Andyani, Rhavida Anniza (2021) Estimasi Parameter Probit Panel Random Effect Menggunakan Integrasi Adaptive Gauss Hermite Quadrature (Studi Kasus : Klasifikasi Tingkat Ekonomi Menurut Provinsi di Indonesia). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Maximum Likelihood Estimation (MLE) merupakan salah satu metode yang banyak digunakan dalam estimasi parameter regresi, karena kemudahan dalam aplikasinya. Namun, aplikasi MLE pada regresi probit panel random effect terdapat kendala, dimana model random effect mengandung variabel laten yang menyebabkan fungsi likelihood yang dihasilkan mengandung integral normal yang sulit diselesaikan secara analitik. Adaptive Gauss Hermite Quadrature (AGHQ) merupakan pengembangan dari metode Gauss Hermite Quadrature, yang merupakan metode integrasi yang sering digunakan dalam penyelesaian estimasi probit panel. AGHQ mampu menangkap puncak integrand lebih baik dan lebih sedikit penggunaan quadrature point dibandingkan dengan metode GHQ. AGHQ memiliki tingkat kecepatan dan akurasi dalam perhitungan yang lebih baik dibandingkan dengan GHQ. Tahap awal estimasi dengan AGHQ adalah mengalikan dan membagi fungsi likelihood dengan PDF normal. Turunan pertama dari fungsi log likelihood tidak memberikan hasil yang closed form, sehingga enyelesaian dilanjutkan dengan menggunakan iterasi Newton Raphson. Aplikasi model regresi probit panel random effect pada tingkat perekonomian di 31 provinsi memberikan hasil bahwa variabel ekspor, Tingkat Partisipasi Angkatan Kerja (TPAK), dan rasio elektrifikasi memberikan pengaruh signifikan terhadap tingkat ekonomi. TPAK memberikan pengaruh terbesar dalam pengklasifikasian provinsi tingkat ekonomi tinggi. Hasil klasifikasi model probit panel pada tahun 2019 memberikan akurasi sebesar 67,74% dengan 10 provinsi terjadi kesalahan klasifikasi.
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Maximum Likelihood Estimation (MLE) is a method commonly used in estimating regression parameters, because of its ease of application. However, the application of MLE in random effect panel probit regression has problems. The random effects model contains latent variables that cause the resulting likelihood function to contain normal integrals that are difficult to solve analytically. Adaptive Gauss Hermite Quadrature (AGHQ) is a development of the Gauss Hermite Quadrature (GHQ) method, an integration method that is often used to solve panel probit estimation. AGHQ can capture integrand peaks better and uses fewer quadrature points than the GHQ. AGHQ has a better level of speed and accuracy in calculations compared to GHQ. The first step of estimation with AGHQ is to multiply and divide the probability function with a normal PDF. The first derivative of the log-likelihood function does not close form result, so the solution is continued by using Newton Raphson iterations. The application of the random effect panel probit regression model at the economic level in 31 provinces shows that export variables, Labor Force Participation Rate (TPAK), and electrification ratio have a significant effect on the economic level. TPAK has the greatest influence in classifying provinces with high economic levels. The result of probit panel model classification in 2019 gives an accuracy of 67.74% with misclassification in 10 provinces.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Adaptive Gauss Hermite Quadrature, Maximum Likelihood Estimation, Tingkat Ekonomi, Probit Data Panel, Random effect, Economic Level, Probit Panel Data |
| Subjects: | H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HD Industries. Land use. Labor > HD108 Classification (Theory. Method. Relation to other subjects ) Q Science |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Rhavida Anniza Andyani |
| Date Deposited: | 09 Sep 2021 08:40 |
| Last Modified: | 09 Sep 2021 08:40 |
| URI: | http://repository.its.ac.id/id/eprint/91913 |
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