Data Analysis Using Regression and Multilevel/Hierarchical Models: Analysis of variance

By Andrew Gelman, Jennifer L. Hill. 2006

63 citations recorded by the source corpus.

Subfields: Forestry, Management, Monitoring, Policy and Law, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b6e1b21fdd7d4d1ed29e844a5a962b5ec672f37f

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Citations in the corpus

Polygenic Modeling with Bayesian Sparse Linear Mixed Models (2012, background): “Standard terminology also refers to the coefficients ~ b as ‘‘fixed effects’’, but this phrase has a range of potential meanings [55] and so we avoid it here.”
Nested by design: model fitting and interpretation in a mixed model era (2013, background): “Nested designs can be fitted in a classical linear model with nested fixed effects, but this task is not entirely trivial, because the degrees of freedom need to be adapted to the experimental design in order to get the correct mean sum of squares (Underwood 1997; Quinn & Keough 2002; Gelman 2005).”
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2004, methodology): “More generally, for more complicated linear models such as the split-plot latin square, sα for any variance component is the root mean square of the coefficients’ residuals after projection to their constraint space (see Gelman, 2005, Section 3.1).”
2. Average Predictive Comparisons for Models with Nonlinearity, Interactions, and Variance Components (2007, methodology): “Evaluating changes about a central value can work well in practice—for example, Gelman and King (1993), Gelman, King, and Liu (1998), and King, Tomz, and Wittenberg (2000) use this approach to summarize and compare logistic regression models with interactions— but problems can arise when the space o”
Should I Use Fixed or Random Effects? (2014, background): “…has been written on the theoretical properties of both approaches (for example, Kreft and DeLeeuw 1998; Robinson 1998; Kennedy 2003; Frees 2004; Gelman 2005; Wilson and Butler 2007; Arceneaux and Nickerson 2009; Wooldridge 2010; Greene 2012), recommendations for applied researchers are often…”
Bayesian functional ANOVA modeling using Gaussian process prior distributions (2010, methodology): “Note that although Gelman (2005) also interpreted the superpopulation variances, which in our model are the marginal variances of the Gaussian processes, in this functional context we advocate simply treating them as higher-level hyper-parameters and not interpreting their marginal posterior…”