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Analysis of the Geographically and Temporally Weighted Regression (GTWR) of the GRDP the Construction Sector in Java Island Sugi Haryanto 1,*.
Muhammad Nur Aidi 2.
Anik Djuraidah 2 Sub directorate of Construction Statistics at BPS-Statistics Indonesia.
Jl.
Sutomo No.
Jakarta Master of Applied Statistics IPB University Lecturer at Statistics Department.
IPB University.
Jl.
Meranti Wing 22 Level 4.
IPB Dramaga.
Bogor 16680.
Indonesia Corresponding Author .
-mail: sugih@bps.
Received: 14 December 2018 / Accepted: 13 August 2019 / Published: 16 August 2019 Abstract.
The construction sector is one of the sectors that has strategic value in the national economy of Indonesia.
Economic activity in an area is measured using Gross Regional Domestic Product (GRDP), therefore the development of economic activities in the construction sector can be seen from its GRDP.
The Geographically and Temporally Weighted Regression (GTWR) model is a development of the Geographically Weighted Regression (GWR) model which takes into account the diversity of locations and times.
This study used secondary data, namely the GRDP of the construction sector as a response variable, and four explanatory variables, namely the size of population, local revenue, area and the number of construction establishments.
The SXUSRVH RI WKH VWXG\ LV WR GHWHUPLQH WKH IDFWRUV WKDW LQyAXHQFH HDFK UHJHQF\PXQLFLSDOLW\ each year observing the GRDP of the construction sector in Java together with the GTWR This model is more effective in describing the GRDP value of the construction sector of regencies/municipalities in Java Island in 2010-2016.
This is indicated by the decrease in the values of Root Mean Square Error (RMSE).
Mean Absolute Deviation (MAD), and the Mean Absolute Percentage Error (MAPE).
Keywords: construction.
GRDP.
GRDP the construction sector.
GTWR, spatial Abstrak.
Sektor konstruksi adalah salah satu sektor yang memiliki nilai strategis dalam perekonomian nasional.
Aktivitas ekonomi di suatu daerah diukur menggunakan Produk Domestik Regional Bruto (PDRB).
Perkembangan kegiatan ekonomi di sektor konstruksi dapat dilihat dari PDRB sektor konstruksi.
Model Geographically and Temporally Weighted Regression (GTWR) adalah pengembangan dari model Geographically Weighted Regression (GWR) dengan mempertimbangkan keragaman lokasi dan waktu.
Penelitian ini menggunakan data sekunder, yaitu data PDRB sektor konstruksi sebagai variabel respon dan empat variabel penjelas, yaitu jumlah penduduk, pendapatan daerah, luas, dan jumlah perusahaan konstruksi.
Tujuan dari penelitian ini adalah untuk menentukan faktor-faktor yang mempengaruhi masing-masing kabupaten / kota dan setiap tahun mengamati PDRB sektor konstruksi di Jawa dengan model GTWR.
Model GTWR lebih efektif untuk menggambarkan nilai PDRB sektor konstruksi kabupaten/kota di Pulau Jawa pada 2010-2016.
Ini ditunjukkan oleh penurunan nilai Root Mean Square Error (RMSE).
Mean Absolute Deviation (MAD), dan Mean Absolute Perscentage Error (MAPE).
Kata kunci: konstruksi.
PDRB.
PDRB sector konstruksi.
GTWR, spasial Analysis of Geographically.
(Haryanto et al.
Introduction Construction is an economic activity that produces goods and services related to buildings, which are integrated with the land where they are located, and used as places of UHVLGHQFH RU IRU RWKHU yAHOGV RI DFWLYLW\ 7KH construction sector has strategic value in the national economy (BPS-Statistics Indonesia.
It plays an important role in national economic conditions, determined by the size of the its contribution to the growth of other business sectors.
The development of the construction sector will support the creation of social and economic infrastructure, creating better accessibility, which can spur the growth of other economic sectors (Giyarsih, 2.
Infrastructure development is the focus of the government development set out in the 20152019 National Medium-Term Development Plan (NMTDP).
It consists of various types of development projects, including the construction of roads, bridges, airports, amongst others.
Based on the ministry/agency agreement only 30 projects were prioritized, most of which were located in Java.
The development of the property sector, which is supported by the growth of the construction sector, can expand central economics (Wibowo et al.
, 2.
The development of the construction sector needs to be monitored and evaluated with actual, accurate and continuous statistical data (BPS-Statistics Indonesia, 2.
The regional economy is said to grow and develop if the goods and services produced in a certain period are greater than in the previous period, which is then reduced to value-added.
Gross Regional Domestic Product (GRDP) is one of the indicators used to measure economic activity in a region.
Therefore, the development of economic activities in the construction sector can be seen from its GRDP.
6HYHUDO VWXGLHV RQ IDFWRUV WKDW LQyAXHQFH *5'3 KDYH EHHQ FRQGXFWHG 6DyAWUL DQG Aliasuddin .
found that the population KDGDSRVLWLYHDQGVLJQLyAFDQWHIIHFW1DVXWLRQ .
examined the effect of PAD on the PDRB RI%DQWHQ3URYLQFHZLWKVLJQLyAFDQWLQyAXHQWLDO ISSN: 0852-0682.
EISSN: 2460-3945 PutraAos .
research established WKDW WKH DUHD KDG D VLJQLyAFDQW LQyAXHQFH EXW in a negative direction, while Afandi and SoesatyoAos .
research shows that the number of industrial manufacturers has a SRVLWLYHLQyAXHQFHRQ*5'3 Data based on the regional and time require analysis that considers the diversity between regions and times.
Such diversity occurs due to differences in characteristics.
ZKLFK DUH LQyAXHQFHG E\ FXOWXUH HFRQRP\ education, thought and recreation, amongst others (Jayadinata, 1.
The development of a region involves the process of changing characteristics over time (Anisah et al.
, 2.
The analytical method used in the study is Geographically and Temporally Weighted Regression (GTWR), developed by Huang et al.
to model housing prices in the city of Calgary (Canad.
in 2002-2004.
The GTWR model is a development of the Geographically Weighted Regression (GWR) method developed by Brunsdon et al.
Fotheringham et al.
and Fotheringham et al.
, which considers the elements of location and time.
The results of GTWR model were regression models whose parameter values apply only to each location and each time of observation (Fotheringham et al.
In GTWR, a weighting matrix element W is used, whose magnitude depends on the proximity between locations and times.
The effect of weighting will be greater the closer a location or time.
The weighting function used for GTWR in this paper is the Kernel Bisquare The study uses GRDP data on the construction sector from 119 regencies/ municipalities in Java from the period 2.
to 2016 as the response variable.
The factors WKDWZLOOEHH[DPLQHGIRUWKHLULQyAXHQFHRQWKH GRDP of the construction sector are population size, local revenue (PAD), area, and the number of construction establishments.
The research data has location and time dimensions, so it is SRVVLEOH WR XVH WKH *7:5 PRGHO 7KH EHQHyAW of this research is to provide information to regency/municipality governments in )RUXP*HRJUDA9RO -XO\ Analysis of Geographically.
(Haryanto et al.
Java regarding the modeling of factors that affect the GRDP of the construction sector.
Consequently, these governments can develop their respective policies more appropriately and evaluate them annually.
The purpose of this study is to determine the factors that LQyAXHQFHWKH*5'3RIWKHFRQVWUXFWLRQVHFWRU in each regency/municipality in Java each Research Method Data The study uses secondary data from Badan Pusat Statistik (BPS-Statistics Indonesi.
and the Directorate General of Fiscal Balance (DGFB), namely the GRDP data of the construction sector as a response variable and four explanatory variables, population size, local revenue, area and the number of construction establishments.
The scope of the research data is 119 regencies/municipalities in Java Island over the period 2010 to 2016.
The variables used in the study are shown in Table Table 1.
'HWDLOVRIWKHYDULDEOHVXVHGDVVHFRQGDU\GDWD
Variable Unit Source Million rupiah BPS-Statistics Indonesia Population (X.
People BPS-Statistics Indonesia Local revenue (X.
Million rupiah
DGFB
Area (X.
Km2 BPS-Statistics Indonesia GRDP of the sector (Y) Number of Construction Establishments (X.
Establishment BPS-Statistics Indonesia Geographically Temporally Weighted Regression (GTWR) Model The Geographically and Temporally Weighted Regression (GTWR) method is a development of the GWR method, taking into account location and time elements )RUXP*HRJUDA9RO -XO\ (Huang et al.
GTWR takes into account non-stationary spatiotemporal aspects in the parameter estimation, with a weighting matrix based on the distance determined from the coordinates .
, y, .
between observation ith and all the other observations, according to the GWR technique (Fotheringham et al.
Huang et al.
formulated the GTWR model to be written as follows:
is the value of the response variable observed at location .
i, v.
and time .
7KH UHJUHVVLRQ FRHIyAFLHQW Ei.
i,vi,t.
at point i is obtained by using the Weighted Least Squares (WLS) method, with the following .
where W.
i, vi, t.
=diag.
i1,w2n,A,wi.
is the weighting matrix at location () and time .
and the temporal distance is dT, then these can be combined to form a spatiotemporal distance .
ZKHUHUDQGADUHVFDOHIDFWRUVWREDODQFHWKH various effects used to measure spatial and temporal distance in the metric system.
If Euclid distance and decay-based distanceGaussian functions are used to construct the spatiotemporal weight matrices, then:
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7KH SDUDPHWHU i LV REWDLQHG IURP WKH FULWHULD by minimizing the cross-validation (CV) by LQLWLDOL]LQJWKHLQLWLDOYDOXHiDVEHORZ .
Determining spatio-temporal bandwidth .
ST).
Calculating the weighting matrix of the GTWR model with kernel bisquare functions.
Estimating the GTWR parameters.
Interpret the results by drawing maps EDVHGRQFRHIyAFLHQWVWKDWKDYHDVLJQLyAFDQW effect on the construction sector GRDP in the GTWR model.
Draw conclusions and make suggestions.
7KH HVWLPDWRU SDUDPHWHUV U DQG s FDQ WKHQ be obtained by an iterative method based on 3.
Results and Discussion WKHHVWLPDWLRQUHVXOWViDQGZKLFKUHVXOWVLQD 3.
Description minimum CV.
The relationship between the response and explanatory variables can be established Data Analysis Procedure based on Pearson correlation values, as shown Analysis and modeling were conducted in Table 2.
Local revenue (X.
is the highest using the statistical program R-3.
The stages FRUUHODWLRQ FRHIyAFLHQW YDOXH EHWZHHQ WKH of analysis in the study were as follows:
explanatory and response variables at 0.
Conduct data exploration to obtain while the lowest correlation is area (X.
, at an overview and information about 7KHFRUUHODWLRQFRHIyAFLHQWEHWZHHQORFDO the response variable and explanatory revenue and the GRDP of the construction variables used.
sector is positive and high, as the infrastructure Employ a normality test for the residuals.
in many regions uses regional income and transformation is used if they are not expenditure (APBD) budget funds, some of which are local revenue.
A multicollinearity test was conducted Identify patterns of relationship between response and explanatory variables using to determine the correlation between the correlation analysis and multicollinearity explanatory variables used.
It is performed by FDOFXODWLQJWKHYDOXHRI9,) 9DULDQFH,QyADWLRQ tests of the explanatory variables.
Identify spatial diversity and time by:
, with k A combined and annual Breusch- Facto.
with the formula Pagan test to observe spatial diversity.
being the many explanatory variables.
is the The boxplot method to observe FRHIyAFLHQWRIGHWHUPLQDWLRQREWDLQHGIURPWKH temporal diversity.
explanatory variable chosen as the response Perform GTWR modeling, which includes: variable, with the other explanatory variables Calculating Euclid distance at becoming the explanatory variables for the coordinates .
i,vi,ti ).
response variable.
E 2EWDLQLQJ RSWLPXP HVWLPDWLRQ RI The results of the multicollinearity test are SDUDPHWHU i LWHUDWLYHO\ ZLWK LQLWLDO shown in Table 3.
VIF values lower than 10 YDOXHV i0 and bST = bS or spatial indicate that there is no multicollinearity in the bandwidth, by comparing the explanatory variable used.
The data used are cross-validation (CV) panel data, so the VIF value is calculated for value, thus obtaining parameter each year and a combination of all years.
HVWLPDWHVADQGU
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Table 2.
3HDUVRQFRUUHODWLRQFRHCOFLHQWEHWZHHQH[SODQDWRU\DQGUHVSRQVHYDULDEOHV
Response Variables Population Local Revenue Area Establishments GRDP of the construction sector Table 3.
9DOXHVWKH9,)RIH[SODQDWRU\YDULDEOHV
Response variable Year Population Local Revenue Area Establishment Combination Table 4.
%UHXVFK3DJDQ7HVW5HVXOWV
Year Breusch-Pagan Value p-value Combination 74 y 10-13* 1RWH VLJQLAFDQWDW VLJQLAFDQWDW Figure 1.
Temporal heterogeneity using a boxplot Testing for the normality of the residuals of linear regression was conducted based on the Shapiro-Wilk (SW) test.
The test results )RUXP*HRJUDA9RO -XO\ obtained a value of 0.
972, with a p-value of This indicates that the distribution of the residuals from the model has not followed ISSN: 0852-0682.
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normal distribution.
Transformation was made by the Box-Cox method to deal with side The Box-Cox transformation results obtained a minimum lambda value The resulting lambda value is approaching 0, so the transformation used in this study is the function of natural logarithms .
in the response variable.
Spatial heterogeneity testing using the Breusch-Pagan test statistic was performed to determine whether there was diversity due WR VSDWLDO LQyAXHQFH 7KH WHVWV DUH FRQGXFWHG annually and simultaneously on the 119 regencies/municipalities in Java Island in The Breusch-Pagan test results are presented in Table 4.
These, in combination DQG DQQXDOO\ DUH VLJQLyAFDQW DW WKH SHUFHQW OHYHO DSDUW IURP ZKHQ LW LV VLJQLyAFDQW at the 10% real level.
It can therefore be said that there is spatial heterogeneity in the GRDP construction sector data of the regencies/ municipalities in Java Island in 2010-2016.
Inequality of spatial diversity is thought to be caused by differences in characteristics in each To ascertain the existence of temporal heterogeneity, the data were described using D ER[SORW DV VKRZQ LQ )LJXUH 7KH yAJXUH shows that the distance between GRDP value quartiles in the construction sector is different each year.
This difference illustrates the diversity of data, so it can be said that between years there is such diversity.
LnGRDP in the construction sector in Java has spatial, as well
DV WHPSRUDO GLYHUVLW\ 2QH RI WKH VXLWDEOH
models to model this in the construction sector in Java Island is the GTWR model.
Geographically and Temporally Weighted Regression (GTWR) Model The weighting matrix used in the study was the Bisquare weighting function, which produces the same bandwidth in each location.
Determination of optimum bandwidth was made by calculating the smallest CV .
ross validatio.
This was 411.
572, with a spatiotemporal bandwidth value .
ST) of 5.
In addition, the RSWLPXP SDUDPHWHU UDWLR i ZDV JHQHUDWHG DW
ZLWK D VSDWLDO GLVWDQFH SDUDPHWHU U RI
DQGWHPSRUDOSDUDPHWHU s RI Estimator of the parameters of the GTWR model A description of the parameter estimator using the GTWR method is given in Table 5.
The estimator of the parameter intercept in GTWR model, the LnPDRB of the construction sector in Java, ranged from 13.
178 to 13.
730, or 528606.
45 million rupiahs if there were no changes in the explanatory variables.
While the explanatory variables of population (X.
, local revenue (X.
and the number of construction establishments (X.
are positive, meaning that if there is an increase in population, local revenue or the number of construction establishments of 1 unit, the value of the GRDP of the construction sector will increase by times if there is no change in the other explanatory variables.
This is inversely proportional to the explanatory variable area (X.
which has a negative value in all regencies/municipalities every year, meaning that an area increase of 1 km2 will reduce the value of the construction sector GRDP by and if there is no change in the other explanatory Table 5.
6XPPDU\RIWKHFRHCOFLHQWHVWLPDWRURIWKHSDUDPHWHUVRIWKH*7:5PRGHO
Variable Minimum Maximum Mean Intercept Population 165y10 Local Revenue 488y10-8 Area Establishment 924y10-4 ISSN: 0852-0682.
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Standard Error
)RUXP*HRJUDA9RO -XO\
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Interpretation of the GTWR model The GTWR model generates different parameter estimating values in each location and year.
This is in accordance with the purpose of its use, which is to form a model in each region for every year (Conita & Purwaningsih.
The results of the model can be used to evaluate the policies that have been applied by each regency/municipality.
In addition, it can also be used as a basis to decide whether the policies are still relevant or need to be updated.
In the GTWR model, each variable has a different effect.
Likewise, the magnitude of the SDUDPHWHUFRHIyAFLHQWYDOXHDOVRYDULHVLQHDFK regency/municipality and year.
For example, the GTWR model for Malang Regency in 2015 is as follows:
For Malang Regency in 2016 it is as follows:
For Malang City in 2015 it is as follows:
And for Malang City in 2016 it is as follows:
The interpretation of the GTWR model for Malang Regency in 2015 is the estimated value of the construction sector GRDP of e13.
31 or 53 million rupiahs if there is no change in the independent variables.
If the population of Malang Regency in 2015 increases by 1 person, it will increase the estimated value of construction sector GRDP by , or 00000105 times, if other explanatory variables )RUXP*HRJUDA9RO -XO\ UHPDLQXQFKDQJHG7KHFRHIyAFLHQWRIWKHORFDO revenue explanatory variable of 8.
96y108 explains that the estimated GRDP of the construction sector will increase by , or 0000000896 times, if local revenue increases by 1 million rupiahs and there is no change in the other explanatory variables.
If there is a change of 1 km2 in the area of Malang Regency in 2015 and other explanatory variables do not change, then the estimated value of the GRDP of the construction sector will decrease by , or 0.
99985301 times.
The estimation of the GRDP of the construction sector Malang Regency in 2015 will increase by , or 1.
00034006 times, when the number of construction establishments increases by 1 and other explanatory variables are unchanged.
Testing the Parameters of the GTWR Model Testing of the GTWR model was conducted to establish the explanatory YDULDEOHVWKDWLQyAXHQFHGWKHUHVSRQVHYDULDEOH for each time and location.
Most regions KDYH GLIIHUHQW LQyAXHQWLDO IDFWRUV ZKLFK DUH because each regency/municipality has different characteristics, both in terms of geography, public facilities, social facilities and JRYHUQPHQW 7KH GLIIHUHQFHV LQ LQyAXHQFLQJ factors allow each location to develop its own policies in accordance with the conditions and needs in their respective regions in order to increase the value of construction sector GRDP.
Regency/municipality grouping based RQ LQyAXHQWLDO IDFWRUV XVLQJ WKH *7:5 PRGHO is illustrated in Figure 2.
In the GTWR model.
WZR JURXSV ZHUH IRUPHG 7KH yAUVW JURXS was the regencies/municipalities whose FRQVWUXFWLRQ VHFWRU *5'3 ZDV LQyAXHQFHG E\ population (X.
, local revenue (X.
and area (X.
The second group comprised regencies/ municipalities whose construction sector *5'3 ZDV LQyAXHQFHG E\ SRSXODWLRQ .
local revenue (X.
, area (X.
and number of construction establishments (X.
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EISSN: 2460-3945
Analysis of Geographically.
(Haryanto et al.
)LJXUH0DSRIUHJHQF\PXQLFLSDOLW\GLVWULEXWLRQEDVHGRQLQyAXHQFLQJIDFWRUV Table 6.
5HJHQF\PXQLFLSDOLW\JURXSLQJEDVHGRQLQyAXHQWLDOIDFWRUV Year X1.
X2.
X1.
X2.
X3.
All regencies/municipalities in Java Pamekasan.
Sumenep.
Lebak
2WKHUUHJHQFLHVPXQLFLSDOLWLHV
Jombang.
Nganjuk.
Madiun.
Magetan.
Sampang.
Pamekasan.
Sumenep.
Surabaya City.
Batu City.
Lebak.
Tangerang
2WKHUUHJHQFLHVPXQLFLSDOLWLHV
Lumajang.
Jember.
Jombang.
Nganjuk.
Madiun.
Magetan.
Sampang.
Pamekasan.
Sumenep.
Kediri City.
Pasuruan City.
Mojokerto City.
Surabaya City.
Batu City.
Lebak.
Tangerang
2WKHUUHJHQFLHVPXQLFLSDOLWLHV
Jombang.
Nganjuk.
Madiun.
Magetan.
Sampang.
Pamekasan.
Sumenep.
Surabaya City.
Batu City.
Lebak
2WKHUUHJHQFLHVPXQLFLSDOLWLHV
All regencies/municipalities in Java All regencies/municipalities in Java ISSN: 0852-0682.
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necessary to increase local revenue as a source of development.
The explanatory variable of area has a negative effect on each regency/ municipality and in each year.
The smaller the area, the easier the access between regions, meaning development is faster and that there is an increase in the GRDP of the construction The explanatory variable of the number of construction establishments have a positive effect on each regency/municipality each Conclusion The factors that affected the GRDP of year.
However, in 2012-2014 some regencies/ the construction sector varied amongst the PXQLFLSDOLWLHVGLGQRWVHHDVLJQLyAFDQWHIIHFW7KH regencies/municipalities in Java in the period increasing number of construction companies is 2010 to 2016.
this can be used as material for H[SHFWHGWRVLJQLyAFDQWO\LQFUHDVHWKH*5'3RI policymaking and evaluation in accordance the construction sector, but in some regencies/ ZLWK WKH GLIIHULQJ LQyAXHQWLDO IDFWRUV 7KH PXQLFLSDOLWLHVWKLVKDVQRVLJQLyAFDQWHIIHFWIRU explanatory variable of population has a example.
Sampang Regency, which has a large SRVLWLYH DQG VLJQLyAFDQW HIIHFW :H NQRZ WKDW QXPEHURIFRPSDQLHVWKDWPDGHQRVLJQLyAFDQW humans need facilities that must be built to contribution to increasing construction sector support their lives .
increasing population in GRDP.
The ease of obtaining permission to establish a company is unable to increase the an area will require many such facilities.
The explanatory variable of local GRDP of the construction sector.
UHYHQXH DOVR KDV D SRVLWLYH DQG VLJQLyAFDQW The construction of facilities built Acknowledgments We would like to acknowledge BPSby local governments involves use of the Regional Revenue and Expenditure Budget.
Statistics Indonesia for data and funding part of which is local revenue.
So if a local support, both thesis mentors for their government wants to increase the construction supporting knowledge, and all the team at the of facilities for the community, it is also Statistics Department of IPB University.
Details of the regency/municipality JURXSLQJV EDVHG RQ LQyAXHQWLDO IDFWRUV DUH presented in Table 6.
The table shows that all regencies/municipalities in Java had the VDPH LQyAXHQWLDO IDFWRUV LQ DQG Changes occurred in 2011-2014, when the explanatory variable of the number of FRQVWUXFWLRQHVWDEOLVKPHQWVZDVQRWVLJQLyAFDQW in several regencies/municipalities.
References