Sains Malaysiana 41(11)(2012): 1483–1487

Parameter Estimation on Zero-Inflated Negative Binomial Regression

with Right Truncated Data

(Anggaran Parameter untuk Regresi Binomial Negatif Sifar-Melambung dengan

Pemangkasan Data Sebelah Kanan)

Seyed Ehsan Saffari* & Robiah Adnan

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia

81310 Skudai, Johor, Malaysia

Received: 25 May 2012 / Accepted: 2 July 2012

ABSTRACT

A Poisson model typically is assumed for count data, but when there are so many zeroes in the response variable, because of overdispersion, a negative binomial regression is suggested as a count regression instead of Poisson regression. In this paper, a zero-inflated negative binomial regression model with right truncation count data was developed. In this model, we considered a response variable and one or more than one explanatory variables. The estimation of regression parameters using the maximum likelihood method was discussed and the goodness-of-fit for the regression model was examined. We studied the effects of truncation in terms of parameters estimation, their standard errors and the goodness-of-fit statistics via real data. The results showed a better fit by using a truncated zero-inflated negative binomial regression model when the response variable has many zeros and it was right truncated.

Keywords: Maximum likelihood; truncated data; zero-inflated negative binomial

ABSTRAK

Model Poisson biasanya diandaikan untuk data bilangan, tetapi apabila terdapat banyak nilai sifar bagi pemboleh ubah bersandar yang disebabkan oleh penyerakan lampau, regresi binomial negatif dicadangkan sebagai regresi bilangan. Dalam artikel ini, model regresi binomial negatif sifar-melambung, dengan pemangkasan data bilangan pada sebelah kanan dibangunkan. Dalam model ini, kami mempertimbangkan satu pemboleh ubah bersandar dan satu atau lebih pemboleh ubah tak bersandar. Anggaran bagi parameter regresi menggunakan kaedah kemungkinan maksimum dibincang dan ujian penyuaian untuk model regresi diperiksa. Kesan pemangkasan dari segi penganggaran parameter dan ralat piawai dikaji menggunakan data sebenar. Keputusan menunjukkan penyuaian adalah lebih baik apabila menggunakan model regresi binomial negatif sifar melambung dengar pemangkasan di sebelah kanan apabila pemboleh ubah respons mempunyai banyak sifar dan dipangkas di sebelah kanan.

Kata kunci: Binomial negatif sifar-melambung; data pangkasan; kemungkinan maksimum

REFERENCES

Cameron, A.C. & Trivedi, P.K. 1998. Regression Analysis of Count Data. Cambridge, UK: Cambridge University Press.

Famoye, F. & Singh, K.P. 2006. Zero-inflated generalized Poisson model with an application to domestic violence data. Journal of Data Science 4(1): 117-30.

Famoye, F. & Wang, W. 2004. Censored generalized Poisson regression model. Computational Statistics and Data Analysis 46: 547-560.

Hall, D.B. 2000. Zero-inflated Poisson and binomial regression with random effects: A case study. Biometrics 56: 1030-1039.

Lambert, D. 1992. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics 34: 1-14.

Saffari, S.E. & Robiah Adnan 2010. Zero-Inflated Negative Binomial Regression Model with Right Censoring Count Data. Proceedings of the Faculty of Science Postgraduate Conference (FSPGC’10); October 5-7, Johor, Malaysia.

*Corresponding author; email: ehsanreiki@yahoo.com