Estimasi Parameter dan Pengujian Hipotesis pada Regresi Zero-inflated Ordered Probit with Correlated Errors

Yudhani, Nidya Putri (2025) Estimasi Parameter dan Pengujian Hipotesis pada Regresi Zero-inflated Ordered Probit with Correlated Errors. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model Zero-inflated Ordered Probit (ZIOP) merupakan pengembangan dari model probit ordinal yang mempertimbangkan keberadaan zero-inflation. Namun, model ZIOP masih memiliki keterbatasan dalam menjelaskan korelasi antar error pada komponen biner dan ordinal. Oleh karena itu, penelitian ini mengembangkan model Zero-inflated Ordered Probit with Correlated Errors (ZIOPC) yang mempertimbangkan korelasi antar error serta melakukan estimasi parameter dan pengujian hipotesis model. Estimasi parameter dilakukan dengan metode Maximum Likelihood Estimation (MLE) yang tidak memiliki bentuk closed form, sehingga memerlukan pendekatan numerik. Algoritma Broyden–Fletcher–Goldfarb–Shanno (BFGS) digunakan pada tahap awal namun gagal konvergen untuk model ZIOPC, sehingga estimasi dialihkan ke algoritma Limited-memory BFGS with Bound constraint (L-BFGS-B) yang lebih stabil dan efisien secara memori. Studi simulasi dilakukan untuk membandingkan performa estimasi model ZIOP dan ZIOPC. Hasilnya menunjukkan bahwa L-BFGS-B berhasil mencapai konvergensi secara konsisten dan nilai log-likelihood ZIOPC lebih tinggi, menandakan kecocokan model yang lebih baik saat error antar proses berkorelasi. Pengujian hipotesis secara simultan dengan metode Maximum Likelihood Ratio Test (MLRT) diperoleh statistik uji dengan menggunakan n besar mengikuti distribusi Chi-square secara asimtotik. Model ZIOPC diterapkan pada data tingkatan rumah tangga miskin di Provinsi D.I. Yogyakarta tahun 2024. Hasil menunjukkan bahwa pendidikan berpengaruh signifikan dalam menurunkan tingkat kemiskinan, sedangkan variabel biner tidak signifikan. Parameter korelasi antar error juga signifikan, menunjukkan bahwa model ZIOPC lebih sesuai dibanding ZIOP.
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The Zero-inflated Ordered Probit (ZIOP) model is an extension of the ordinal probit model that accounts for the presence of zero inflation. However, ZIOP still has limitations in capturing the correlation between errors in the binary and ordinal components. Therefore, this study develops the Zero-inflated Ordered Probit with Correlated Errors (ZIOPC) model, which incorporates such error correlation and conducts parameter estimation and hypothesis testing. Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method, which does not yield closed form solutions and thus requires a numerical approach. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is initially applied but fails to converge for the ZIOPC model. Consequently, estimation is shifted to the Limited-memory BFGS with Bound constraints (L-BFGS-B) algorithm, which is more numerically stable and memory-efficient. A simulation study is conducted to compare the estimation performance of the ZIOP and ZIOPC models. The results indicate that L-BFGS-B consistently achieves convergence, and the ZIOPC model produces a higher log-likelihood value, suggesting better model fits when an error correlation exists between the binary and ordinal processes. Hypothesis testing is performed simultaneously using the Maximum Likelihood Ratio Test (MLRT), where the test statistics asymptotically follow a Chi-square distribution under large sample conditions. The ZIOPC model is applied to data on household poverty levels in the D.I Yogyakarta for the year 2024. The results show that education has a significant negative effect on poverty levels, while some binary variables are not statistically significant. The correlation parameter between errors is also significant, indicating that the ZIOPC model provides a better fit compared to the ZIOP model.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Korelasi Error, L-BFGS-B, Regresi Probit, Tingkat Kemiskinan, ZIOPC, Error Correlation, L-BFGS-B, Probit Regression, Poverty Level, ZIOPC
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Nidya Putri Yudhani
Date Deposited:	17 Jul 2025 09:45
Last Modified:	17 Jul 2025 09:45
URI:	http://repository.its.ac.id/id/eprint/119948

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