Estimator Probit Biner Semiparametrik Spline Truncated (Studi Kasus: Status Psersentase Penduduk Miskin)

Tahwin, Rizki Adisetya (2026) Estimator Probit Biner Semiparametrik Spline Truncated (Studi Kasus: Status Psersentase Penduduk Miskin). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis regresi adalah metode statistik yang digunakan untuk memodelkan hubungan antara variabel prediktor dan variabel respons. Untuk menganalisis variabel respons kategori, salah satu metode yang dapat digunakan adalah regresi probit. Terdapat tiga model probit berdasarkan jenis variabel respons, yaitu probit biner, probit multinomial, dan probit ordinal. Probit biner adalah metode yang digunakan untuk menganalisis variabel respons dengan dua kategori. Terdapat tiga jenis model probit biner berdasarkan pendekatan kurva, yaitu parametrik, nonparametrik, dan semiparametrik. Probit semiparametrik dipilih karena merupakan penggabungan dari komponen parametrik dan nonparametrik. Probit semiparametrik didekati dengan spline truncated. Spline truncated merupakan potongan polinomial yang tersegmen dan kontinu dengan titik knot yang menandakan perubahan pola data. Penelitian ini bertujuan untuk mengestimasi model probit biner semiparametrik yang didekati dengan spline truncated menggunakan maximum likelihood estimation. Estimasi yang dihasilkan tidak closeform, sehingga perlu dilanjutkan penyelesaiannya dengan iterasi numerik newton raphson sampai konvergen. Model probit biner semiparametrik spline truncated diterapkan pada data status persentase penduduk miskin. Pada akhir analisis dilakukan perbandingan model probit biner parametrik, probit biner nonparametrik spline truncated, dan probit biner semiparametrik spline truncated. Hasil evaluasi performa model probit biner semiparametrik spline truncated menunjukkan bahwa model terbaik diperoleh dengan satu titik knot, yang memiliki nilai APER sebesar 15,79%, accuracy sebesar 84,21%, sensitivity sebesar 85%, specificity sebesar 83,33% dan AUC sebesar 0,84 yang menunjukkan bahwa klasifikasi model sangat baik. Hasil evalusi yang diperoleh menunjukkan bahwa model probit biner semiparametrik spline truncated lebih unggul dibanding model parametrik dan nonparametrik.
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Regression analysis is a statistical method used to model the relationship between predictor variables and response variables. To analyse categorical response variables, one method that can be used is probit regression. There are three probit models based on the type of response variable, namely binary probit, multinomial probit, and ordinal probit. Binary probit is a method used to analyse response variables with two categories. There are three types of binary probit models based on the curve approach, namely parametric, nonparametric, and semiparametric. Semiparametric probit was chosen because it is a combination of parametric and nonparametric components. Semiparametric probit is approached with a truncated spline. A truncated spline is a segmented and continuous polynomial with knot points that indicate changes in data patterns. This study aims to estimate a semiparametric binary probit model approached with truncated splines using maximum likelihood estimation. The resulting estimates are not closed-form, so they need to be completed with Newton-Raphson numerical iteration until convergence. The truncated spline semiparametric binary probit model is applied to data on the percentage of poor people. At the end of the analysis, a comparison is made between the parametric binary probit model, the nonparametric truncated spline binary probit model, and the truncated spline semiparametric binary probit model. The results of the performance evaluation of the truncated spline semiparametric binary probit model show that the best model is obtained with one knot point, which has an APER value of 15.79%, accuracy of 84.21%, sensitivity of 85%, specificity of 83.33% and AUC of 0.84, indicating that the model classification is very good. The evaluation results obtained show that the truncated spline semiparametric binary probit model is superior to parametric and nonparametric models.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Persentase Penduduk Miskin, Probit, Semiparametrik, Spline Truncated ======================================================================================================================== Percentage of the Poor Population, Probit, Semiparametric, Spline Truncate
Subjects:	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:	Rizki Adisetya Tahwin
Date Deposited:	27 Jan 2026 06:42
Last Modified:	27 Jan 2026 06:42
URI:	http://repository.its.ac.id/id/eprint/130514

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