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Data Analysis Using Regression and Multilevel/Hierarchical Models
Andrew Gelman,Yu-Sung Su +1 more
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TLDR
Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models.Abstract:
Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.read more
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Journal ArticleDOI
Fitting Linear Mixed-Effects Models Using lme4
TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.
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A general and simple method for obtaining R2 from generalized linear mixed-effects models
TL;DR: In this article, the authors make a case for the importance of reporting variance explained (R2) as a relevant summarizing statistic of mixed-effects models, which is rare, even though R2 is routinely reported for linear models and also generalized linear models (GLM).
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Generalized linear mixed models: a practical guide for ecology and evolution
Benjamin M. Bolker,Mollie Elizabeth Brooks,Connie J. Clark,Shane W. Geange,John R. Poulsen,M. Henry H. Stevens,Jada-Simone S. White +6 more
TL;DR: The use (and misuse) of GLMMs in ecology and evolution are reviewed, estimation and inference are discussed, and 'best-practice' data analysis procedures for scientists facing this challenge are summarized.
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Random effects structure for confirmatory hypothesis testing: Keep it maximal
TL;DR: It is argued that researchers using LMEMs for confirmatory hypothesis testing should minimally adhere to the standards that have been in place for many decades, and it is shown thatLMEMs generalize best when they include the maximal random effects structure justified by the design.
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Collinearity: a review of methods to deal with it and a simulation study evaluating their performance
Carsten F. Dormann,Jane Elith,Sven Bacher,Carsten M. Buchmann,Gudrun Carl,Gabriel Carré,Jaime Ricardo García Márquez,Bernd Gruber,Bruno Lafourcade,Pedro J. Leitão,Tamara Münkemüller,Colin J. McClean,Patrick E. Osborne,Björn Reineking,Boris Schröder,Andrew K. Skidmore,Damaris Zurell,Sven Lautenbach +17 more
TL;DR: It was found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection and the value of GLM in combination with penalised methods and thresholds when omitted variables are considered in the final interpretation.