Model Regresi Log-Gamma-Logistik dan Log-Logistik 3-Parameter (Waktu Rawat Inap Pasien DBD di RSUD Haji Provinsi Jawa Timur)

Sulistyaningsih, Tria (2024) Model Regresi Log-Gamma-Logistik dan Log-Logistik 3-Parameter (Waktu Rawat Inap Pasien DBD di RSUD Haji Provinsi Jawa Timur). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Regresi Log-Gamma-Logistik (LGLR) dan Regresi Log-Logistik 3-Parameter (LL3R) merupakan metode-metode yang cocok digunakan untuk memodelkan data kontinu non-negatif. Data kontinu seringkali menimbulkan tantangan analitis seperti skewness dan asimetri, terutama ketika datanya strictly positive dan right skewed sehingga model regresi linier tradisional tidak efektif untuk menanganinya. Regresi Nonlinier yang dibentuk dari Generalized Linear Model memfasilitasi penggunakan fungsi link-log dari parameter distribusi keluarga eksponensial untuk dimodelkan dalam regresi. Regresi ini mampu menangkap hubungan yang lebih kompleks seperti hubungan non-linier antara variabel respon dengan variabel prediktor. Regresi LGLR dan LL3R merupakan regresi nonlinier yang dibangun berdasarkan pengembangan distribusi Log-Gamma-Logistik dan Log-Logistik 3-Parameter mampu menangkap ketidaksimetrisan data. Tujuan dari penelitian ini adalah untuk membandingkan model LGLR dan LL3R dengan mengestimasi parameter dan menguji hipotesis pada model serta menerapkannya pada kasus waktu rawat inap pasien Demam Berdarah Dengue (DBD) tahun 2022 di RSUD Haji Provinsi Jawa Timur. Variabel responnya adalah lama rawat inap dengan mempertimbangkan 13 prediktor. Parameter model LGLR dan LL3R diestimasi menggunakan Maximum Likelihood Estimation (MLE), khususnya teknik Berndt–Hall–Hall–Hausman (BHHH) untuk iterasi numerik. Pengujian hipotesis menggunakan Maximum Likelihood Ratio Test (MLRT). Efektivitas model diukur melalui Akaike Information Criterion corrected (AICc). Hasil menunjukkan model LL3R mengungguli model LGLR dengan AICc model LL3R yaitu 146,3841 sedangkan model LGLR memiliki AICc sebesar 272,0007. Sehingga model terbaiknya adalah model LL3R. Pada tingkat signifikansi 5% menunjukkan pengujian dengan MLRT model LL3R secara serentak menolak hipotesis nol, dan pengujian parsial mengungkapkan pengaruh signifikan lima variabel prediktor antara lain tekanan darah diastolik, frekuensi denyut nadi, suhu tubuh, jenis kelamin, jenis pembiayaan pada dummy variable pada kategori; 1: JKN NON-BPI, 0: Umum, terhadap waktu rawat inap pasien DBD.
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Log-Gamma-Logistic Regression (LGLR) and 3-Parameter Log-Logistic Regression (LL3R) are methods that are suitable for modeling non-negative continuous data. Continuous data often poses analytical challenges such as skewness and asymmetry, especially when the data is strictly positive and right skewed so that traditional linear regression models are not effective in handling them. Nonlinear regression formed from the Generalized Linear Model facilitates the use of the link-log function of the exponential family distribution parameters to be modeled in regression. This regression is able to capture more complex relationships such as non-linear relationships between response variables and predictor variables. LGLR and LL3R regression are nonlinear regressions built based on the development of the Log-Gamma-Logistic and 3-Parameter Log-Logistic distributions capable of capturing data asymmetries. The aim of this research is to compare the LGLR and LL3R models by estimating parameters and testing hypotheses in the model and applying them to the case of duration of hospitalization until recovery for Dengue Hemorrhagic Fever (DHF) patients in 2022 at the RSUD Haji, East Java Province. The response variable is the duration of hospitalization until recovery by considering 13 predictors. LGLR and LL3R model parameters were estimated using Maximum Likelihood Estimation (MLE), specifically the Berndt–Hall–Hausman (BHHH) technique for numerical iteration. Hypothesis testing uses the Maximum Likelihood Ratio Test (MLRT). The effectiveness of the model is measured through Akaike Information Criterion correction (AICc). The results show that the LL3R model outperforms the LGLR model with an AICc of the LL3R model, namely 146.3841, while the LGLR model has an AICc of 272.0007. So the best model is the LL3R model. At a significance level of 5%, it shows that testing with the MLRT model LL3R simultaneously rejects the null hypothesis, and partial testing reveals the significant influence of five predictor variables including diastolic blood pressure, pulse frequency, body temperature, gender, type of financing on dummy variables in categories; 1: JKN NON-BPI, 0: General, on hospitalization time for DHF patients.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Berndt-Hall-Hall-Hausman, demam berdarah dengue, Regresi Log-Gamma-Logistik, Regresi Log-Logistik 3-Parameter, waktu rawat inap. Berndt-Hall-Hall-Hausman, dengue hemorrhagic fever, duration of hospitalization, Log-Gamma-Logistic Regression, 3-Parameter Log-Logistic Regression.
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HA Statistics > HA31.7 Estimation R Medicine > RB Pathology
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Tria Sulistyaningsih
Date Deposited:	09 Jul 2024 02:03
Last Modified:	09 Jul 2024 02:03
URI:	http://repository.its.ac.id/id/eprint/108197

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