Nisa', Ifah Durrotun (2023) Pemodelan Multivariate Adaptive Inverse Gaussian Regression Spline untuk Estimasi Pengeluaran Konsumsi Per Kapita Rumah Tangga di Kabupaten Pohuwato. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Multivariate Adaptive Regression Spline (MARS) merupakan pendekatan regresi nonparametrik yang cukup banyak digunakan karena mampu mengakomodir pengaruh aditif dan interaksi antar variabel prediktor. Metode ini digunakan untuk pemodelan data berdimensi tinggi. Pengembangan model MARS untuk variabel respon yang memiliki karakteristik skewness positif adalah MAGRS, yaitu gabungan antara MARS dan regresi gamma. Namun pada kasus tertentu, variabel respon memiliki karakteristik skewness positif yang lebih besar dari satu (highly skewness). Contoh riilnya adalah distribusi pengeluaran per kapita. Pendekatan yang dapat digunakan untuk kondisi data tersebut adalah distribusi inverse Gaussian. Multivariate Adaptive Inverse Gaussian Regression Spline (MAIGRS) merupakan pengembangan dari metode MARS dan regresi Inverse Gaussian. Penaksiran parameter model diperoleh dengan metode Weighted Least Square (WLS) dan Maximum Likelihood Estimation (MLE). Pengujian secara serentak menggunakan Maximum Likelihood Ratio Test (MLRT). Penerapan model MAIGRS dilakukan untuk estimasi pengeluaran per kapita rumah tangga di Kabupaten Pohuwato. Data yang digunakan bersumber dari data sekunder Survei Sosial Ekonomi Nasional (SUSENAS) Kabupaten Pohuwato dengan jumlah observasi sebanyak 1082 rumah tangga. Berdasarkan hasil trial dan error kombinasi Basis Fungsi (BF), Maksimum Interaksi (MI), dan Minimum Observasi (MO), model terbaik adalah kombinasi BF=76, MI=3, MO=1. Hasil penelitian menunjukkan, berdasarkan nilai kepentingan variabel prediktor, empat variabel yang memiliki peranan besar dalam pemodelan pengeluaran per kapita rumah tangga adalah persentase ART berpendidikan SMA ke atas, Jenis lantai, Jumlah ART usia produktif, dan Jumlah ART usia nonproduktif, dengan nilai kepentingan variabel lebih dari 80 persen. Nilai MAPE dari hasil pemodelan ini adalah sebesar 36,014 persen, yang terkategori sebagai reasonable prediction atau model yang dihasilkan layak untuk prediksi.
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Multivariate Adaptive Regression Spline (MARS) is a nonparametric regression approach that widely used because it is able to accommodate additive and interactions effects between predictor variables. This method is used for modeling high-dimensional data. MARS model development for response variables that have positive skewness characteristics is MAGRS, which is a combination of MARS and gamma regression. However, in certain cases, the response variable has a positive skewness characteristic that is greater than one (highly skewness). The real example is the distribution of expenditure per capita. The approach that can be used for these data conditions is inverse Gaussian distribution. Multivariate Adaptive Inverse Gaussian Regression Spline (MAIGRS) is combination of MARS method and Inverse Gaussian regression. Estimation of model parameters is obtained by Weighted Least Square (WLS) and Maximum Likelihood Estimation (MLE). Simultaneous testing using Maximum Likelihood Ratio Test (MLRT). Application of the MAIGRS model is carried out to estimate household per capita expenditure in Pohuwato Regency. Secondary data from Pohuwato Regency National Socioeconomic Survey (SUSENAS) was used with number of observation is 1082 households. Based on the results on trial and error combinations of Basis Function (BF), Maximum Interaction (MI), and Minimum Observation (MO), the best model is a combination of BF=76, MI=3, MO=1. The results showed that based on the importance value of predictor variable, four variables that have major role in modeling household per capita expenditure were proportion of household members with high school education and above, type of floor, number of productive age household members, and number of non-productive age household members, with a value of the variable interest of more than 80 percent. MAPE value from this modeling is 36,014 percent, which is categorized as a reasonable prediction or the provided model is feasible for prediction.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | MAIGRS, MARS, MLE, Pengeluaran per Kapita, WLS, Per capita expenditure |
| Subjects: | H Social Sciences > HA Statistics > HA29 Theory and method of social science statistics H Social Sciences > HA Statistics > HA31.3 Regression. Correlation H Social Sciences > HB Economic Theory > HB801 Consumer behavior. Q Science > QA Mathematics > QA275 Theory of errors. Least squares. Including statistical inference. Error analysis (Mathematics) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Ifah Durrotun Nisa' |
| Date Deposited: | 09 Aug 2023 13:07 |
| Last Modified: | 09 Aug 2023 13:07 |
| URI: | http://repository.its.ac.id/id/eprint/104431 |
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