Unbalanced Panel Data Regression Modelling Using Maximum Likelihood Method with Minimum Variance Quadratic Unbiased Estimation Weighting
Keywords:
Unbalanced Panel Data, one-way Error Component, MIVQUE, ML
Abstract
Panel data analysis integrates cross-sectional and time-series information, enabling inference on interfirm differences and temporal dynamics. In practice, observations are often incomplete across time, producing an unbalanced panel structure that requires appropriate estimation. This study applies a one-way error component panel regression model in which unobserved heterogeneity is captured by individual-specific effects. Error variance components are estimated using Minimum Variance Quadratic Unbiased Estimation (MIVQUE), while regression parameters are obtained via Maximum Likelihood (ML). The dataset comprises manufacturing firms listed on the Indonesia Stock Exchange over 2017–2021. The study aims to construct an unbalanced panel regression framework for assessing the effects of financial indicators on stock returns in the Indonesian manufacturing sector. The estimation results yield β0=0.0690, β1 =-0.0207, and β2=0.1045, producing the fitted model Yit=0.0690-0.0207(X1)it+0.1045(X2 )it. The debt-to-equity ratio is negatively associated with stock returns, whereas the net profit margin shows a positive relationship. Overall, combining ML estimation with MIVQUE-based variance component estimation provides an effective approach for modeling stock returns under an unbalanced one-way error component setting.
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References
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[2] C. Tania and B. Kurniawan, “Pajak, Tunneling Incentive, Mekanisme Bonus Dan Keputusan Transfer Pricing (Studi Empiris Pada Perusahaan Manufaktur Yang Terdaftar Di Bursa Efek Indonesia Tahun 2014-2017),” TECHNOBIZ: International Journal of Business, vol. 2, no. 2, p. 82, 2019, doi: 10.33365/tb.v3i2.329.
[3] M. Irman and A. A. Purwati, “Analysis On The Influence of Current Ratio, Debt to Equity Ratio, and Total Asset Turnover Toward Return on Assets on the Otomotive and Component Company That Has Been Registered in Indonesia Stock Exchange Within 2011-2017,” International Journal of Economics Development Research (IJEDR), vol. 1, no. 1, pp. 36–44, Jan. 2020, doi: 10.37385/ijedr.v1i1.26.
[4] N. Shrestha, “Detecting Multicollinearity in Regression Analysis,” Am J Appl Math Stat, vol. 8, no. 2, pp. 39–42, Jun. 2020, doi: 10.12691/ajams-8-2-1.
[5] U. H. Humaira and J. Nugraha, “Analysis of Factors Affecting the Human Development Index in West Kalimantan Province using Data Panel Data Regression,” EKSAKTA: Journal of Sciences and Data Analysis, vol. 18, pp. 97–105, 2018, doi: 10.20885/eksakta.vol18.iss2.art2.
[6] M. Elfriede and D. A. Suryawan, “Determinants of Poverty in North Sumatra in 2017-2021 using Panel Data Regression Analysis Method,” Journal of Analytical Research, Statistics and computation, vol. 2, no. 2, pp. 52–65, 2023, [Online]. Available: https://jarsic.org/main/article/view/22%0Ahttps://jarsic.org/main/article/download/22/14
[7] R. D. W. I. Astuti, “Analisis Data Panel Tidak Lengkap Model Komponen Error Dua Arah dengan Metode Minimum Variance Quadratic Unbiased Estimation (MIVQUE),” Semarang: Universitas Diponegoro, 2010.
[8] E. N. Amaliah, D. Darnah, and S. Sifriyani, “Regresi Data Panel dengan Pendekatan Common Effect Model (CEM), Fixed Effect model (FEM) dan Random Effect Model (REM) (Studi Kasus: Persentase Penduduk Miskin Menurut Kabupaten/Kota di Kalimantan Timur Tahun 2015-2018),” ESTIMASI: Journal of Statistics and Its Application, vol. 1, no. 2, p. 106, Jul. 2020, doi: 10.20956/ejsa.v1i2.10574.
[9] B. H. Baltagi and Y.-J. Chang, “Incomplete panels,” J Econom, vol. 62, no. 2, pp. 67–89, Jun. 1994, doi: 10.1016/0304-4076(94)90017-5.
[10] S. U. Dilla, Y. Andriyana, and Sudartianto, “The influence of SO4 and NO3 to the acidity (pH) of rainwater using minimum variance quadratic unbiased estimation (MIVQUE) and maximum likelihood methods,” 2017, p. 020039. doi: 10.1063/1.4979455.
[11] S. A. Ania, “Analisis Data Panel Tidak Lengkap Model Komponen Galat Dua Arah Dengan Metode Restricted Maximum Likelihood,” Makassar: Universitas Hasanuddin, 2020.
[12] J. Wahdaniyah, “Pemodelan Regresi Data Panel Tidak Seimbang Menggunakan Metode Feasible Generalized Least Square Pada Data Perusahaan Manufaktur Di Bursa Efek Indonesia,” Makassar: Universitas Hasanuddin, 2022.
[13] M. D. Purnama and M. E. Mustafidah, “Relationship Between Temperature and Humidity on Rainfall,” Engineering, Mathematics and Computer Science Journal (EMACS), vol. 6, no. 2, pp. 151–156, May 2024, doi: 10.21512/emacsjournal.v6i2.11466.
[14] S. Weisberg, Applied linear regression. Canada: John Wiley & Sons., 2005.
[15] A. Dewi Anggraeni Chairunnisa and A. Fauzan, “Implementation of Panel Data Regression in the Analysis of Factors Affecting Poverty Levels in Bengkulu Province in 2017-2020,” EKSAKTA: Journal of Sciences and Data Analysis, pp. 40–45, Jan. 2023, doi: 10.20885/EKSAKTA.vol4.iss1.art5.
[16] S. Athey, M. Bayati, N. Doudchenko, G. Imbens, and K. Khosravi, “Matrix Completion Methods for Causal Panel Data Models,” J Am Stat Assoc, vol. 116, no. 536, pp. 1716–1730, Oct. 2021, doi: 10.1080/01621459.2021.1891924.
[17] T. Rahayu, “Pemodelan Regresi Data Panel Dengan Pendekatan Model Efek Umum Menggunakan Metode Kuadrat Terkecil Pada Laju Inflasi di Sulawesi,” 2021. [Online]. Available: https://repository.unhas.ac.id/id/eprint/7061/%0Ahttps://repository.unhas.ac.id/id/eprint/7061/2/H051171509_skripsi bab 1-2.pdf
[18] S. S. Purwaningsih, E. Habinuddin, and E. Sartika, “Model Regresi Data Panel Dalam Reksadana Dengan Indeks Harga Saham Gabungan (Ihsg) Untuk Investasi Jangka Panjang,” Sigma-Mu, vol. 5, no. 1, pp. 1–21, Jan. 1970, doi: 10.35313/sigmamu.v5i1.846.
[19] C. A. Jacob, I. W. Sumarjaya, and M. Susilawati, “Analisis Model Regresi Data Panel Tidak Lengkap Komponen Galat Dua Arah dengan Penduga Feasible Generalized Least Square (FGLS),” Jurnal Matematika, vol. 4, no. 1, pp. 22–38, 2014.
[20] B. H. Baltagi, Econometric Analysis of Panel Data. Wiley, 2005. [Online]. Available: https://books.google.co.id/books?id=yTVSqmufge8C
[21] T. Wansbeek and A. Kapteyn, “Estimation of the error-components model with incomplete panels,” J Econom, vol. 41, no. 3, pp. 341–361, Jul. 1989, doi: 10.1016/0304-4076(89)90066-3.
[22] C. R. Rao, “Minimum variance quadratic unbiased estimation of variance components,” J Multivar Anal, vol. 1, no. 4, pp. 445–456, Dec. 1971, doi: 10.1016/0047-259X(71)90019-4.
[23] J. Isabona, “Maximum Likelihood Parameter Based Estimation for In-Depth Prognosis Investigation of Stochastic Electric Field Strength Data,” vol. 4, no. 1, pp. 127–136, 2019.
[24] A. Oman, D. Fitrianingsih, A. F. Salam, and H. Aeni, “Pengaruh Current Ratio, Debt To Equity Ratio dan Return On Equity Terhadap Return Saham Pada Perusahaan Property dan Real Estate yang Terdaftar di Bursa Efek Indonesia,” Journal of Economic, Bussines and Accounting (COSTING), vol. 4, no. 2, pp. 547–556, Mar. 2021, doi: 10.31539/costing.v4i2.1533.
[25] D. T. Kencana, “Pengaruh Manajemen Laba Terhadap Return Saham Dengan Variabel Kontrol Return on Equity Pada Perusahaan Manufaktur Dalam Bursa Efek Indonesia,” TECHNOBIZ: International Journal of Business, vol. 4, no. 2, p. 74, 2021, doi: 10.33365/tb.v4i2.1390.
[26] C. Choiriyah, F. Fatimah, S. Agustina, and U. Ulfa, “The Effect Of Return On Assets, Return On Equity, Net Profit Margin, Earning Per Share, And Operating Profit Margin On Stock Prices Of Banking Companies In Indonesia Stock Exchange,” International Journal of Finance Research, vol. 1, no. 2, pp. 103–123, 2021, doi: 10.47747/ijfr.v1i2.280.
[27] E. Endri, M. Rinaldi, D. Arifian, B. Saing, and A. Aminudin, “Oil Price and Stock Return: Evidence of Mining Companies in Indonesia,” International Journal of Energy Economics and Policy, vol. 11, no. 2, pp. 110–114, Feb. 2021, doi: 10.32479/ijeep.10608.
Published
2026-10-24
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Copyright (c) 2026 Refa Joyce Semida, Raupong Raupong, Siswanto Siswanto, A. Muthiah Nur Angriany
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