Selecting the Best Linear Mixed Model Under REML

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On the Unnecessary Ubiquity of Hierarchical Linear Modeling (2017, background): “This topic has been recently researched (e.g., Gurka, 2006; Lukočienė, Varriale, & Vermunt, 2010; Whittaker & Furlow, 2009) although no consensus has been reached.”
New important developments in small area estimation (2013, methodology): “Gurka (2006) validates by simulations that one can use also in this case the mAIC with ψ̂REML, despite the use of different fixed effects design matrices under different models.”
Reproductive success of house sparrows along an urban gradient (2008, methodology): “As information theoretic approaches cannot generally be used to assess the importance of fixed factors in mixed models (Verbeke & Molenberghs, 2000; Gurka, 2006), Wald tests were used to select significant predictors of nesting success.”