Penaksiran Parameter Dan Statistik Uji Model Multivariate Adaptive Generalized Poisson Regression Spline Pada Kasus Jumlah Penderita ISPA Pada Bayi Di Surabaya Tahun 2017

Hidayati, Sri (2019) Penaksiran Parameter Dan Statistik Uji Model Multivariate Adaptive Generalized Poisson Regression Spline Pada Kasus Jumlah Penderita ISPA Pada Bayi Di Surabaya Tahun 2017. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi Poisson merupakan model standar untuk memodelkan data yang berbentuk count (jumlah) dan termasuk dalam model nonlinear. Terdapat asumsi yang harus dipenuhi dalam regresi poisson, yaitu equidispersi. Equidispersi adalah kasus dimana nilai variansi variabel respon sama dengan nilai rata-rata varia-bel respon. Pada kasus nyata sering ditemui kasus overdispersi atau underdispersi. Generalized Poisson Regression adalah salah satu metode yang dapat mengatasi kasus overdispersi atau underdispersi. Multivariate Adaptive Regression Spline adalah salah satu model regresi nonparametrik, yaitu model yang mengasumsikan bentuk hubungan fungsional antara variabel respon dan prediktor tidak diketahui.Multivariate Adaptive Regression Spline adalah kombinasi yang kompleks antara metode spline dengan rekursif partisi untuk menghasilkan esti-masi fungsi regresi yang kontinu, dan digunakan untuk prediksi dan klasifikasi. Multivariate Adaptive Generalized Poisson Regression Spline merupakan pengem-bangan dari metode Multivariate Adaptive Regression Spline dan Generalized Poisson Regression. Penerapan model MAGPRS dilakukan pada kasus jumlah penderita ISPA pada bayi di Surabaya 2017. Hasil penelitian menunjukkan bahwa penaksiran parameter menggunakan Weighted Least Square serta pengujian hipotesis serentak dan parsial menggunakan Maximum Likelihood Ratio Test. Berdasarkan trial dan error kombinasi Basis Fungsi (BF), Maksimum Interaksi (MI), Minimum Observasi (MO), model terbaik adalah model ke 50 dengan BF, MI, dan MO berturut-turut sebesar 28, 3, dan 1. Hasil penelitian menunjukkan berdasarkan nilai kepentingan variabel prediktor, variabel yang mempengaruhi jumlah penderita ISPA pada bayi di Surabaya adalah persentase bayi berat lahir rendah (X2), persentase tidak rumah sehat (X5), dan persentase pemberian ASI non-eksklusif pada bayi (X1).
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Poisson regression is a standard model for counts data that can be used to determine these factors and it is included in a non-linear model. There is an assumption that must be fulfilled in Poisson regression, namely equidispersion. Equidispersion is a case which the response variable variance value is equal to the average variable response value. However, in real cases, overdispersion or underdispersion happened more often. Therefore, Generalized Poisson Regression is used to overcome this case. Multivariate Adaptive Regression Spline is one of the nonparametric regression models, which is a model that assumes the form of functional relationships between response variables and predictors is unknown. Multivariate Adaptive Regression Spline is a complex combination of spline methods with recursive partitions to produce a continuous regression function estimation and it is used for prediction and classification. Multivariate Adaptive Generalized Poisson Regression Spline is a development of the Multivariate Adaptive Regression Spline and Generalized Poisson Regression methods. The application of the Multivariate Adaptive Generalized Poisson Regression Spline model was carried out in the case of the number of Acute Respiratory Infections in babies in Surabaya 2017. The results showed that parameter estimation using Weighted Least Square and simultaneous and partial hypothesis testing using the Maximum Likelihood Ratio Test. Based on trial and error combination using Basis Function (BF), Maximum Interaction (MI), Minimum Observation (MO), the best model is the 50th model with BF, MI, and MO in a row of 28, 3, and 1. The results showed that based on the value of the importance of predictor variables, the variable affecting the number of ARI sufferers in infants in Surabaya was the percentage of low birth weight babies (X2), the percentage of not healthy house (X5), and the percentage of non-exclusive breastfeeding in infants (X1).

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Generalized Poisson Regression, Multivariate Adaptive Regression Spline, Multivariate Adaptive Generalized Poisson Regression Spline, Weighted Least Square, Maximum Likelihood Ratio Test.
Subjects:	Q Science
Divisions:	Faculty of Mathematics, Computation, and Data Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	Sri Hidayati
Date Deposited:	23 Jul 2026 05:59
Last Modified:	23 Jul 2026 05:59
URI:	http://repository.its.ac.id/id/eprint/68042

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