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Statistical inference using generalized linear mixed models under informative cluster sampling
Author(s) -
Kim Jae Kwang,
Park Seunghwan,
Lee Youngjo
Publication year - 2017
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11339
Subject(s) - cluster sampling , statistics , estimator , statistical inference , mathematics , inference , sampling distribution , sampling (signal processing) , generalized linear mixed model , population , sample size determination , generalized linear model , computer science , artificial intelligence , demography , filter (signal processing) , sociology , computer vision
When a sample is obtained from a two‐stage cluster sampling scheme with unequal selection probabilities the sample distribution can differ from that of the population and the sampling design can be informative. In this case making valid inference under generalized linear mixed models can be quite challenging. We propose a novel approach for parameter estimation using an EM algorithm based on the approximate predictive distribution of the random effect. In the approximate predictive distribution instead of using the intractable sample likelihood function we use a normal approximation of the sampling distribution of the profile pseudo maximum likelihood estimator of the random effects in the level‐one model. Two limited simulation studies show that the proposed method using the normal approximation performs well for modest cluster sizes. The proposed method is applied to the real data arising from 2011 Private Education Expenditures Survey (PEES) in Korea. The Canadian Journal of Statistics 45: 479–497; 2017 © 2017 Statistical Society of Canada