Model Regresi Logistik Ordinal Polinomial Multivariat

Rifada, Marisa (2024) Model Regresi Logistik Ordinal Polinomial Multivariat. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi logistik merupakan metode analisis data yang menggambarkan hubungan antara variabel respon yang bersifat kategori dengan satu atau lebih variabel prediktor yang bersifat kategori maupun kontinu. Apabila variabel respon memiliki skala ordinal maka dinamakan regresi logistik ordinal. Pemodelan regresi logistik yang melibatkan lebih dari satu variabel respon dan antar variabel respon saling berkorelasi dinamakan regresi logistik multivariat. Penelitian mengenai regresi logistik telah banyak dilakukan dengan mengasumsikan bahwa variabel prediktor kontinu dan fungsi link logitnya memiliki hubungan linier. Namun kenyataannya dalam beberapa kasus ditemukan bahwa hubungannya tidak selalu linier, melainkan bisa kuadratik, cubic, atau berbentuk kurva lainnya sehingga asumsi linieritas tersebut menjadi tidak benar. Oleh karena itu, penelitian ini melakukan studi teoritis mengenai pengembangan regresi logistik ordinal yang melibatkan lebih dari satu variabel respon dimana hubungan antara variabel prediktor kontinu dan logitnya dimodelkan sebagai bentuk polinomial yang dinamakan model Regresi Logistik Ordinal Polinomial Multivariat (RLOPM). Tujuan penelitian ini adalah mendapatkan penaksir parameter model RLOPM, mendapatkan statistik uji dari parameter model RLOPM, serta memodelkan risiko kejadian diabetes dan hipertensi menggunakan model RLOPM. Dalam penelitian ini, dibahas model RLOPM untuk 2 variabel respon, yaitu RLOPB 2x2 dan RLOPB 3x3. Penaksir parameter model diperoleh dengan menggunakan metode Maximum Likelihood Estimation (MLE), namun turunan pertama dari fungsi ln likelihood tidak berbentuk closed form sehingga diperlukan iterasi numerik seperti iterasi Berndt-Hall-Hall-Hausman (BHHH). Pengujian hipotesis secara serentak dengan metode Maximum Likelihood Ratio Test (MLRT) diperoleh statistik uji G2 dengan menggunakan n besar mengikuti distribusi Chi-square secara asimtotik dan pengujian hipotesis secara parsial menggunakan uji Wald. Hasil pemodelan risiko kejadian diabetes dan hipertensi berdasarkan model RLOPB 2x2 dan RLOPB 3x3 menunjukkan bahwa faktor-faktor yang berpengaruh signifikan terhadap risiko kejadian diabetes dan hipertensi adalah Usia, Indeks Massa Tubuh, Lingkar Pinggang dan Kadar Kolesterol LDL. Berdasarkan ukuran kebaikan atau kesesuaian model diperoleh bahwa pendekatan polinomial menghasilkan model yang lebih baik dibandingkan dengan pendekatan linier.
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Logistic regression is a data analysis method that describes the relationship between a categorical response variable and one or more categorical or continuous predictor variables. If the response variable has an ordinal scale, it is called ordinal logistic regression. Logistic regression modeling that involves more than one response variable and the response variables are correlated with each other is called multivariate logistic regression. Much research on logistic regression has been carried out assuming that the predictor variables are continuous and the logit link function has a linear relationship. However, in reality, in some cases it is found that the relationship is not always linear, but can be quadratic, cubic, or in the form of other curves so that the assumption of linearity is not correct. Therefore, this research carries out a theoretical study regarding the development of ordinal logistic regression involving more than one response variable where the relationship between continuous predictor variables and their logit is modeled as a polynomial form called the Multivariate Polynomial Ordinal Logistic Regression (Regresi Logistik Ordinal Polinomial Multivariat, RLOPM) model. The aim of this research is to obtain an estimate of the RLOPM model parameters, obtain test statistics from the RLOPM model parameters, and model the risk of diabetes and hypertension using the RLOPM model. In this research, the RLOPM model is discussed for 2 response variables, namely RLOPB 2x2 and RLOPB 3x3. The model parameter estimates are obtained using the Maximum Likelihood Estimation (MLE) method, but the first derivative of the ln likelihood function is not in closed form so numerical iteration is required such as Berndt-Hall-Hall-Hausman (BHHH) iteration. Simultaneous hypothesis testing using the Maximum Likelihood Ratio Test (MLRT) method obtained test statistics G2 using large n following the Chi-square distribution asymptotically and partial hypothesis testing using the Wald test. The results of modeling the risk of diabetes and hypertension based on the RLOPB 2x2 and RLOPB 3x3 models show that the factors that have a significant influence on the risk of diabetes and hypertension are Age, Body Mass Index, Waist Circumference and LDL Cholesterol Levels. Based on the measure of goodness or suitability of the model, it was found that the polynomial approach produced a better model compared to the linear approach.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	Diabetes, Hipertensi, Ordinal, Polinomial, Regresi Logistik Multivariat, Diabetes, Hypertension, Ordinal, Polynomial, Multivariate Logistic Regression.
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Marisa Rifada
Date Deposited:	02 Aug 2024 03:44
Last Modified:	02 Aug 2024 03:44
URI:	http://repository.its.ac.id/id/eprint/111015

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