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These models are unified under the conjugate generalized linear mixed models framework, where conjugate refers to the fact that the marginal likelihood can be expressed in closed form, rather than implying inference via the Bayesian paradigm. The proposed framework allows simultaneous conjugacy for Gaussian, Poisson and gamma responses, and thus can accommodate both unit- and group-level covariates. Only group-level covariates can be incorporated for the binomial distribution. In a simulation of Poisson data, our framework outperformed its competitors in terms of computational time, and was competitive in terms of robustness against misspecification of the random effects distributions.<\/jats:p>","DOI":"10.1093\/biomet\/asz053","type":"journal-article","created":{"date-parts":[[2019,9,6]],"date-time":"2019-09-06T11:38:38Z","timestamp":1567769918000},"source":"Crossref","is-referenced-by-count":0,"title":["Analysis of grouped data using conjugate generalized linear mixed models"],"prefix":"10.1093","author":[{"given":"Jarod Y L","family":"Lee","sequence":"first","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter J","family":"Green","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Louise M","family":"Ryan","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,10,25]]},"reference":[{"journal-title":"lme4: Linear Mixed-Effects Models using \u2018Eigen\u2019 and S4","year":"2017","author":"Bates,","key":"2019102505494097000_B1"},{"key":"2019102505494097000_B2","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/01621459.1993.10594284","article-title":"Approximate inference in generalized linear mixed models","volume":"88","author":"Breslow,","year":"1993","journal-title":"J. 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