Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

  • Lusi Eka Afri Universitas Pasir Pengaraian
Keywords: overdispersion, negative binomial regression, Conway-Maxwell-Poisson regression

Abstract

Regresi Binomial Negatif dan regresi Conway-Maxwell-Poisson merupakan solusi untuk mengatasi overdispersi pada regresi Poisson. Kedua model tersebut merupakan perluasan dari model regresi Poisson. Menurut Hinde dan Demetrio (2007), terdapat beberapa kemungkinan terjadi overdispersi pada regresi Poisson yaitu keragaman hasil pengamatan keragaman individu sebagai komponen yang tidak dijelaskan oleh model, korelasi antar respon individu, terjadinya pengelompokan dalam populasi dan peubah teramati yang dihilangkan. Akibatnya dapat menyebabkan pendugaan galat baku yang terlalu rendah dan akan menghasilkan pendugaan parameter yang bias ke bawah (underestimate). Penelitian ini bertujuan untuk membandingan model Regresi Binomial Negatif dan model regresi Conway-Maxwell-Poisson (COM-Poisson) dalam mengatasi overdispersi pada data distribusi Poisson berdasarkan statistik uji devians. Data yang digunakan dalam penelitian ini terdiri dari dua sumber data yaitu data simulasi dan data kasus terapan. Data simulasi yang digunakan diperoleh dengan membangkitkan data berdistribusi Poisson yang mengandung overdispersi dengan menggunakan bahasa pemrograman R berdasarkan karakteristik data berupa , peluang munculnya nilai nol (p) serta ukuran sampel (n). Data dibangkitkan berguna untuk mendapatkan estimasi koefisien parameter pada regresi binomial negatif dan COM-Poisson.  

Kata Kunci: overdispersi, regresi binomial negatif, regresi Conway-Maxwell-Poisson

Negative binomial regression and Conway-Maxwell-Poisson regression could be used to overcome over dispersion on Poisson regression. Both models are the extension of Poisson regression model. According to Hinde and Demetrio (2007), there will be some over dispersion on Poisson regression: observed variance in individual variance cannot be described by a model, correlation among individual response, and the population group and the observed variables are eliminated. Consequently, this can lead to low standard error estimation and to downward bias parameter estimation (underestimate). This study aims to compare the Negative Binomial Regression model and Conway-Maxwell-Poisson (COM- Poisson) regression model to overcome over dispersion of Poisson distribution data based on deviance test statistics. The data used in this study are simulation data and applied case data. The simulation data were obtained by generating the Poisson distribution data containing over dispersion using the R programming language based on data characteristic such as ?, the probability (p) of zero value and the sample size (n). The generated data is used to get the estimated parameter coefficient of the negative binomial regression and COM-Poisson.

Keywords: overdispersion, negative binomial regression and Conway-Maxwell-Poisson regression 

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Published
2017-03-30
How to Cite
Afri, L. E. (2017). Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson. Jurnal Gantang, 2(1), 79-87. https://doi.org/10.31629/jg.v2i1.66