Estimasi Model Regresi Poisson Menggunakan Metode Iteratively Reweighted Least Square
Abstract: Poisson regression model is a
regression model that included
the application of theGeneralized
Linear Model (GLM) which does not require the assumption of normality of the
response variables and homogeneity of variance. The purpose of this final
project is using an iterative technique that produces the maximum likelihood
estimator for the regression coefficient β�through
the procedure with the approach Iteratively Reweighted Least Square (IRWLS) and
testing the goodness of fit for the model. To estimate the model parameters can
be obtained by solving the equation of the form: ∂ℓ ∂β j=�yixij −�exp�𝐗𝐢𝐓𝛃�.xijni=1ni=1=0 ,j =0,1,…,k
Above equation can only be expressed in implicit form that must be solved
using numerical iteration. In this final project used IRWLS iteration
algorithm. This Poisson regression model can be applied on the data of number
of Dengue Hemorrhagic Fever (DHF)
patients in each district / city in East Java province in 2009 with 28
observations. The variable response is the
number of Dengue Hemorrhagic Fever (DHF) patients (y),
whereas the predictor responses are the percentage of households who
have health waste (x1), the percentage of households who free from mosquito larva
of Aedes Aegepty (x2), the percentage of households who use clean water (x3)
and the percentage of households who have healthy haouse (x4). The estimation
result using S-Plus 2000 is:𝐸(𝑦𝑖|𝒙𝑖)=𝑒𝑥𝑝(8.840−0.095𝑥1𝑖
−0.028𝑥2𝑖 −0.017𝑥3𝑖
−0.571𝑥4𝑖)
The result of the Poisson regression model goodness of fit test with
deviance statistic test can be concluded that the expectation model and the
real model are fit.
Keywords: Generalized Linear
Model, Poisson Regression, Maximum Likelihood, IRWLS Algorithm,
Deviance Statistic Test
Penulis: Sandy Fauzi, Toha
Saifudin, Suliyanto
Kode Jurnal: jpmatematikadd130071
