Estimation of Labor Force Participation Rate (TPAK) in Java's Data-Scarce Areas Using Ordinary Cokriging

Sofia Angelina, Nurul Gusriani, Firdaniza Firdaniza

Abstract


The quality of the labor force is crucial for economic development, and the Labor Force Participation Rate (TPAK) is a key employment indicator. In 2024, TPAK data collection in Java Island faced gaps in DKI Jakarta and Banten Provinces, limiting comprehensive labor mapping. To overcome this, spatial estimation methods are needed using data from surrounding areas and auxiliary variables. The Open Unemployment Rate (TPT) has a strong inverse relationship with TPAK, each 1\% TPAK increase lowers TPT by 14,82\%, making it a suitable auxiliary variable. This study estimates the 2024 TPAK for DKI Jakarta and Banten using the ordinary cokriging method, with TPT as the secondary variable. Spatial autocorrelation analysis confirmed that TPAK and TPT exhibit spatial patterns, are normally distributed, and meet stationarity assumptions. The best cross semivariogram model was identified using k-fold cross validation, which selected the spherical model with the lowest average RMSE of 4,24. The resulting ordinary cokriging model accurately predicted TPAK values, achieving a MAPE of 3,25\%. These estimates enable spatial visualization of TPAK in previously unobserved areas, contributing to a more complete understanding of labor participation across Java Island.

Keywords


ordinary cokriging; TPAK; k-fold cross validation; labor market

Full Text:

PDF

References


A. E. Ariesti and K. Asmara, “Analisis Faktor-Faktor Yang Mempengaruhi Tingkat Partisipasi Angkatan

Kerja (TPAK) di Pulau Jawa,” 2023.

R. P. Gautama, “Pengaruh Pengeluaran Perkapita, Jumlah Penduduk Miskin, Tingkat Pengangguran

Terbuka (TPT), dan Tingkat Partisipasi Angkatan Kerja (TPAK) Terhadap Pendapatan Pajak Provinsi

Jawa Tengah,” Emerging Statistics and Data Science Journal, vol. 2, no. 1, 2024.

Direktorat Statistik Kependudukan dan Ketenagakerjaan, “Booklet Sakernas Agustus 2024,” Aug. 2024.

Accessed: Mar. 09, 2025. [Online]. Available: https://www.bps.go.id/id/publication/2024/12/20/

b7ca9b2e159c6c0493290/booklet-sakernas-agustus-2024.html

Badan Pusat Statistik, “Jumlah Penduduk Menurut Provinsi di Indonesia (Ribu Jiwa), 2024,” Ac

cessed: Mar. 10, 2025. [Online]. Available: https://sulut.bps.go.id/id/statistics-table/2/OTU4IzI=

/jumlah-penduduk-menurut-provinsi-di-indonesia.html

N. Syamsuddin et al., “Pengaruh Tingkat Partisipasi Angkatan Kerja dan Pendidikan terhadap Pertum

buhan Ekonomi di Provinsi Aceh,” Jurnal Sosiohumaniora Kodepena, vol. 1, no. 2, May 2021. [Online].

Available: http://jsk.kodepena.org/index.php/jsk

G. A. Vanessa, X. Guilin, and D. Jiao, “The Effect of Labor Force Participation Rate (TPAK), Human

Development Index (HDI), and Unemployment on Poverty in Central Java in 2022,” International Journal

of Noesantara Islamic Studies, vol. 1, no. 1, 2024, doi: 10.70177/ijnis.v1i1.834

T. Saifudin, A. Faiza, L. Puspasari, and Z. ’Ilmatun Nurrohmah, “Estimating The Concentration of NO2

with The Cokriging Method in The Capital City of Jakarta,” BAREKENG: Jurnal Ilmu Matematika dan

Terapan, vol. 17, no. 4, pp. 1985–1996, Dec. 2023, doi: 10.30598/barekengvol17iss4pp1985-1996

H. Purnomo, S. A. Rande, and R. Prastowo, “Pemetaan Spasial Kadar Kobal pada Endapan Laterit dengan

Metode Ordinary Cokriging dan Inverse Distance Weighting,” Jurnal Sains Teknologi & Lingkungan, vol.

, no. 1, pp. 73–86, Jun. 2022, doi: 10.29303/jstl.v8i1.317

B. Pavani-Biju, J. G. Borges, S. Marques, and A. C. Teodoro, “Enhancing Forest Site Classification in

Northwest Portugal: A Geostatistical Approach Employing Cokriging,” Sustainability (Switzerland), vol.

, no. 15, Aug. 2024, doi: 10.3390/su16156423

N. A. Salsabila, S. Andriani, Mirisda, and D. A. Nohe, “Analisis Pengaruh Tingkat Partisipasi Angkatan

Kerja dan Indeks Pembangunan Manusia Terhadap Tingkat Pengangguran Terbuka Menggunakan Regresi

Probit Dan Logit,” May 2022.

F. D. P. Ramadhani and R. Widianita, “Analisis Dampak Tingkat Partisipasi Angkatan Kerja (TPAK)

terhadap Tingkat Kemiskinan di Provinsi Sumatera Barat,” Jurnal Multidisiplin Inovatif, vol. 8, no. 12,

pp. 2246–6110, 2024.

R. Usali, N. Nurwan, F. A. Oroh, and M. R. F. Payu, “Pemodelan Regresi Spasial Dependensi pada

Tingkat Partisipasi Angkatan Kerja di Indonesia Tahun 2020,” BAREKENG: Jurnal Ilmu Matematika

dan Terapan, vol. 15, no. 4, pp. 687–696, Dec. 2021, doi: 10.30598/barekengvol15iss4pp687-696

E. P. Putra, R. Goejantoro, and D. Suyitno, “Penaksiran Kandungan Klorida di Sungai Mahakam Wilayah

Samarinda Tahun 2017 dengan Metode Cokriging,” Jurnal EKSPONENSIAL, vol. 11, no. 2, 2020.

R. Mailanda, D. Kusnandar, and N. Miftahul Huda, “Analisis Autokorelasi Spasial Kasus Positif Covid-19

Menggunakan Indeks Moran dan LISA,” Buletin Ilmiah Math. Stat. dan Terapannya (Bimaster), vol. 11,

no. 3, pp. 483–492, 2022.

A. A. Rodrigues, T. M. Siqueira, T. L. C. Beskow, and L. C. Timm, “Ordinary Cokriging applied to generate

intensity-duration-frequency equations for Rio Grande do Sul State, Brazil,” Theor Appl Climatol, vol. 155,

no. 3, pp. 2365–2378, Mar. 2024, doi: 10.1007/s00704-024-04829-6

D. N. Gujarati and D. C. Porter, Basic Econometrics, Fifth Edition. McGraw-Hill Education, 2008.

E. A. Varouchakis, “Gaussian Transformation Methods for Spatial Data,” Geosciences (Basel), vol. 11, no.

, May 2021, doi: 10.3390/geosciences

A. Tsanawafa, D. A. Kusuma, and B. N. Ruchjana, “Penerapan Model Spatial Autoregressive Exogenous

pada Data Penetapan Warisan Budaya Takbenda di Pulau Jawa,” Jurnal Matematika Integratif, vol. 19,

no. 2, p. 137, Dec. 2023, doi: 10.24198/jmi.v19.n2.46526.137-147

J. LeSage and R. K. Pace, Introduction to Spatial Econometrics, 1st ed. New York: Chapman and

Hall/CRC, 2009, doi: 10.1201/9781420064254

R. Yendra and R. R. Risman, “Penerapan Metode Ordinary Kriging pada Pendugaan Kriminalitas di Kota

Pekanbaru Riau,” Jurnal Sains Matematika dan Statistika, vol. 5, no. 1, 2019.

A. Muhtar, D. Ningrum, and R. M. A. Hutagaol, “Penerapan Time Series Forecasting untuk Memprediksi

Pertumbuhan Ekonomi Indonesia 2024,” Data Sciences Indonesia (DSI), vol. 3, no. 2, pp. 79–89, May

, doi: 10.47709/dsi.v3i2.3263

M. Beenstock and D. Felsenstein, The Econometric Analysis of Non-Stationary Spatial Panel Data.

Springer International Publishing, 2019, doi: 10.1007/978-3-030-03614-0

M. C. Safira, A. Fauzan, M. Alfafisurya, and S. Adhiwibawa, “Interpolasi Polutan Nitrogen Dioksida (NO2)

di Kota Yogyakarta dengan Pendekatan Ordinary Kriging dan Inverse Distance Weighted,” Jurnal Aplikasi

Statistika & Komputasi Statistik, vol. 14, no. 2, pp. 55–66, Dec. 2022, doi: https://doi.org/10.34123/

jurnalasks.v14i2.359

N. N. Rohma, “Pendugaan Metode Ordinary Kriging (Studi Kasus Data Curah Hujan di Malang Raya),”

Jurnal Penelitian Ilmu Sosial dan Eksakta, vol. 2, no. 1, pp. 21–29, Sep. 2022, doi: 10.47134/trilogi.

v2i1.33

C. O. Wilke, Fundamentals of Data Visualization: A Primer on Making Informative and Compelling

Figures, 1st ed., vol. 1. Taiwan: O’Reilly Media, Inc., 2019.

J. Cao, C. Li, Q. Wu, and J. Qiao, “Improved Mapping of Soil Heavy Metals Using a Vis-NIR Spectroscopy

Index in an Agricultural Area of Eastern China,” IEEE Access, vol. 8, pp. 42584–42594, 2020, doi: 10.

/ACCESS.2020.2976902

X. Zhang, L. Lian, and F. Zhu, “Parameter fitting of variogram based on hybrid algorithm of particle

swarm and artificial fish swarm,” Future Generation Computer Systems, vol. 116, pp. 265–274, Mar. 2021,

doi: 10.1016/j.future.2020.09.026

A. Seddiki and S. Dehimi, “Effect of choosing a variogram model to predict salinity and its impact on the

environment and geotechnical structures,” Technium Social Sciences Journal, vol. 39, pp. 860–872, Jan.

[Online]. Available: www.techniumscience.com

P. Goovaerts, Geostatistics for Natural Resources Evaluation. New York: Oxford University Press, 1997.

B. Usowicz and J. Lipiec, “Spatial Variability of Saturated Hydraulic Conductivity and its Links with other

Soil Properties at the Commune Scale,” 2021, doi: 10.21203/rs.3.rs-138269/v1

K. Srinivasan et al., “An efficient implementation of artificial neural networks with K-fold cross validation

for process optimization,” Journal of Internet Technology, vol. 20, no. 4, pp. 1213–1225, 2019, doi: 10.

/160792642019072004020

X. Zhang and C.-A. Liu, “Model Averaging Prediction by K-Fold cross validation,” 2022, doi: https:

//doi.org/10.1016/j.jeconom.2022.04.007Getrightsandcontent

Y. Widyaningsih, G. P. Arum, and K. Prawira, “Aplikasi K-Fold Cross Validation dalam Penentuan Model

Regresi Binomial Negatif Terbaik,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 15, no. 2,

pp. 315–322, Jun. 2021, doi: 10.30598/barekengvol15iss2pp315-322

A. Antal, P. M. P. Guerreiro, and S. Cheval, “Comparison of spatial interpolation methods for estimating

the precipitation distribution in Portugal,” Theor Appl Climatol, vol. 145, no. 3–4, pp. 1193–1206, Aug.

, doi: 10.1007/s00704-021-03675-0

P. A. Dowd and E. Pardo-Ig´ uzquiza, “The Many Forms of Co-kriging: A Diversity of Multivariate Spatial

Estimators,” Math Geosci, vol. 56, no. 2, pp. 387–413, Feb. 2024, doi: 10.1007/s11004-023-10104-7

K. D. Lawrence, R. K. Klimberg, and S. M. Lawrence, Fundamentals of Forecasting using Excel. Industrial

Press, 2009.




DOI: https://doi.org/10.24198/jmi.v21.n2.65239.229-244

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Jurnal Matematika Integratif

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Published By:

Department of Matematics, FMIPA, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang KM. 21 Jatinangor


Indexed by:

width=width= width= width= width= width=

 

Visitor Number : free hit counter View My Stats


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.