Abstract:
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When the sample is obtained from a two-stage cluster sampling with unequal selection probabilities, the sample distribution can be different from that of the population and the sampling design can be informative. In this case, making valid inference under generalized linear mixed model can be quite challenging. In this paper, we propose a novel approach of parameter estimation using normal approximation of the sampling distribution of the profile pseudo maximum likelihood estimator of the random effects in the level one model. The computation for parameter estimation can be performed by either Monte Carlo EM algorithm or direct maximization of the pseudo marginal log-likelihood. Two limited simulation studies show that the proposed method using normal approximation performs well for modest cluster sizes.
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