Robust Analysis of Salamander Data, Generalized Linear Model with Random Effects
S T Boris Chan, S K Choy. Jennifer, Carrie Ho Kwan Yam · 2003
Abstract The salamander mating data reported by McCullogh and Nelder (1989) have been analyzed by many researchers using both classical and Bayesian approaches. The study design in the data is crossed rather than nested. This imposes great computation difficulties when using the classical approach because the likelihood function cannot be factorized. Moreover, the likelihood function will become very complicated when non-normal random effects distributions are adopted. Hence, previous researches have always assumed normal distributions for the random effects. In this paper, we adopt a Bayesian approach and choose the Students distribution as an alternative to the normal distribution in order to allow for the possible thick tail behavior of the random effects and hence to provide a robust analysis. To identify possible outlying random effects, we represent the Students distribution as a scale mixtures of normal distribution within the Bayesian framework and the models are implemented using the Markov chain Monte Carlo method, in particular, the Gibbs sampler. Finally, we highlight the novel and interesting features of this data set.