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All Journal Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam Jurnal Varian ESTIMASI: Journal of Statistics and Its Application
Raupong, Raupong
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Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Mathematics Social Sciences Other

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Mengatasi Overdispersi Menggunakan Regresi Binomial Negatif dengan Penaksir Maksimum Likelihood pada Kasus Demam Berdarah di Kota Makassar Fadil, Muhammad; Raupong, Raupong; Ilyas, Nirwan
ESTIMASI: Journal of Statistics and Its Application Vol. 5, No. 1, Januari, 2024 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ejsa.v5i1.14552

Abstract

The basic assumption in Poisson regression is that the mean value is the same as the variance value, which is called equidispersion. However, in some cases, this assumption is not met. A variance value that is greater than the average is called overdispersion and is called underdispersion if the variance value is smaller than the average value. So the Poisson regression model is no longer suitable for modeling this type of data because it will produce biased parameter estimates, therefore a negative binomial regression model is used. The research results show that estimating the parameters of the negative binomial regression model uses the maximum likelihood estimation method and then continues with the Newton-Raphson iteration method. The results obtained show that the negative binomial regression model overcomes the overdispersion that occurs in data on the number of dengue fever cases in Makassar City with the model  and an AIC value of 236.06647. The negative binomial regression model produces many models and then the best model with the smallest AIC criteria is selected.
Penerepan Analisis Diskriminan Kuadratik Robust Pada Klasifikasi Desa Asnidar, Asnidar; Ilyas, Nirwan; Raupong, Raupong
ESTIMASI: Journal of Statistics and Its Application Vol. 5, No. 2, Juli, 2024 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ejsa.v5i2.27002

Abstract

Discriminant analysis is a method used in separating objects into different groups and allocating objects into a predetermined group. Discriminant analysis is bound by the assumption that the mean vector for each group is different, the data is normally distributed multivariate and the covariance variance matrix between groups is the same. If there is a covariance variance matrix between different groups, then quadratic discriminant analysis is used for the classification process. However, sometimes it is found that data contains outliers, so a robust estimator is used, namely the Minimun Covariance Determinant with the fast-MCD algorithm. Therefore, robust quadratic discriminant analysis can be used to classify 128 villages and 48 sub-districts in Wajo district. It was found that 106 villages were correctly classified into village groups and 22 villages were misclassified into sub-district groups and 35 sub-districts were correctly classified as sub-district groups and 13 sub-districts were misclassified into village groups and produced an accuracy of classification results of 80.11%.
Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square Islamiyati, Anna; Anisa, Anisa; Raupong, Raupong; Massalesse, Jusmawati; Sirajang, Nasrah; Sahriman, Sitti; Wahyuni, Alfiana
Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam Vol. 10 No. 2 (2022): Al-Khwarizmi : Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam had Accr
Publisher : Prodi Pendidikan Matematika FTIK IAIN Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24256/jpmipa.v10i2.3197

Abstract

Abstract:Nonparametric regression is used for data whose data pattern is non-parametric. One of the estimators that can be developed is a segmented cubic spline which is able to show several segmentation changes in the data. This article examines the estimation of segmented cubic spline nonparametric regression models using the Penalized Least Square estimation criteria. The method involves knot points and smoothing parameters simultaneously. In addition, the model is used to analyze data on BPJS claims based on patient age. The results show that the optimal model is at two-knot points, namely 26 and 52 with a smoothing parameter of 0.89. There are three segmentation changes from the cubic data, which consist of young people up to 26 years old, 26-52 years old, and 52 years and over. Abstrak:Regresi nonparametrik digunakan untuk data yang pola datanya bentuk non parametrik. Salah satu estimator yang dapat dikembangkan adalah spline kubik tersegmen yang mampu menunjukkan beberapa segmentasi perubahan pada data. Artikel ini mengkaji estimasi model regresi nonparametrik spline kubik tersegmen melalui kriteria estimasi menggunakan Penalized Least Square. Metode tersebut melibatkan titik knot dan parameter penghalus secara bersamaan. Selain itu, model digunakan untuk menganalisis data klaim BPJS berdasarkan usia pasien. Hasil menunjukkan bahwa model optimal pada dua titik knot yaitu 26 dan 52 dengan parameter penghalus sebesar 0,89. Terdapat tiga segmentasi perubahan data secara kubik, yaitu usia muda hingga 26 tahun, usia 26-52 tahun, dan usia 52 tahun ke atas. 
Pendekatan Zero-Inflated Poisson Inverse Gaussian dalam Pemodelan Kasus Malaria di Puskesmas Kota Makassar Nurhidayah, Fauziah; Raupong, Raupong; Angriany, A.Muthiah Nur
ESTIMASI: Journal of Statistics and Its Application Vol. 6, No. 1, Januari, 2025 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.70561/ejsa.v6i1.43164

Abstract

Poisson regression is one of the approaches used to model count data. However, this method has an assumption of equidispersion that is not always met in actual data. One problem that often arises is overdispersion, especially when there are excess zeros in the dependent variable. The Mixed Poisson method, namely Zero-Inflated Poisson Inverse Gaussian (ZIPIG) regression is one approach that can be used when there is overdispersion in the data.  Parameter estimation in the ZIPIG model is done using the Maximum Likelihood Estimation (MLE) method through Fisher Scoring Algorithm iterations. This study discusses how ZIPIG modeling is used to identify factors that influence the number of malaria cases in Makassar City Health Center in 2021. The results of the analysis show that the independent variables that have a significant effect on the number of malaria cases are the number of family heads with access to proper sanitation facilities (X1) and the presence of public places that meet health requirements  (X2).
Pemodelan Regresi Seemingly Unrelated Menggunakan Metode Maximum Likelihood pada Data Panel Hikmah, Nurul; Raupong, Raupong; Sirajang, Nasrah
ESTIMASI: Journal of Statistics and Its Application Vol. 6, No. 2, Juli, 2025 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ejsa.v6i2.34463

Abstract

This study aims to model and predict the Human Development Index (HDI) values in South Sulawesi Province for the period 2014–2022 using a multiple linear regression approach with the Maximum Likelihood Estimation (MLE) method. Multiple linear regression analysis often encounters multicollinearity issues among independent variables; therefore, Principal Component Analysis (PCA) is employed as a dimensionality reduction technique to eliminate correlations among explanatory variables. In addition, due to the potential correlation of residuals among equations in a multivariate model, the Seemingly Unrelated Regression (SUR) approach is used, which is also estimated using the MLE method. The data utilized in this study is panel data, which offers advantages in obtaining more comprehensive and accurate information regarding the relationships between the analyzed variables. The estimation results of the SUR model indicate that variables such as Life Expectancy (UHH), Mean Years of Schooling (RLS), Expected Years of Schooling (HLS), and Adjusted Per Capita Expenditure have a significant influence on HDI across all districts/cities in South Sulawesi. One of the estimated equations from the SUR model is y22t=81.44+0.670KU122 which illustrates the relationship between the principal component and HDI in a specific region.
Panel Data Regression Modeling with Weighted Least Squares Method Using Fair Weights Ferdiansyah, Muhammad; Raupong, Raupong; Siswanto, Siswanto
Jurnal Varian Vol. 8 No. 2 (2025)
Publisher : Universitas Bumigora

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30812/varian.v8i2.4392

Abstract

Panel data regression is a robust method for analyzing relationships between dependent and independent variables by combining time-series and cross-sectional data. Its reliability hinges on key assumptions, particularly homoscedasticity. Violations, known as heteroscedasticity, lead to inefficient estimates and biased inference, as estimators fail to meet the Best Linear Unbiased Estimator criteria. The Weighted Least Squares (WLS) method addresses heteroscedasticity by weighting observations based on the inverse of their variance. WLS assumes prior knowledge of the heteroscedasticity structure, which is often impractical, creating gap in evaluating its effectiveness compared to alternative methods. The purpose of this study is to examines life expectancy in South Sulawesi as the dependent variable, with expected years of schooling, per capita expenditure, and average years of schooling as independent variables. The research methode used WLS with reasonable weighting, successfully addressing heteroscedasticity. The fixed-effects model was identified as the most appropriate, with an R-squared of 99.45%. Life expectancy was explained by the model. Results shows all variables positively and significantly influence life expectancy. In conclusion, the WLS method effectively overcomes heteroscedasticity in panel data regression, providing reliable estimators. This study highlights the importance of method selection in panel data analysis and offers insights for policymakers aiming to improve life expectancy in South Sulawesi.
Co-Authors Angriany, A.Muthiah Nur Anisa Anisa Anna Islamiyati Asnidar Asnidar Jusmawati Massalesse Muhammad Fadil Muhammad Ferdiansyah, Muhammad Nirwan Ilyas Nurhidayah, Fauziah Nurul Hikmah S Siswanto Sahriman, Sitti Sirajang, Nasrah Wahyuni, Alfiana