Implementasi Zero Inflated Beta Regression Model pada Proporsi Kematian Ibu di Kota Bandung Tahun 2020

Labana Kaulika; Nusar Hajarisman

doi:10.29313/bcss.v3i2.7879

Labana Kaulika Statistika, MIPA
Nusar Hajarisman Statistika, MIPA

DOI: https://doi.org/10.29313/bcss.v3i2.7879

Keywords: Maximum Likelihood Estimation, Proporsi Kematian Ibu, Zero Inflated Beta Regression

Abstract

Abstract. Zero inflated beta is a mixture of the continous distribution on (0, 1) and the generated distribution which can produce a non-negative probability to 0. Zero Inflated Beta Regression (BeZI) is a method that can handle or model data that has a high proportion of zeros or there are excess zeros in the data. In this study, the response variable y has a mix between the beta distribution and the point mass at zero. Estimation of the regression parameters from the zero inflated beta regression model uses the Maximum Likelihood Estimation (MLE), where the estimation process is solved numerically. The numerical method used is the Fisher’s scoring method based on the score vector and the Fisher Information matrix to estimate the parameters of the maternal mortality rate in the city of Bandung in 2020. The results of the research on the count regression model show that the percentage variable K1 has a negative effect on the proportion of maternal deaths in Bandung City in 2020, while in the zero inflation model it is found that there are no variables that have an influence on the proportion when maternal deaths do not occur.

Abstrak. Zero inflated beta merupakan campuran distribusi kontinu pada (0, 1) dan distribusi yang dibangkitkan dimana dapat menghasilkan probabilitas non-negatif ke 0. Zero Inflated Beta Regression (BeZI) merupakan metode yang dapat menangani atau memodelkan suatu data yang memiliki proporsi nol yang tinggi atau terdapat excess zero dalam data. Dalam skripsi ini, variabel respon memiliki percampuran antara distribusi beta dan titik massa pada nol. Penaksiran parameter regresi dari model regresi zero inflated beta menggunakan Maximum Likelihood Estimation (MLE), dimana proses penaksirannya diselesaikan secara numerik. Metode numerik yang digunakan yaitu metode Fisher’s scoring berdasarkan pada vektor skor dan matriks informasi Fisher untuk menaksir parameter dari angka kematian ibu di kota bandung tahun 2020. Hasil penelitian pada model count regression diperoleh bahwa variabel persentase K1 memiliki pengaruh negatif terhadap proporsi kematian ibu Kota Bandung tahun 2020, sedangkan pada model zero inflation diperoleh bahwa tidak ada variabel yang memiliki pengaruh terhadap proporsi pada saat tidak terjadinya kematian ibu.

References

Hajarisman, N. (2012, Mei). Penaksiran Parameter Model Regresi Beta untuk Memodelkan Data Proporsi. Statistika, Vol. 12 No. 1, 9-18.

Peng, X., Li, G., & Liu, Z. (2015). Zero-Inflated Beta Regression for Differential Abundance Analysis with Metagenomics Data. Journal of Computational Biology, Volume 23, Number 2, 1 - 9.

Masserini, L., Bini, M., & Pratesi, M. (2016). Effectiveness of Non-selective Evaluation Test Scores for Predicting First-year Performance in University Career: a Zero-inflated Beta Regression Approach. Springer, 1-16.

Walpole, R., Myers, R., Myers, S., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists, 9th ed. Boston: Pearson Education, Inc.

Junior, O. A., Guedes, T. A., Zuliani, A. M., & Nunes, W. M. (2017). Zero-inflated Beta Regression Model for Leaf Citrus Canker Incidence in Orange Genotypes Grafted Onto Different Rootstocks. Acta Scientiarum, Vol. 39, No. 2, 161-171.

Famoye, F., & Singh, K. P. (2006). Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data. Journal of Data Science, 4, 117-130.

Ospina, R., & Ferrari, S. L. (2012). A General Class of Zero-or-one Inflated Beta Regression Models. Elsevier, 1609-1623.

Ospina, R., & Ferrari, S. L. (2010). Inflated Beta Distributions. Springer, 111-126.

Jumiartanti, M., Indahwati, & Kurnia, A. (2017). Zero Inflated Beta Model in Small Area Estimation to Estimate Poverty Rates on Village Level in Langsa Municipality. IJCSN - International Journal of Computer Science and Network, Volume 6, 812-819.

Anderson, D., Burnham, K., & White, G. (1998). Comparison of Akaike Information Criterion and Consistent Akaike Information Criterion for Model Selection and Statistical Inference from Capture-Recapture Studies. Journal of Applied Statistics, Vol. 25 No. 2, 263-282.

Hosmer, D. W., & Lemeshow, S. (2000). Applied Logistic Regression. Canada: John Wiley & Sons, Inc.

Kurniawan, R., & Yuniarto, B. (2016). Analisis Regresi: Dasar dan Penerapannya dengan R. Jakarta: Kencana.

Lisnawati, & Prahastuti, D. L. (2021, Desember 2). Pengaruh Pendidikan Kesehatan Menggunakan Media Video Animasi Terhadap Kesiapan Ibu Hamil Dalam Menghadapi Persalinan. Jurnal Media Kesehatan, Vol. 14, No. 2, 146-154.

Tawangki Sri Fadilah and Abdul Kudus, “Penerapan Metode Regresi Kernel Smoothing untuk Imputasi Data Lama Waktu Terinfeksi Covid-19,” Jurnal Riset Statistika, pp. 51–60, Jul. 2023, doi: 10.29313/jrs.v3i1.1802.