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Multinomial Logistic Regression To Model The Combination Of Phdi Status And Hdi Status Of Districts/Cities In Kalimantan Island

Regresi Logistik Multinomial untuk Memodelkan Kombinasi antara Status IPKM dan Status IPM Kabupaten/Kota di Pulau Kalimantan

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 3 (2023) · pp. 460–472

DOI
10.20956/j.v19i3.22299
ISSN
2614-8811, 1858-1382
Published
2023-05-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Multinomial Logistics Regression (MLR) is a regression model developed from the Binary Logistics Regression (BLR) model. The response variable of the RLM model has three or more categories and has a multinomial distribution, with the data scale being nominal. The response variable in this study is a combination of the Public Health Development Index (PHDI) status and the Human Development Index (HDI) status of districts/cities in Kalimantan Island, 2018, divided into four categories with category one as a comparison. The predictor variables used were the number of the public health center, the percentage of poor people, economic growth, the pure junior high school participation rate, and the percentage of the population with a minimum of junior high school education. The MLR parameter model was estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson iteration. The hypothesis testing of the MLR model was used by the Likelihood Ratio Test (LRT) method and the Wald test. The best model selection in this study uses the backward method, and the interpretation of the best MLR model uses the odds ratio value. The results showed that the best MLR model is a model that has three predictor variables. The factors that significantly influenced the combination of PHDI status and the HDI status of districts/cities in Kalimantan Island in 2018 were the percentage of poor people, economic growth, and the percentage of people with the minimum level of education in junior high school.

Bahasa Indonesia

Regresi Logistik Multinomial (RLM) merupakan model regresi yang dikembangkan dari model Regresi Logistik Biner (RLB). Variabel respon model RLM mempunyai tiga atau lebih kategori dan berdistribusi multinomial dengan skala datanya adalah nominal. Variabel respon dalam penelitian yaitu kombinasi antara status Indeks Pembangunan Kesehatan Masyarakat (IPKM) dan status Indeks Pembangunan Manusia (IPM) kabupaten/kota di pulau Kalimantan tahun 2018 yang terbagi dalam empat kategori dengan kategori satu sebagai pembanding. Variabel prediktor yang digunakan yaitu jumlah puskesmas, persentase penduduk miskin, pertumbuhan ekonomi, angka partisipasi murni SMP, dan persentase penduduk yang berpendidikan minimal SMP. Penaksiran parameter model RLM dilakukan dengan menggunakan metode Maximum Likelihood Estimation (MLE) dan iterasi Newton-Raphson. Pengujian hipotesis parameter model RLM menggunakan metode Likelihood Ratio Test (LRT) dan uji Wald. Pemilihan model terbaik dalam penelitian ini menggunakan metode backward dan interpretasi model RLM terbaik menggunakan nilai odds ratio. Hasil penelitian menunjukkan bahwa model RLM terbaik adalah model yang mempunyai tiga variabel prediktor. Faktor-faktor yang berpengaruh signifikan terhadap kombinasi antara status IPKM dan status IPM kabupaten/kota di pulau Kalimantan tahun 2018 adalah persentase penduduk miskin, pertumbuhan ekonomi, dan persentase penduduk yang berpendidikan minimal SMP.

Keywords

Collaboration network of the authors

33 authors · 77 co-authorship links

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  • Monash University
  • Affiliation unknown
  • Different organisations
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Show as table
Co-authorOrganisationJoint articles
Endang NurcahyaniAffiliation unknown6
Bambang IrawanMonash University4
Meiliyani SiringoringoAffiliation unknown3
Sumardi SumardiAffiliation unknown2
YuliantyAffiliation unknown2
Asrul SaniAffiliation unknown1
Muhammad SudiaAffiliation unknown1
Rochmah AgustrinaAffiliation unknown1
Herta M. ManullangAffiliation unknown1
Darnah DarnahAffiliation unknown1
Selsi SelsiAffiliation unknown1
Risma RasmaniAffiliation unknown1
Tundjung Tripeni HandayaniAffiliation unknown1
Resta TaniaAffiliation unknown1
Wanda AmeliaAffiliation unknown1
vega abresaAffiliation unknown1
Endang Nurcahyani2Affiliation unknown1
Lili ChrisnawatiAffiliation unknown1
Nurshella AphertaAffiliation unknown1
Resya Tamara AgustinAffiliation unknown1
Lutfiah YuniarAffiliation unknown1
Rezza Kusumma DewiyatnoAffiliation unknown1
Kharisma Purnama AgustinAffiliation unknown1
Melisa ArumsariAffiliation unknown1
Novita AndrianiAffiliation unknown1
Memi Nor HayatiAffiliation unknown1
Kartika RamadaniAffiliation unknown1
Adelia RamadhaniAffiliation unknown1
Rito GoejantoroAffiliation unknown1
Ardiman WiranataAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Multinomial Logistic Regression  To Model The Combination Of Phdi Status And Hdi Status Of Districts/Cities  In Kalimantan Island</dc:title>
	<dc:title xml:lang="id">Regresi Logistik Multinomial untuk Memodelkan Kombinasi antara Status IPKM dan Status IPM Kabupaten/Kota  di Pulau Kalimantan</dc:title>
	<dc:creator xml:lang="en">Paliling, Yusrian</dc:creator>
	<dc:creator xml:lang="en">Fathurahman, M.</dc:creator>
	<dc:creator xml:lang="en">Wahyuningsih, Sri </dc:creator>
	<dc:subject xml:lang="en">PHDI</dc:subject>
	<dc:subject xml:lang="en">HDI</dc:subject>
	<dc:subject xml:lang="en">LRT</dc:subject>
	<dc:subject xml:lang="en">MLE</dc:subject>
	<dc:subject xml:lang="en">Newton-Raphson</dc:subject>
	<dc:subject xml:lang="en">MLR</dc:subject>
	<dc:subject xml:lang="en">Wald test</dc:subject>
	<dc:subject xml:lang="id">IPKM</dc:subject>
	<dc:subject xml:lang="id">IPM</dc:subject>
	<dc:subject xml:lang="id">LRT</dc:subject>
	<dc:subject xml:lang="id">MLE</dc:subject>
	<dc:subject xml:lang="id">Newton-Raphson</dc:subject>
	<dc:subject xml:lang="id">RLM</dc:subject>
	<dc:subject xml:lang="id">Uji Wald</dc:subject>
	<dc:description xml:lang="en">Multinomial Logistics Regression (MLR) is a regression model developed from the Binary Logistics Regression (BLR) model. The response variable of the RLM model has three or more categories and has a multinomial distribution, with the data scale being nominal. The response variable in this study is a combination of the Public Health Development Index (PHDI) status and the Human Development Index (HDI) status of districts/cities in Kalimantan Island, 2018, divided into four categories with category one as a comparison. The predictor variables used were the number of the public health center, the percentage of poor people, economic growth, the pure junior high school participation rate, and the percentage of the population with a minimum of junior high school education. The MLR parameter model was estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson iteration. The hypothesis testing of the MLR model was used by the Likelihood Ratio Test (LRT) method and the Wald test. The best model selection in this study uses the backward method, and the interpretation of the best MLR model uses the odds ratio value. The results showed that the best MLR model is a model that has three predictor variables. The factors that significantly influenced the combination of PHDI status and the HDI status of districts/cities in Kalimantan Island in 2018 were the percentage of poor people, economic growth, and the percentage of people with the minimum level of education in junior high school.</dc:description>
	<dc:description xml:lang="id">Regresi Logistik Multinomial (RLM) merupakan model regresi yang dikembangkan dari model Regresi Logistik Biner (RLB). Variabel respon model RLM mempunyai tiga atau lebih kategori dan berdistribusi multinomial dengan skala datanya adalah nominal. Variabel respon dalam penelitian yaitu kombinasi antara status Indeks Pembangunan Kesehatan Masyarakat (IPKM) dan status Indeks Pembangunan Manusia (IPM) kabupaten/kota di pulau Kalimantan tahun 2018 yang terbagi dalam empat kategori dengan kategori satu sebagai pembanding. Variabel prediktor yang digunakan yaitu jumlah puskesmas, persentase penduduk miskin, pertumbuhan ekonomi, angka partisipasi murni SMP, dan persentase penduduk yang berpendidikan minimal SMP. Penaksiran parameter model RLM dilakukan dengan menggunakan metode Maximum Likelihood Estimation (MLE) dan iterasi Newton-Raphson. Pengujian hipotesis parameter model RLM menggunakan metode Likelihood Ratio Test (LRT) dan uji Wald. Pemilihan model terbaik dalam penelitian ini menggunakan metode backward dan interpretasi model RLM terbaik menggunakan nilai odds ratio. Hasil penelitian menunjukkan bahwa model RLM terbaik adalah model yang mempunyai tiga variabel prediktor.&amp;nbsp;Faktor-faktor yang berpengaruh signifikan terhadap kombinasi antara status IPKM dan status IPM kabupaten/kota di pulau Kalimantan tahun 2018 adalah persentase penduduk miskin, pertumbuhan ekonomi, dan persentase penduduk yang berpendidikan minimal SMP.</dc:description>
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	<dc:date>2023-05-05</dc:date>
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	<dc:identifier>10.20956/j.v19i3.22299</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 3 (2023): MAY, 2023; 460-472</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/22299/9708</dc:relation>
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	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
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