Judul: Estimator Robust Terhadap Pencilan Untuk Model Regresi Data Panel Tidak Seimbang Dengan Pendekatan Fixed-Effects===Robust Estimator To Outliers For Unbalanced Panel Data Regression Model With Fixed-Effects Approach
Pengarang: Abdurakhman ; Dedi Rosadi ; Desi Yuniarti
Penerbit: FMIPA UGM
Tahun: 2024
Tipe: Disertasi
Lokasi: Perpustakaan Fakultas MIPA
ABSTRAK
hubungan antara suatu variabel dependen dengan satu atau lebih variabel independen.
Analisis regresi yang menggunakan data panel dikenal sebagai analisis
regresi data panel. Data panel merupakan gabungan data cross-section dan data
time-series. Data panel ini tidak lepas dari kemungkinan adanya pencilan yang dapat
menyebabkan estimasi model regresi data panel dapat menjadi bias. Sehingga
diperlukan suatu metode robust untuk mendapatkan estimator yang sudah tidak dipengaruhi
oleh pencilan. Penelitian disertasi ini bertujuan untuk mengembangkan
suatu estimator robust bagi model regresi data panel tidak seimbang dengan pendekatan
fixed-effects, menyelidiki sifat-sifat estimator yang diperoleh serta melakukan
penerapan metode robust tersebut pada data riil.
Berdasarkan hasil penelitian disertasi ini diperoleh bahwa penanganan pencilan
pada model regresi data panel tidak seimbang satu arah dengan pendekatan
fixed-effects dapat dilakukan menggunakan metode robust Within-Groups Generalized
M-Estimators (WGM), Groupwise Principal Sensitivity Components (GPSC)
dan matriks pengaruh panel. Penelitian ini juga telah mengembangkan metode robust
menggunakan matriks pengaruh panel dalam menentukan estimasi robust bagi
model regresi data panel tidak seimbang satu arah dengan pendekatan fixed-effects.
Metode robust menggunakan matriks pengaruh panel lebih memperhatikan struktur
data panel yang terdiri atas beberapa unit cross-section karena pembentukan
matriks pengaruh panel dilakukan bagi masing-masing unit cross-section sehingga
hasil estimasi robust yang diperoleh dapat lebih baik.
Sifat-sifat estimator dari metode robust ditentukan melalui studi simulasi.
Hasil studi simulasi untuk metode WGM diperoleh bahwa masing-masing penerapan
estimator multivariat lokasi dan skala pada metode WGM menghasilkan nilai
Mean Squared Error (MSE) residual tidak jauh berbeda dalam mengatasi pencilan
vertikal dan pencilan vertikal blok, namun untuk pencilan leverage dan pencilan
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leverage blok diperoleh bahwa S-multivariat memberikan rata-rata nilai MSE residual
yang lebih baik. Selanjutnya berdasarkan hasil studi simulasi terhadap metode
robust menggunakan matriks pengaruh panel diperoleh bahwa metode ini memberikan
persentase ketepatan pendeteksian pencilan vertikal dan vertikal blok yang
sangat baik. Selain itu, metode robust ini menghasilkan nilai MSE parameter yang
baik dalam mengestimasi model regresi data panel yang memuat pencilan leverage
dan pencilan leverage blok. Hasil yang sama dapat dilihat dari nilai MSE residual
di mana metode ini juga memberikan nilai MSE residual yang rendah untuk data
panel yang memuat pencilan leverage dan leverage blok. Hasil studi simulasi juga
dilakukan dalam membandingkan hasil estimasi menggunakan metode robust WG,
WGM, GPSC dan matriks pengaruh panel. Berdasarkan hasil studi simulasi perbandingan
metode robust diperoleh bahwa metode GPSC dapat mengatasi semua
pencilan pada data panel dengan baik. Sedangkan metode WGM lebih baik dalam
mengatasi pencilan vertikal dan vertikal blok. Selanjutnya metode robust menggunakan
matriks pengaruh panel lebih baik dalam mengatasi pencilan leverage dan
leverage blok.
Selanjutnya berdasarkan hasil penerapan pada data riil menunjukkan bahwa
metode robust menggunakan matriks pengaruh panel memberikan nilai MSE yang
lebih baik dibanding metode estimasi robust menggunakan GPSC, WGM dan metode
robust menggunakan matriks pengaruh tanpa mempertimbangkan struktur data
panel.===variable and one or more independent variables. Regression analysis that uses panel
data is known as panel data regression analysis. Panel data combines cross-section
data and time-series data. This panel data is not accessible due to the possibility of
outliers, which can cause the estimation of the panel data regression model biased.
So, we need a robust method to get an estimator that is not influenced by outliers.
This dissertation research aims to develop a robust estimator for unbalanced panel
data regression models using the fixed-effects approach, investigate the properties
of the estimator obtained, and apply the robust method to actual data.
Based on the results of this dissertation research, it was found that handling
outliers in one-way unbalanced panel data regression models using a fixed-effects
approach can be carried out using robust methods, namely Within-Groups Generalized
M-Estimators (WGM), Groupwise Principal Sensitivity Components (GPSC),
and panel influence matrix. This research has also developed a robust method using
a panel influence matrix to determine robust estimates for a one-way unbalanced
panel data regression model using a fixed-effects approach. The robust method using
a panel influence matrix pays more attention to the panel data structure, which
consists of several cross-section units because the formation of the panel influence
matrix is carried out for each cross-section unit so that the robust estimation results
obtained can be better.
The estimator properties of the robust method are determined through simulation
studies. The simulation study results for the WGM method show that each
application of the location and scale multivariate estimator in the WGM method
produces residual Mean Squared Error (MSE) values that are not much different
in dealing with vertical and block vertical outliers. However, the results obtained
that S-multivariate provides a better average residual MSE value in dealing with
leverage and block leverage outliers. Furthermore, based on a simulation study of
the robust method using a panel influence matrix, it was found that this method proxvii
xviii
vides a good percentage of accuracy in detecting vertical and block vertical outliers.
In addition, this robust method produces good MSE parameter values in estimating
panel data regression models that contain leverage outliers and block leverage outliers.
The same results can be seen from the residual MSE value, where this method
also provides low residual MSE values for panel data containing leverage outliers
and block leverage. The simulation study results were also carried out to compare
the estimation results using the robust WG, WGM, GPSC, and panel influence matrix
methods. Based on the results of a comparative simulation study of robust methods,
it was found that the GPSC method can handle all outliers in panel data well.
Meanwhile, the WGM method is better at dealing with vertical and block vertical
outliers. Furthermore, the robust method using a panel influence matrix is better at
overcoming leverage and block leverage outliers.
Furthermore, based on the results of application to actual data, it shows that
the robust method using a panel influence matrix provides better MSE values than
the robust estimation method using GPSC, WGM and the robust method using an
influence matrix without considering the panel data structure.
ABSTRACT
variable and one or more independent variables. Regression analysis that uses panel
data is known as panel data regression analysis. Panel data combines cross-section
data and time-series data. This panel data is not accessible due to the possibility of
outliers, which can cause the estimation of the panel data regression model biased.
So, we need a robust method to get an estimator that is not influenced by outliers.
This dissertation research aims to develop a robust estimator for unbalanced panel
data regression models using the fixed-effects approach, investigate the properties
of the estimator obtained, and apply the robust method to actual data.
Based on the results of this dissertation research, it was found that handling
outliers in one-way unbalanced panel data regression models using a fixed-effects
approach can be carried out using robust methods, namely Within-Groups Generalized
M-Estimators (WGM), Groupwise Principal Sensitivity Components (GPSC),
and panel influence matrix. This research has also developed a robust method using
a panel influence matrix to determine robust estimates for a one-way unbalanced
panel data regression model using a fixed-effects approach. The robust method using
a panel influence matrix pays more attention to the panel data structure, which
consists of several cross-section units because the formation of the panel influence
matrix is carried out for each cross-section unit so that the robust estimation results
obtained can be better.
The estimator properties of the robust method are determined through simulation
studies. The simulation study results for the WGM method show that each
application of the location and scale multivariate estimator in the WGM method
produces residual Mean Squared Error (MSE) values that are not much different
in dealing with vertical and block vertical outliers. However, the results obtained
that S-multivariate provides a better average residual MSE value in dealing with
leverage and block leverage outliers. Furthermore, based on a simulation study of
the robust method using a panel influence matrix, it was found that this method proxvii
xviii
vides a good percentage of accuracy in detecting vertical and block vertical outliers.
In addition, this robust method produces good MSE parameter values in estimating
panel data regression models that contain leverage outliers and block leverage outliers.
The same results can be seen from the residual MSE value, where this method
also provides low residual MSE values for panel data containing leverage outliers
and block leverage. The simulation study results were also carried out to compare
the estimation results using the robust WG, WGM, GPSC, and panel influence matrix
methods. Based on the results of a comparative simulation study of robust methods,
it was found that the GPSC method can handle all outliers in panel data well.
Meanwhile, the WGM method is better at dealing with vertical and block vertical
outliers. Furthermore, the robust method using a panel influence matrix is better at
overcoming leverage and block leverage outliers.
Furthermore, based on the results of application to actual data, it shows that
the robust method using a panel influence matrix provides better MSE values than
the robust estimation method using GPSC, WGM and the robust method using an
influence matrix without considering the panel data structure.
Subyek/Kata Kunci: estimator robust; pencilan; regresi data panel tidak seimbang
