International Journal of Engineering Bussines
and Social Science
Vol. 1 No. 3, January-February 2023, pages: 201 -207
e-ISSN: 2980-4108, p-ISSN: 2980-4272
https://ijebss.ph/index.php/ijebss
201
Introduction
The increase in population accompanied by economic growth in the Province of Aceh has increased the
ownership of motorcycles and private cars from year to year. Both modes of transportation have different capacities
that certainly have a significant impact on land transportation. The use of motor vehicles is already widespread not
only due to the growth of the population accompanied by an improvement in public welfare but also accompanied by
an increase in the activities of the population covering economic, social-cultural, and political fields, the extent of
activity in each field, the limited access to public transportation, and the number of public transportation available.
Transportation must provide maximum benefits to the community by minimizing time and cost. If the level
of public transportation service is low, then the public's interest in using private vehicles is much higher. Besides the
low level of public transportation service, many private transportation producers, especially motorcycles and private
Car Ownership Modeling in Aceh Province Using a Spatial
Regression Approach
Renni Anggraini
1
, Hikmah Mulyadi
2
, Zurnila Marli Kesuma
3
1,2
Faculty of Civil Engineering, Universitas Syiah Kuala,Banda Aceh, Indonesia
3
Faculty of Mathematics and Natural Science, Universitas Syiah Kuala,Banda Aceh, Indonesia
Email: hikmahmul[email protected]m, renni.anggraini@unsyiah.ac.id, zur[email protected]c.id
Corresponding Author: renni.angg[email protected]
Submitted: 08-02-2023 Revised: 12-02-2023, Publication: 20-02-2023
Keywords
Abstract
Keywords
Modeling;
Vehicle ownership;
Private cars;
Spatial regression;
Geoda;
The rise in car ownership in Aceh Province has been driven by population growth and
economic development. The location of the owner's residence impacts vehicle
ownership. There are common spatial dependencies in this area, meaning the
significance of an observation in one area is influenced by its importance in another.
Factors such as population, regional income, wages and salaries, area size, and road
length are believed to impact vehicle ownership. This study aimed to determine the
variables affecting vehicle ownership in Aceh Province. Spatial regression analysis
was used to identify the determinants of vehicle ownership in Aceh Province.
Secondary data was obtained from the Aceh Province One-Stop Administration
System Office (SAMSAT) for vehicle ownership documentation, the Aceh Province
Wealth and Income Service for vehicle ownership recap data, and other sources such
as the Central Bureau of Statistics of Aceh Province for information on population,
regional income, wages/salaries, area, road length, and ages. The results showed that
car ownership is dependent on geography. The Spatial Error Model (SEM) with an
Akaike Info Criterion (AIC) value of 107,919 was found to be the best spatial
regression model. Population (X1), regional income (X2), road length (X5), and age
over 17 (X6) were found to be the parameters with a significant level of 5% that
impact vehicle ownership in Aceh Province
e-ISSN: 2980-4108 p-ISSN: 2980-4272 IJEBSS
IJEBSS Vol. 1 No.3, January-February 2023, pages: 201 -207
202
cars, provide intensive promotions to increase sales, such as bonuses, low credit interest, and extended credit periods,
making the community tempted to own private vehicles.
Moreover, public transportation is considered no longer effective and efficient compared to private
transportation, such as the number of transfers required to reach the destination, the unpredictable frequency and
waiting time for public transportation, and the considerable distance for potential passengers to reach public
transportation. This condition will ultimately drive potential public transportation users to use private transportation
in their movements. This then leads to an increase in private transportation movements and causes various urban
transportation problems, such as the accumulation of transportation modes on city road networks, air pollution,
traffic accidents, and other transportation problems(Kawengian, Jansen, & Rompis, 2017). Therefore, the
government must implement policies limiting private vehicles and promoting reliable public transportation facilities.
Based on the above discussion, a spatial approach method was utilized to understand the complexity of the
transportation system. This method allows the visualization of vehicle ownership and its influencing variables to
provide easy-to-understand information and analysis, especially in terms of comparison(Susantono, Santosa, &
Budiyono, 2011). The variables used in this study were the population size, the regional income, the number of
wages/salaries of workers, the area size, the length of roads, and the people over 17 years old. This study aimed to
determine the relationship between the increase in private car ownership in each district/city in the Province of Aceh
and its influencing factors by using the aforementioned variables through spatial analysis. The ownership of private
cars is of great importance in the transportation system and is closely related to land-use planning.
Materials and Methods
The research variables consisted of independent variables (X) and dependent variable (Y). Independent
variables included population (X1) in terms of the number of people, regional income (X2) in terms of millions of
rupiah, wage amount (X3) in terms of rupiah, land area (X4) in terms of area, road length (X5) in terms of
kilometers, and people over 17 years old (X6) in terms of the number of people. The dependent variable was the
ownership of vehicles (Y) in terms of units.
Data analysis techniques can be described as follows:
1. Data Preparation
The data preparation process was performed using Microsoft Excel software. The first step was to select data in
each regency/municipality based on the variables used in the research. The total data obtained was 7, consisting
of 1 dependent variable and 6 independent variables. Furthermore, the data were combined into one sheet. The
districts/cities were alphabetically sorted so that it was equal to the district/city in the attribute table in the Arc-
GIS software.
2. Descriptive analysis
The descriptive analysis was carried out to explore the data to get a general picture of the data used. The data
exploration in this research was done by looking at the thematic map and summary statistics. The thematic map
was used to understand the pattern of vehicle ownership distribution in the Province of Aceh using the quantile
value in classifying the data distribution where the variable value is divided into four categories based on its
value interval, and summary statistics were used to look at the data distribution description.
3. Inferential analysis
Inferential analysis was performed through Pearson correlation and spatial regression analysis(Yuriantari, Hayati,
& Wahyuningsih, 2017). The steps are as follows:
a. Performing a Pearson correlation analysis
Pearson's correlation coefficient analysis was used to determine the independent variables that had a
significant relationship with the dependent variable. If the p-value <α, then the variable is used in the
formation of the model.
b. Forming a spatial weighting matrix
IJEBSS e-ISSN: 2980-4108 p-ISSN: 2980-4272
IJEBSS Vol. 1 No.3 February 2023, pages: 201 -207
203
The formation of the spatial weight matrix in this research used the queen contiguity type. The spatial weight
matrix with the queen contiguity type was suitable for use in regions with an asymmetrical shape, such as the
Province of Aceh. The first step was determining the number of closest neighbors (k) for the optimal spatial
weight matrix for each district/city. The determination of the k value was seen from Moran’s I statistic, which
was done iteratively. The value of Moran’s I was chosen based on the largest value produced. After the k
value had been determined, the spatial weight matrix could be formed.
c. Performing a spatial autocorrelation test
1) Global Moran Index
The global spatial autocorrelation test examined the spatial relationship among the districts/cities in the
Province of Aceh. The hypothesis used for the spatial autocorrelation test with the Global Moran's Index is
as follows:
a) H0: I = 0 (there is no global spatial autocorrelation among the regencies /municipalities in the
Province of Aceh).
b) H1: I ≠ 0 (there is global spatial autocorrelation among the regencies /municipalities in the Province
of Aceh).
2) Local Moran Index
The test of local spatial autocorrelation was performed to examine the spatial relationship in each
regency/city in the Province of Aceh that was truly affected by its neighboring regions. The hypothesis
used for the test of local spatial autocorrelation with the local Moran index is as follows:
a) H0: Ii = 0 (there is no local spatial autocorrelation in the i-th regency/municipality in the Province of
Aceh).
b) H1: Ii ≠ 0 (there is local spatial autocorrelation in the i-th regency/municipality in the Province of
Aceh).
The rejection criteria for decision-making in the global and local Moran index tests are to reject H0 if the
value of Z(I) > Z(α/2) or p-value < α.
3) Moran Scatter Plot
The local Moran index test results were visualized in the form of a Moran scatterplot. In the visualization,
the x-axis represented the prevalence of motor vehicle ownership, and the y-axis represented the
standardized average number of motor vehicle ownership in the i-th regency/municipality.
d. Interpreting spatial regression models and drawing conclusions
Results and Discussions
The Spread of Private Car Ownership
The data used in this research was secondary data from the Central Bureau of Statistics, published on the internet.
The Vehicle Ownership Data in the Province of Aceh in 2021 consisted of 23 Regencies/Municipalities. The
description of the Vehicle Ownership Data in the Province of Aceh is shown by a map based on the geographical
location of the Regencies/Municipalities as follows:
e-ISSN: 2980-4108 p-ISSN: 2980-4272 IJEBSS
IJEBSS Vol. 1 No.3, January-February 2023, pages: 201 -207
204
Figure 1. The mapping of the number of private cars
The output from the GeoDa software shows that the darker the color on the map, the higher the ownership of
vehicles in a particular area(Mariani & Fauzi, 2017). This is further presented in Table 1 for clarity.
Table 1.
The spread of private cars in the Province of Aceh
Color
Area
Number of Regency/
Municipality
Very high
1 Regency/ Municipality
High
1 Regency/ Municipality
Medium
6 Regencies/ Municipalities
Low
15 Regencies/ Municipalities
Based on Table 1 above, private vehicle ownership is high in Banda Aceh. It can be concluded that Banda
Aceh, which is the center of all economic, political, social, and cultural activities influencing the economic
movement, is experiencing an increase. Therefore, many people from outside the area are settling in Banda Aceh.
Pearson Correlation Testing
The purpose of the Pearson correlation test is to determine the significant impact of the dependent variable
on the independent variable. The results of the Pearson correlation test are presented in Table 2.
Table 2.
Pearson correlation analysis
Variable Definition
Correlation Value
Description
IJEBSS e-ISSN: 2980-4108 p-ISSN: 2980-4272
IJEBSS Vol. 1 No.3 February 2023, pages: 201 -207
205
Ownership of Private Cars (Y1)
Total Population (X1)
0.333
Weak
Regional Income (X2)
0.741**
Strong
Wages/Salary (X3)
0.656**
Strong
Area Size (X4)
-0.256
Weak
Road Length (X5)
-0.064
Very Weak
Age >17th (X6)
0.408
Medium
Table 2 indicates that among the six variables used in this study, two independent variables significantly
affect the ownership of private cars, including the amount of local revenue (X1) and salary (X3). These variables will
be used in further analysis.
Private Car Ownership
Based on the results of the Lagrange Multiplier statistical test, it can be shown that the spatial
autocorrelation in the spatial lag is significant with a p-value of 0.04101, which is less than 0.05. On the other hand,
the p-value for spatial autocorrelation in the spatial error is greater than 0.05, which is 0.08167, indicating that the
spatial autocorrelation in the spatial error is not significant. From the Lagrange Multiplier test, it can be concluded
that the modeling is less accurate using the OLS method as OLS ignores the spatial aspect of the data. Therefore, the
modeling is completed using the Spatial Autoregressive (SAR) and Spatial Error (SEM) regression methods(Yusnita,
Roza, & Rusli, 2020).
Moran Scatter Plot
Figure 2. Moran scatter plot
According to Figure 2, 5 regencies/municipalities have positive spatial autocorrelation, with one
regency/municipality located in quadrant I and four regencies/municipalities located in quadrant III. For a clearer
explanation, it is presented in Table 3.
Table 3.
Moran's scatter plot results
Factor
Indicator
Quadrant I (High-High)
Banda Aceh Municipality
Quadrant III (Low-Low)
Subulussalaam Municipality, Aceh Selatan Regency, Aceh Tenggara Regency dan Gayo Lues Regency
e-ISSN: 2980-4108 p-ISSN: 2980-4272 IJEBSS
IJEBSS Vol. 1 No.3, January-February 2023, pages: 201 -207
206
The regencies/municipalities in quadrant I indicate that Banda Aceh Municipality has a high rate of private
car ownership and is surrounded by neighboring areas with a high rate of private car ownership. The
regencies/municipalities in quadrant III indicate that Subulussalaam Municipality, Aceh Selatan Regency, Aceh
Timur Regency, and Gayo Lues Regency have a low rate of private car ownership and are surrounded by
neighboring areas that also have a low rate of private car ownership.
Spatial Error Model (SEM)
The Spatial Error Model (SEM) is a spatial regression model with spatial dependence through errors. This
means that SEM arises when the error values in one area are correlated with the error values in the surrounding area,
or in other words, there is a spatial correlation among errors. This is further presented in Table 4.
Table 4.
The results of the spatial error regression model
Variable
Coefficient
Probability
Description
Constant
3.28
0.385
Total Population (X1)
-2.98
0.000
Significant
Regional Income (X2)
1.588
0.000
Significant
Wages/Salary (X3)
0.993
0.719
Not Significant
Area Size (X4)
0.256
0.155
Not Significant
Road Length (X5)
-1.348
0.000
Significant
Age >17th (X6)
2.407
0.000
Significant
LAMBDA
0.835
0.000
Significant
significance α = 0.05
Based on Table 4, the resulting model is
 








, where ui = 0,835,


. The coefficient of the population is 2.298. This means that for every 1%
increase in population, private vehicle ownership in each regency/municipality will decrease by 2.298%. The
coefficient of regional income is 1.588. This means that for every 1% increase in regional income, private vehicle
ownership in each regency/municipality will increase by 1.588%. The coefficient of road length is 1.348. This means
that for every 1% increase in road length, private vehicle ownership in each regency/municipality will decrease by
1.348%. The coefficient of age over 17 years is 2.407. This means that for every 1% increase in the age above 17
years, private vehicle ownership in each regency/municipality will increase by 2.407%.
The matrix w_ij u_j can be interpreted as the impact of the change in the spatial residual in the neighboring
areas of a regency/municipality on the number of private vehicle ownership in that regency/municipality. In other
words, if the spatial residual in the neighboring area of a regency/municipality increases or decreases, then the
ownership of motor vehicles in that regency/municipality will also increase or decrease. Based on the calculation of
the Wy matrix using a spatial regression model that contains dependence, there are 23 spatial regression models for
each regency/municipality with its neighboring area using SEM that have been included in the equation. The models
for the 23 regencies/municipalities can be seen in Annex B.3.11 as an example of the interpretation of SEM for Aceh
Besar Regency is: :

   

 

 

 

 
 
 

The interpretation for the SEM in the Aceh Besar Regency region is that if the spatial residual in Aceh Jaya
Regency (u_2) increases by 1%, then the spatial residual in Bireuen Regency will increase by 0.278%, assuming the
other variables remain constant. The same goes for the influence of Pidie Regency (u_8) and Banda Aceh
Municipality (u_10) on Aceh Besar Regency, which can be interpreted similarly.
IJEBSS e-ISSN: 2980-4108 p-ISSN: 2980-4272
IJEBSS Vol. 1 No.3 February 2023, pages: 201 -207
207
Conclusion
The high concentration of private vehicle ownership was observed in Banda Aceh City, which can be
concluded that Banda Aceh City, being the center of all economic, political, social, and cultural activities, has
experienced an increase in economic activity. This results in an influx of people from outside the area settling in
Banda Aceh City. In the spatial error regression model, the influence of spatial correlation was accommodated by
incorporating the spatial weighting variable Lambda. The Probability value for this variable is 0.0000 < 0.05,
indicating evidence that the addition of this variable has a significant impact on the model. Additionally, in the
Diagnostic for Spatial Dependence, the values under the Probability column also show a value of 0.00014 > 0.05.
Furthermore, based on the R-Square value of the spatial error model 0.919778 or 91%, it can be concluded that the
Spatial Error Model (SEM) provides a better estimate. The Spatial Error Model (SEM) equation is based on the best
regression model with an AIC value of 107.909, with the following equation.:
 







.
Acknowledgments
I am / We are grateful to two anonymous reviewers for their valuable comments on the earlier version of this paper.
References
Kawengian, Erlangga, Jansen, Freddy, & Rompis, Semuel Y. R. (2017). Model Pemilihan Moda Transportasi
Angkutan Dalam Provinsi. Jurnal Sipil Statik, 5(3).
Mariani, Scolastika, & Fauzi, Fatkhurokhman. (2017). The arcview and GeoDa application in optimization of spatial
regression estimate. Journal of Theoretical and Applied Information Technology, 95(5), 1102.
Susantono, Bambang, Santosa, Wimpy, & Budiyono, Arif. (2011). Kepemilikan kendaraan dan pola perjalanan di
wilayah Jabodetabek. Jurnal Transportasi, 11(3).
Yuriantari, Nurmalia Purwita, Hayati, Memi Nor, & Wahyuningsih, Sri. (2017). Analisis autokorelasi spasialtitik
panas di Kalimantan Timur menggunakan indeks moran dan local indicator of spatial autocorrelation (LISA).
Eksponensial, 8(1), 63–70.
Yusnita, Yessy, Roza, Angelalia, & Rusli, Andi Mulya. (2020). Model Pemilihan Moda Berdasarkan Variabel
Kepemilikan Kendaraan Dan Kategori Luas Lahan Parkir Dengan Teknik Analisis Regresi. PYTHAGORAS:
Journal of the Mathematics Education Study Program, 9(2), 95–105.
© 2023 by the authors. Submitted
for possible open access publication
under the terms and conditions of the Creative Commons Attribution (CC BY SA) license
(https://creativecommons.org/licenses/by-sa/4.0/).