern so it could be concluded that the
assumption of independent errors was
fulfilled. Although the error in the
regression were independent, testing for
error with include spatial weighting
matrix need to be done to knew whether
they had spatial autocorrelation in these
regression models. It could be done by
using Moran’s Index.

Spatial lag values

Testing for Spatial Effects
Testing for spatial effects were done to
saw if there were spatial effects in data.
Testing for spatial dependence used statistical
Moran's Index. This test is a test of residual
with included spatial weighting matrix.
Moran's Index value = 0.48747 with p-value =
7.927e-05. This suggests that there was spatial
autocorrelation in residual derived from the
multiple regression model, so that need to be
made a model that could accommodate spatial
effects, namely spatial regression. In Figure 7
exhibit that there was spatial dependence
effect on the dependent variable (Y) where
there were a pattern of clustered data.

Residual from regression

Figure 7 Moran’s scatterplot

Moran’s Index could also to identified
spatial outliers, namely upper spatial outlier
(hotspot) and under spatial outlier (coldspot).
Base on Figure 7 there were upper spatial
outliers (hotspots), they were exhibited as the
numbered points 22, 18 and 1 in quadrant I at
Moran’s scatter plot. The numbered points
were
Cimahi
Municipality,
Bandung
Municipality and Bandung District. Cimahi
Municipality, Bandung Municipality and
Bandung District had percentage of human
trafficking victims above the average of others
districts/municipalities. There were did not
found the coldspots in quadrant III, it could
be caused the percentage in quadrant III more
uniform.
Once known proven that there were
influenced of spatial effects, further step was
to identified whether the type of spatial effects
created. Spatial effects need to be identified
were spatial dependence and spatial
heterokedasticity.
Testing
for
spatial
dependence by using Lagrange Multiplier test
(LM). This test was used to detect
dependencies in lag, error, or both (lag and
error). The results of spatial dependence
could be seen in Table 2.
Table 2 The results of spatial dependence
Spatial Dependence
Value
P-value
Test
Lagrange Multiplier 10.744 1.046e-03*
(lag)
Lagrange Multiplier 1.4688 2.255e-01
(eror)
Lagrange
17.392 1.672e-04*
Multiplier (lag
and eror)
*) Significant on α=0.05

According to Table 2 it could be seen that
the p-value LM Lag = 1.046e-3 (less than α =
0.05). In conclusion reject H0. It means that
there was a lag of spatial dependence that
need to be followed to creation of Spatial
Autoregressive Model (SAR). Lagrange
Multiplier lag and error could be used to
identified the phenomena of combination,
which identified dependence in lag and
dependence in error between district/
municipality. Still based on Table 2 it could
be seen that the p-value of LM lag and
error=1.672e-4 (less than α = 0.05). The
conclusion reject H0, it means that there were
a lag of spatial dependence in lag and error, so
that need to be followed to creation of General
Spatial Model too. Testing for spatial
heterokedasticity by using Breush-Pagan

10

(BP). BP-value = 5.2897 where the
p-value=6.247e-1 is greater than α = 0.05.
This test showed that there was no spatial
heterokedasticity. It means that did not need
using spatial regression models geographically weighted.
Spatial Autoregressive Model (SAR)
Based on LM tests there was spatial lag
dependence, this condition need to be
continued to Spatial Autoregressive Model.
Based on Table 3 it can be seen that the R2a =
57.45%, it means that the model able to
explain the variation of the percentage of
human trafficking victims until 57.45% and
the remaining 42.55% is explained by other
variables outside the model. Independent
variables that significantly influences at α =
0.05 were X5 (the average of population with
dead divorce status), X11 (the average of
population with risen migrant status) and X13
(the average of population with maximum
education in junior high school).

normality, homoskedasticity and independent
error. In this model all the assumptions were
fulfilled (Appendix 4 and Appendix 5).
General Spatial Model (GSM)
Based on LM tests there were spatial lag
and error dependencies, so that need to be
continued to General Spatial Model.
According to Table 4 it could be seen that R2a
=71.34%, it means that the model was able to
explain the variation of the percentage of
human trafficking victims reach 71.34% and
the remaining 28.66% is explained by the
other variables outside the model. P-value
significant at α = 0.05 were variable X4 (the
average of population with live divorce
status), variable X5 (the average of population
with dead divorce status), variable X11 (the
average of population with risen migrant
status) and variable X13 (the average of
population with maximum education in junior
high school).

Table 3 The parameters estimation for SAR
Variable Coefficient
z
P-value
ρ
6.288e-01
4.823 2.677e-4*
Intercept 7.582e-04
0.262 7.927e-1
X2
-6.329e-06 -0.299 7.650e-1
X3
5.006e-04
0.321 7.480e-1
X4
-1.537e-02 -1.745 8.096e-2
X5
-1.640e-02 -3.460 5.400e-4*
X8
-1.305e-05 -1.024 3.056e-1
X11
-7.475e-03 -3.856 1.152e-4*
X13
8.186e-03
3.194 1.402e-3*
*) Significant α=0.05
R2a = 57.45% AIC-value = -356.7

Table 4 The parameters estimation for GSM
Variable Coefficient
z
P-value
ρ
8.025e-01
8.819
2.2e-16*
λ
-8.029e-01
-3.446 5.68e-4*
Intercept
-9.462e-04
-0.479 6.31e-1
X2
6.3903-06
0.467
6.40e-1
X3
1.232e-03
1.080
2.80e-1
X4
-2.311e-02
-3.209 1.33e-3*
X5
-1.550e-02
-4.007 6.10e-5*
X8
-1.514e-05
-1.563 1.183-1
X11
-7.843e-03
-5.048 1.00e-6*
X13
8.995e-03
4.281
1.80e-5*
*) Significant α=0.05
R2a= 71.34% AIC-value= -361.46

SAR model is as follows:
̂ = 0.62879 WY + 0.0007582 - 0.0164030
X5-0.0074755 X11 + 0.00818620 X13.

GSM model is as follows:
̂ = 0.80251WY - 0.80298 WU - 0.023112X4
-0.015506X5+0.0078429 X11 +
0.0089949 X13

The value of autoregressive spatial lag
coefficient (ρ) obtained amounting 0.6288, it
means that districts/municipalities had the
highest percentage of human trafficking
victims were suspected influenced by the
districts/ municipalities that became their
neighbors amounting 0.6288 multiplied by the
average percentage of human trafficking
victims in the districts/ municipalities around
them with the assumption that the other
variables fixed valuable. The assumptions
test were also performed on SAR model. The
assumptions that must be fulfilled were

The value of ρ and λ means that there were a
combined effect of spatial (lag and error) from
the adjacent districts/municipalities would
affect to the observation. The effect of local
proximity (spatial lag) was positively
correlated and spatial error between the
adjacent
districts/
municipalities
was
negatively correlated. The value of spatial
lag coefficient (ρ) amounting 0.8025 indicated
that if a district/municipality surrounded by as
many as m districts/municipalities, so the
influenced of each district/ municipality
which surrounds it amounting 0.8025
multiplied by the average percentage of

11

human trafficking victims in the surrounding
area. The spatial error
coefficient (λ)
amounting 0.8029 indicated that the error
correlation between the district/municipality
with other district/municipality that became
their neighbors amounting 0.8029 multiplied
by the average error in districts/municipalities
that surround it. The assumptions test were
also performed on GSM. The assumptions
that must be fulfilled were normality,
homoskedasticity and independent error. In
this model all the assumptions were fulfilled
(Appendix 6 and Appendix 7).
The Factors which Affected Percentage of
Human Trafficking Victims in West Java
Before determining the factors that
influenced the percentage of human
trafficking victims in West Java, it was
necessary to determined the best model with
the indicator of goodness using of AIC-value
(Akaike Information Criterion) which is a
measure of the relative goodness of fit of a
statistical model. It could be said to described
the trade off between bias and variance in
model construction, or loosely speaking
between accuracy and complexity of the
model. The smaller value of AIC could be
said to get better model. In addition, the value
of R2a could also be indicator of best model
selection. The comparison of AIC-value and
R2a in multiple regression model, SAR and
GSM could be seen in Table 5.
Table 5 The indicators of goodness model
Multiple
SAR
Indicator Regression
GSM
Model
Model
AIC
-345.41
-356.7
-361.46
R2a
38.42%
57.45%
71.34%
Based on Table 5 it could be concluded that
the GSM is the best model for this case. In
GSM model, the independent variables that
affected the percentage of human trafficking
victims were:
1. X4 = the average of population with live
divorce status.
2. X5 = the average of population with dead
divorce status.
3. X11 = the average of population with
local migrant (risen migrant) status.
4. X13 = the average of population with
maximum education in junior high
school.
Thus it could be seen that the factors affecting
percentage of human trafficking victims in
West Java in 2010 considering the influenced

of spatial districts/municipalities included
divorce, local migrant (risen migrant) status
and level of education.

CONCLUSIONS AND
RECOMMENDATION
Conclusions
The percentage of human trafficking
victims for certain district/municipality was
influenced by the percentage of human
trafficking victims in the surrounding
districts/municipalities. Best model to
modeling percentage of human trafficking
victims in West Java in this study is General
Spatial Model (GSM). The factors affecting
percentage of human trafficking victims in
West Java in 2010 by considering the
influenced of spatial based on GSM as
follows: the average of population with life
divorce status, the average of population with
dead divorce status, the average population
with local migrant (risen migrant) status, and
the average of population with maximum
education in junior high school.
Recommendation
This study only used data in 2010 were
handled by Integrated Service Center for
Women and Children (ID). Further research
should be done used previous and beyond
year to see what factors are influential in each
year. In addition, for the next research very
recommended to use spatial poisson
regression to compare the results.

REFERENCES
[AED] Academy for Educational Development.
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Indonesia.
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Anselin L. 1999. Spatial Econometrics.
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Arbia G. 2006. Spatial Econometrics:
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Belser P. 2005. Forced labour and human
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An
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13

APPENDIXES

14

Appendix 1 The independent variables
The
independent
Variable
X1
X2
X3
X4
X5
X6
X7
X8
X9
X10
X11
X12
X13
X14
X15
X16

The name of variable

Population density in each district/municipality in West Java (people/km2)
Sex ratio in each district/ municipality in West Java
Average of population had married in each district/ municipality in West Java
Average of population with live divorce status in each district/ municipality in West
Java.
Average of population with dead divorce status in each district/ municipality in West
Java.
Average of
population who the first marriage