Modeling of School Participation Rate for Senior High School in
Indonesia Using Mixed Geographically Weighted Regression Model
Febrina Kusumaningati
1
, Jefri E.B.Utomo
1
, Maya M.M. Zach
1
, Ayu Puspitawati
1
and Nur Chamidah
2
1
Student of Study Program of Statistics, Department of Mathematics,Universitas Airlangga, Surabaya, Indonesia
2
Department of Mathematics, Faculty of Sciences and Technology, Universitas Airlangga, Surabaya, Indonesia
Keywords: School Participation Rate, Senior High School, Mixed Geographically Weighted Regression.
Abstract: The quality of education can be determined by looking at school participation rate (SPR). The SPR in
Indonesia has increased in 2013-2016, but SPR for the age of 16-18 years has the lowest value when
compared with the age of 7-12 years and 13-15 years. This study aims to model and analyze the results of
SPR modeling and interpret the factors that affect the SPR in every province in Indonesia by using Mixed
Geographically Weighted Regression (MGWR) model presented in thematic map. Based on the analysis
result, there were 5 provinces where the SPR affected by rate of economic growth; 13 provinces were
affected by the number of school and rate of economic growth; 13 provinces were affected by the number of
school, rate of economic growth, and Gini Ratio; and 3 provinces were affected by rate of economic growth
and rate of labor participation. Also, we obtained through the MGWR model of Papua province that rate of
economic growth as a global variable decreased the SPR due to lack of good equity while rate of labor
participation reduced the SPR because many students prefer to work than study.
1 INTRODUCTION
The quality of education in Indonesia can be
examined by looking at school participation rate
according to BPS (2013). School participation rate is
the sum of all students who are still in school
compared to the whole population within the same
age group. From 2013 to 2016, school participation
rate in the 7-12 year population increases by 0.67%,
13-15 years increases by 4.07%, and 16-18 years
increases 6.99%.
School participation rate for 16-18
years (70.83%) has the lowest score compared to 7-
12 years (99.09%) and 13-15 years (94.88%).
Rahmatin and Soejoto (2017) studied the
influence of poverty rate and number of schools on
school participation rate (SPR) in Surabaya city by
using multiple linear regression method. The
obtained results were the poverty level factor and
the number of schools significant to the SPR in
Surabaya city.
The vulnerability of dengue hemorrhagic fever
disease in Surabaya was studied by Chamidah, et al
(2014) by using spatial logistic regression approach,
the result showed that every district in Surabaya has
different characters or relatively heterogeneous.
This also applies in education. Education in each
region is different, for example it can be seen from
the luxurious infrastructure that only exist in big
cities. Risking those assets, the automatic significant
factor for each region is relatively heterogeneous. To
discuss the heterogeneity, the researchers used the
special method specially mixed geographically
weighted regression (MGWR) approach to find out
the best SPR model in Indonesia and their
significant factors. MGWR is combination between
linear regression and Geographically Weighted
Regression, so MGWR can be used to identify
significant factors on SPR locally and globally.
Kusumaningati, F., Utomo, J., Zach, M., Puspitawati, A. and Chamidah, N.
Modeling of School Participation Rate for Senior High School in Indonesia Using Mixed Geographically Weighted Regression Model.
DOI: 10.5220/0007554409390943
In Proceedings of the 2nd International Conference Postgraduate School (ICPS 2018), pages 939-943
ISBN: 978-989-758-348-3
Copyright
c
2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
939
2 LITERATUR REVIEW
2.1 School Participation Rate
School participation rate is the proportion of all
children who are still in school in one particular age
group against the population with the appropriate
age group (BPS,2017).
2.2 Factors that Influence School
Participation Rate
There are some factors which suspected to influence
school participation rate:
2.2.1 Number of Schools
Number of schools is a number of SMA/SMK in
each province in Indonesia.
2.2.2 The Rate of Economic Growth (PDRB)
The Rate of Economic Growth on BPS calculation is
based on production of products and services growth
in certain time. The calculated of PDRB :
=
% (1)
2.2.3 Gini Ratio
Gini ratio used to measure the level of overall
income inequality. The calculated of gini ratio:
=−
∑
(
+
)
(2)
2.2.4 Percentage of Poor People
Poor people are people who have an average per
capita expenditure below the poverty line.
Percentage of poor people in BPS calculated :
=
∑
(3)
2.2.5 Rate of Labor Force Participation
The labor force participation rate (TPAK) is the
percentage of the population aged 15 years and over
which is labor forced. The calculation rate of force
participation is:
=
% (4)
2.3 Geographically Weighted
Regression Method
Geographically Weighted Regression (GWR)
method is a technique used in spatial regression
model that takes the framework of a simple
regression model by weighted regression
(Fotheringham, et al.,). GWR model is expressed as
follows:
() ()
0
1
,,
p
iii kiiiki
k
yuv uvx
ββ
ε
=
=+ +
∑
………(5)
2.4 Mixed Geographically Weighted
Regression Method
Mixed Geographically Weighted Regression
(MGWR) model is a combination model of global
regression with GWR that considers a situation
where several predictor variables that influence
global responses and other predictor variables are
local. The MGWR model can be written as follows:
() ()
0
11
,,
qp
iii kiiik kiki
kkq
yuv uvx x
ββ β
ε
==+
=+ ++
∑∑
…..(6)
The estimation of this model parameter can use
the Weighted Least Square (WLS) approach. The
estimated parameters of the MGWR model are as
follows:
()
,
iii
yuv=++
ii gg
xβ x βε
(7)
3 MATERIAL AND METHODS
3.1 Data and Data Sources
The data used in this study was secondary data of
2017 obtained from the publication of the Central
Bureau of Statistics (BPS). The data obtained consist
of a percentage of upper secondary level SPR or age
group 16-18 years and the factors that influence it.
In this research, there were 35 provinces in
Indonesia becoming the unit of observation.
ICPS 2018 - 2nd International Conference Postgraduate School
940
3.2 Research Variables
Variables in this research were a response variable
and five predictor variables. The response variable
was school participation rate (SPR).
Table 1: Predictor Variables
Predictor
Variables
Description Data Type
X
1
Number of Schools Discrete
X
2
Economic Growth
Rate (PDRB)
Continuous
X
3
Gini Ratio Continuous
X
4
Percentage of Poor
People
Continuous
X
5
Percentage of
Work Force on
Working Age
Population
Continuous
In addition, geographic variables were longitude
(u
i
) and latitude (v
i
).
3.3 Step Analysis
Modelling and analyzing the upper secondary level
SPR for each province in Indonesia using the
MGWR method with the following steps:
3.3.1 Test Spatial Assumption
Conducting assumption test against response
variable. Following steps to test assumptions:
a. Perform normality test against response variable.
Data should be normal.
b. Conducting multicollinearity data test. If the
value of VIF> 10 then there is a high
multicollinearity indication in the data.
c. Conducting heteroscedasticity test with GeoDa
software. If the value of p-value> α then there is
no heteroscedasticity.
d. Testing the assumption of spatial dependencies
in the data using Moran's I test using GeoDa
software.
3.3.2 Analyze with GWR Method
Analyze the upper secondary level school participation
rate
model in each province in Indonesia using GWR
method with the following steps:
a. Determine longitude and latitude for each
province in Indonesia.
b. Calculate the euclidian distance (d
ij
) between the
i-th location of the j-th location at the
coordinates.
c. Determine the optimum bandwidth by using
Cross Validation (CV) method.
d. Calculates a weighted matrix by using kernel
function for optimum bandwidth.
e. Estimate GWR model parameters by including
all predictor variables.
f. Perform partial significance test parameters.
3.3.3 Analyze with MGWR Method
Analyze the upper secondary level school participation
rate model in each province in Indonesia using the
MGWR method with the following steps:
a. Obtain the model parameter estimator MGWR
by using the optimum bandwidth and the same
weighting as in the GWR model.
b. Testing the suitability of the MGWR model.
c. Conducting simultaneous testing on global
predictor variable parameters in the MGWR
model.
d. Perform partial testing on the parameters of local
predictor variables on the MGWR model.
e. Compare the GWR model with the MGWR
model with AICc criteria
4 RESULTS AND DISCUSSION
4.1 Description Research Variables
The following is a descriptive analysis of research
variables used:
Table 2: Description research variables.
Varia
b
el
N Mean Minimum Maximum
X1 34 775.88 85 4225
X2 34 5.2408 0.02 7.67
X3 34 0.3608 0.28 0.44
X4 34 11.135 3.78 27.69
X5 34 68.752 62.63 77.12
4.2 Spatial Assumption
The spatial assumption test aims to determine
whether the data to be analyzed has satisfied the
Modeling of School Participation Rate for Senior High School in Indonesia Using Mixed Geographically Weighted Regression Model
941
basic assumptions of spatial regression. From
normality test, data is normally distributed.
Multicollinearity shows if VIF value<10. The
following is VIF value from predictor variables:
Table 3: Variance influence factors value.
Predictor Variables VIF Value
Number of Scholl (X
1
) 1.20
PDRB (X
2
) 1.08
Gini Ratio (X
3
) 1.27
Percentage of Poor People (X
4
) 1.20
Percentage of Work Force on
Working Age Population (X
5
)
1.15
To test the effect of spatial heterogeneity, it was
used Breusch-Pagan test. Based on the test result, it
was obtained p-value, i.e., 0.01994 less than
=0.05. It means that there was heterogeneity
spatial in data. Furthermore, Moran’s I test was
implemented to find out the effect of spatial
dependency and get p-value=0.000. Finally, it was
concluded that there was spatial dependency in data.
4.3 Estimation Spatial Regression
This research has fulfilled the basic assumptions of
spatial regression thereby the next was step to
estimate the parameters of the spatial regression
model and to determine the weighted. The weighted
used were the kernel function weights while the
kernel function used was Fixed-Gaussian. To
determine the best model, look at the comparison of
AICc values between GWR and MGWR methods.
The summary of AICc values is represented in Table
4:
Table 4: Comparison of AICc value between GWR and
MGWR methods.
Methods AIC’c Values
Fixed Gaussian GWR method 242,280491
Fixed Gaussian MGWR
method
227,937452
Based on Table 4, the best method is the method
that has the smallest AICc value that is Fixed
Gaussian method MGWR method with AICc value
227.9374. Therefore, the method used to estimate
the best model in this research was Fixed Gaussian
MGWR method.
4.4 Partial Test of Local and Global
Parameters
After the best model was obtained, the next step was
to test the significance of global parameters with
GWR 4.0 software. Based on the calculation, the
variables that affect global was X
2
with standard
residual is 0.667, t-value is -2.078, and the
estimation is -.1371.
The other variables are local and the values
depend on each region. The summary of significant
variables can be seen in Table 5 as follows:
Table 5: Significant variables in each region
Province Significant Variables
DI Yogyakarta X1, X2, X3
Papua X2, X5
MGWR model for province of DIY is as follows:
=−0.002392
1
–1.371757X
2
+75.174818
3
Based on the model above, it can be said that
every increase of number of school (X
1
) will
decrease school participation rate as big as
0.002392, every increase of economic growth rate
(X
2
) will decrease school participant rate as big as
1.371757, and every increase of gini ratio (X
3
) will
increase school participation rate as big as
75.174818.
MGWR model for province of Papua is as
follow:
y = 166.903313 – 1.371757 X
2
– 1.062467 X
5
Based on the model above, can be said that every
increase of economic growth rate (X2) will decrease
school participation rate as big as 1.371757 and
every increase of percentage of work force on
working age population (X5) will decrease school
participation rate as big as 1.062467.
Predictor variables estimation that influences
both provinces is different. Their economic growth
rate is not increasing school participation rate. This
is because high economic growth rate is not always
causing all of the people to be prosperous, because
economic growth rate is often not followed by good
equity. Economic growth rate is significant in 34
provinces in Indonesia, but the other predictor
variables just influence locally. Hence, modeling of
school participation rate for senior high school is
ICPS 2018 - 2nd International Conference Postgraduate School
942
different too. Significant variables for every
province in Indonesia, is showed in Table 6.
Table 6: Significant variables in every province in
Indonesia.
Province
Significant
Variables
Aceh, North Sumatera , North
Sulawesi, Gorontalo, North
Maluku
X2
West Sumatera, Riau, Jambi,
Bengkulu, Kepulauan Riau,
NTT,
East Kalimantan, North
Kalimantan, Central Sulawesi,
South Sulawesi, Southeast
Sulawesi, West Sulawesi
X1, X2
South Sumatera, Lampung,
Kepulauan Bangka Belitung,
DKI
Jakarta, West Java, Central
Java,
DI Yogyakarta, East Java,
Banten, Bali, NTB, West
Kalimantan, Central
Kalimantan,
South Kalimantan
X1, X2, X3
Maluku, West Papua, Papua X2, X5
The thematic map of the significant variables of
every province in Indonesia is shown in Figure 1.
Figure 1: The thematic map of the significant
variablesof every province in Indonesia.
4.5 Conformity Test of MGWR Model
After MGWR model obtained by result of parameter
estimation, the next step was conformity testing for
MGWR model. Result of conformity test of MGWR
model is summarized in table 7.
Table 7: Result of conformity test of MGWR model.
Source DF SS MS F
Global 28 943.5
Residual 77
MGWR
Improvemen
t
6.85
3
418.1
20
61.0
14
MGWR
Residual
21.1
4
525.4
57
24.8
48
2.4555
Table 7 shows that F value, i.e., 2.4555 > F table,
i.e., 2.36. Therefore, the estimated MGWR model is
appropriate.
5 CONCLUSION
Based on the analysis and result which has been
done, it is concluded as follows:
Analysis result of school participation rate in
Indonesia by using mixed geographically weighted
regression (MGWR) model found that global
predictor variable was economy growth rate which
have a significant effect. Then, local predictor
variables are number of schools, gini ratio,
percentage of poor people, and percentage of work
force on working age population.
By using mixed geographically weighted
regression (MGWR) estimation, it was obtained
different model for every province because
significant predictor variables for every province in
Indonesia are the same.
REFERENCES
Badan Pusat Statistik., 2017. https://www.bps.go.id
/dynamictable/2015/12/22/1054/angka-partisipasi-
sekolah-aps-menurut-provinsi-2011-2017.html.
Accessed on 4
th
April 2018.
Chamidah, N., Syaifudin, T., and Rifada, M., 2014. The
Vulnerability of Dengue Hemorrhagic Fever Disease
in Surabaya Based on Spatial Logistic Regression
Approach. Journal of Applied Mathematical Sciences,
Vol.8, No.28, pp.1369-1379.
Fotheingham A.S., Brunsdon C., Charlton M., 2002.
Geographically Weighted Regression the Analysis of
Spatial Varying Relationships. United Kingdom: John
Wiley & Sons.
Mei, C.L. , He, S.Y. and Fang. K.T., 2004. A Note on the
Mixed Geographically Weighted Regression Model.
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Rahmatin, U.Z, dan Soejoto, A., 2017. Pengaruh Tingkat
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Modeling of School Participation Rate for Senior High School in Indonesia Using Mixed Geographically Weighted Regression Model
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