• k-component Poisson mixture;
  • random effect;
  • residual maximum likelihood estimation;
  • robust estimation;
  • variance component

A robust version of residual maximum likelihood estimation for Poisson log-linear mixed model is developed, and the method is extended to k-component Poisson mixture with random effects. The method not only provides the robust estimators for the fixed effects and variance component parameters but also gives the robust prediction of random effects. Simulation results show that the proposed method is effective in limiting the impact of outliers under different data contamination schemes. The method is adopted to analyze the epilepsy seizure count data and the urinary tract infections data, which are deemed to contain several potential outliers. The results show that the proposed method provides better goodness of fit to the data and demonstrate the effect of the robust tuning mechanism. Copyright © 2012 John Wiley & Sons, Ltd.