Minimum Hellinger Distance Estimation for k-Component Poisson Mixture with Random Effects

The k-component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component param...

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Bibliographic Details
Published in:Biometrics 2008-06, Vol.64 (2), p.508-518
Main Authors: Xiang, Liming, Yau, Kelvin K. W., Van Hui, Yer, Lee, Andy H.
Format: Article
Language:English
Subjects:
Biometric Methodology
Biometrics
Biometry - methods
Cluster Analysis
Computer Simulation
Data Interpretation, Statistical
Datasets
Estimating techniques
Estimation methods
Estimators
Gaussian quadratures
k-component Poisson mixture
Maximum likelihood estimation
Minimum Hellinger distance
Models, Statistical
Poisson Distribution
Population Dynamics
Probability
Probability distributions
Random effects
Regression analysis
Regression coefficients
Research methodology
Residual maximum likelihood estimation
Robustness
Urinary tract infections
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Summary:The k-component Poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations. However, the residual maximum likelihood estimation (REML) of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination. In the literature, the minimum Hellinger distance (MHD) estimation has been investigated to obtain robust estimation for finite Poisson mixtures. This article aims to develop a robust MHD estimation approach for k-component Poisson mixtures with normally distributed random effects. By applying the Gaussian quadrature technique to approximate the integrals involved in the marginal distribution, the marginal probability function of the k-component Poisson mixture with random effects can be approximated by the summation of a set of finite Poisson mixtures. Simulation study shows that the MHD estimates perform satisfactorily for data without outlying observation(s), and outperform the REML estimates when data are contaminated. Application to a data set of recurrent urinary tract infections (UTI) with random institution effects demonstrates the practical use of the robust MHD estimation method.
ISSN:0006-341X
1541-0420
DOI:10.1111/j.1541-0420.2007.00920.x