[Abad et al., 2010]

Ariel Alonso Abad, Saskia Litière, and Geert Molenberghs. Testing for misspecification in generalized linear mixed models. Biostatistics (Oxford, England), 11(4):771–786, October 2010. (doi:10.1093/biostatistics/kxq019)

[Agresti, 2002]

Alan Agresti. Categorical Data Analysis. Wiley, Hoboken, NJ, 2d edition, 2002.

[Alonso et al., 2008]

A. Alonso, S. Litière, and G. Molenberghs. A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models. Computational Statistics & Data Analysis, 52(9):4474–4486, May 2008. (doi:10.1016/j.csda.2008.02.033)

[Anderson et al., 2022]

Sean C. Anderson, Eric J. Ward, Philina A. English, Lewis A. K. Barnett, and James T. Thorson. sdmTMB: An R package for fast, flexible, and user-friendly generalized linear mixed effects models with spatial and spatiotemporal random fields, March 2022. (doi:10.1101/2022.03.24.485545)

[Angrist and Pischke, 2009]

Joshua D. Angrist and Jörn-Steffen Pischke. Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press, Princeton, 1 edition edition, January 2009.

[Arnqvist, 2020]

Göran Arnqvist. Mixed Models Offer No Freedom from Degrees of Freedom. Trends in Ecology & Evolution, 35(4):329–335, April 2020. (doi:10.1016/j.tree.2019.12.004)

[Augustin et al., 2012]

Nicole H. Augustin, Erik-André Sauleau, and Simon N. Wood. On quantile quantile plots for generalized linear models. Computational Statistics & Data Analysis, 56(8):2404–2409, August 2012. (doi:10.1016/j.csda.2012.01.026)

[Baird and Maxwell, 2016]

Rachel Baird and Scott E. Maxwell. Performance of time-varying predictors in multilevel models under an assumption of fixed or random effects. Psychological Methods, 21(2):175–188, 2016. (doi:10.1037/met0000070)

[Banta et al., 2010]

Joshua A. Banta, Martin H. H. Stevens, and Massimo Pigliucci. A comprehensive test of the 'limiting resources' framework applied to plant tolerance to apical meristem damage. Oikos, 119(2):359–369, February 2010. (doi:10.1111/j.1600-0706.2009.17726.x)

[Barr et al., 2013]

Dale J. Barr, Roger Levy, Christoph Scheepers, and Harry J. Tily. Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3):255–278, April 2013. (doi:10.1016/j.jml.2012.11.001)

[Barr, 2020]

Dale J. Barr. Learning Statistical Models Through Simulation in R. PsyTeachR books. 2020.

[Bates and Maechler, 2010]

Douglas Bates and Martin Maechler. lme4: Linear mixed-effects models using S4 classes, 2010. R package version 0.999375-33.

[Bates et al., 2015]

Douglas Bates, Reinhold Kliegl, Shravan Vasishth, and Harald Baayen. Parsimonious Mixed Models. arXiv:1506.04967 [stat], June 2015. arXiv: 1506.04967.

[Bates et al., 2015]

Douglas Bates, Martin Mächler, Benjamin M. Bolker, and Steven C. Walker. Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1):1–48, 2015. (doi:10.18637/jss.v067.i01)

[Bates, 2017]

Douglas Bates. MixedModels.jl: A Julia package for fitting (statistical) mixed-effects models, November 2017. original-date: 2013-03-29T21:24:25Z.

[Bell and Grunwald, 2010]

Melanie L. Bell and Gary K. Grunwald. Small sample estimation properties of longitudinal count models. Journal of Statistical Computation and Simulation, 81(9):1067–1079, 2010. (doi:10.1080/00949651003674144)

[Bellio and Brazzale, 2011]

Ruggero Bellio and Alessandra R. Brazzale. Restricted likelihood inference for generalized linear mixed models. Statistics and Computing, 21(2):173–183, April 2011. (doi:10.1007/s11222-009-9157-4)

[Bellio et al., 2023]

Ruggero Bellio, Swarnadip Ghosh, Art B. Owen, and Cristiano Varin. Scalable Estimation of Probit Models with Crossed Random Effects, August 2023. arXiv:2308.15681 [stat]. (doi:10.48550/arXiv.2308.15681)

[Belshe et al., 2013]

E. F. Belshe, E. A. G. Schuur, and B. M. Bolker. Tundra ecosystems observed to be CO₂ sources due to differential amplification of the carbon cycle. Ecology Letters, 16:1307–1315, 2013. (doi:10.1111/ele.12164)

[Ben and Yohai, 2004]

Marta García Ben and Víctor J Yohai. Quantile-Quantile Plot for Deviance Residuals in the Generalized Linear Model. Journal of Computational and Graphical Statistics, 13(1):36–47, March 2004. (doi:10.1198/1061860042949_a)

[Berger et al., 1999]

J. O. Berger, B. Liseo, and R. L. Wolpert. Integrated likelihood methods for eliminating nuisance parameters. Statistical Science, 14(1):1–22, 1999.

[Bhattacharya and Dunson, 2011]

A. Bhattacharya and D. B. Dunson. Sparse Bayesian infinite factor models. Biometrika, 98(2):291–306, June 2011. (doi:10.1093/biomet/asr013)

[Biswas, 2015]

Keya Biswas. Performances of different estimation methods for generalized linear mixed models. Master's thesis, McMaster University, 2015.

[Bliss, 1935]

C. I. Bliss. The calculation of the dosage-mortality curve. Annals of Applied Biology, 22(1):134–167, 1935. (doi:10.1111/j.1744-7348.1935.tb07713.x)

[Bolker et al., 2009]

Benjamin M. Bolker, Mollie E. Brooks, Connie J. Clark, Shane W. Geange, John R. Poulsen, M. Henry H. Stevens, and Jada-Simone S. White. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology & Evolution, 24:127–135, 2009. (doi:10.1016/j.tree.2008.10.008)

[Bolker et al., 2013]

Benjamin M. Bolker, Beth Gardner, Mark Maunder, Casper W. Berg, Mollie Brooks, Liza Comita, Elizabeth Crone, Sarah Cubaynes, Trevor Davies, Perry de Valpine, Jessica Ford, Olivier Gimenez, Marc Kéry, Eun Jung Kim, Cleridy Lennert-Cody, Arni Magnusson, Steve Martell, John Nash, Anders Nielsen, Jim Regetz, Hans Skaug, and Elise Zipkin. Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS. Methods in Ecology and Evolution, 4(6):501–512, June 2013. (doi:10.1111/2041-210X.12044)

[Bolker, 2008]

Benjamin M. Bolker. Ecological Models and Data in R. Princeton University Press, Princeton, NJ, 2008.

[Bolker, 2015]

Benjamin M. Bolker. Linear and generalized linear mixed models. In Gordon A. Fox, Simoneta Negrete-Yankelevich, and Vinicio J. Sosa, editors, Ecological Statistics: Contemporary theory and application, chapter 13. Oxford University Press, 2015.

[Booth and Hobert, 1999]

James G. Booth and James P. Hobert. Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society. Series B, 61(1):265–285, 1999. (doi:10.1111/1467-9868.00176)

[Booth et al., 2003]

James Booth, George Casella, Herwig Friedl, and James Hobert. Negative binomial loglinear mixed models. Statistical Modelling, 3(3):179–191, 2003.

[Breiman, 2001]

Leo Breiman. Statistical Modeling: The Two Cultures. Statistical Science, 16(3):199–215, August 2001. There are two cultures in the use of statistical modeling to reach conclusions from data. One assumes that the data are generated by a given stochastic data model. The other uses algorithmic models and treats the data mechanism as unknown. The statistical community has been committed to the almost exclusive use of data models. This commitment has led to irrelevant theory, questionable conclusions, and has kept statisticians from working on a large range of interesting current problems. Algorithmic modeling, both in theory and practice, has developed rapidly in fields outside statistics. It can be used both on large complex data sets and as a more accurate and informative alternative to data modeling on smaller data sets. If our goal as a field is to use data to solve problems, then we need to move away from exclusive dependence on data models and adopt a more diverse set of tools.

[Breslow, 1984]

N. E. Breslow. Extra-Poisson variation in log-linear models. Journal of the Royal Statistical Society C, 33:38–44, 1984.

[Breslow, 2004]

N. E. Breslow. Whither PQL? In Danyu Y. Lin and P. J. Heagerty, editors, Proceedings of the second Seattle symposium in biostatistics: Analysis of correlated data, pages 1–22. Springer, 2004.

[Bridge et al.]

Helen Bridge, Katy E. Morgan, and Chris Frost. Negative variance components and intercept-slope correlations greater than one in magnitude: How do such “non-regular” random intercept and slope models arise, and what should be done when they do?. Statistics in Medicine, n/a(n/a). _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.10070. (doi:10.1002/sim.10070)

[Brooks et al., 2017]

Mollie E. Brooks, Kasper Kristensen, Koen J. van Benthem, Arni Magnusson, Casper W. Berg, Anders Nielsen, Hans J. Skaug, Martin Mächler, and Benjamin M. Bolker. glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. R Journal, 9:378–400, 2017.

[Browne et al., 2005]

W. J Browne, S. V. Subramanian, K. Jones, and H. Goldstein. Variance partitioning in multilevel logistic models that exhibit overdispersion. Journal of the Royal Statistical Society A, 168(3):599–613, 2005. (doi:10.1111/j.1467-985X.2004.00365.x)

[Burnham and Anderson, 2002]

K. P. Burnham and D. R. Anderson. Model Selection and Multimodel Inference. Springer, New York, 2d edition, 2002.

[Bürkner, 2017]

Paul-Christian Bürkner. brms: An R Package for Bayesian Multilevel Models Using Stan. Journal of Statistical Software, 80, 2017. (doi:10.18637/jss.v080.i01)

[Carpenter et al., 2016]

Bob Carpenter, Andrew Gelman, Matt Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Michael A. Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. Stan: A probabilistic programming language. Journal of Statistical Software, 20, 2016.

[Carpenter, 2017]

Bob Carpenter. Computational and statistical issues with uniform interval priors, November 2017.

[Carvalho et al., 2009]

Carlos M. Carvalho, Nicholas G. Polson, and James G. Scott. Handling Sparsity via the Horseshoe. In Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, pages 73–80. PMLR, April 2009. ISSN: 1938-7228.

[Chambers and Hastie, 1992]

John M. Chambers and Trevor J. Hastie. Statistical Models. In Statistical Models in S. Routledge, 1992. Num Pages: 32.

[Chung et al., 2013]

Yeojin Chung, Sophia Rabe-Hesketh, Vincent Dorie, Andrew Gelman, and Jingchen Liu. A nondegenerate penalized likelihood estimator for variance parameters in multilevel models. Psychometrika, pages 1–25, 2013. (doi:10.1007/s11336-013-9328-2)

[Clark and Linzer, 2015]

Tom S Clark and Drew A Linzer. Should I use fixed or random effects? Political Science Research and Methods, 3(02):399–408, 2015.

[Cleveland, 1993]

William Cleveland. Visualizing Data. Hobart Press, Summit, NJ, 1993.

[Cordeiro and Ferrari, 1998]

Gauss M. Cordeiro and Silvia L. P. Ferrari. A note on Bartlett-type correction for the first few moments of test statistics. Journal of Statistical Planning and Inference, 71(1-2):261–269, August 1998. (doi:10.1016/S0378-3758(98)00005-6)

[Cordeiro et al., 1994]

Gauss M. Cordeiro, Gilberto A. Paula, and Denise A. Botter. Improved likelihood ratio tests for dispersion models. International Statistical Review / Revue Internationale de Statistique, 62(2):257–274, 1994. (doi:10.2307/1403512)

[Crawley, 2002]

Michael J. Crawley. Statistical Computing: An Introduction to Data Analysis using S-PLUS. John Wiley & Sons, 2002.

[Cribari-Neto and Zeileis, 2009]

Francisco Cribari-Neto and Achim Zeileis. Beta Regression in R. Technical Report 98, WU Vienna University of Economics and Business, Vienna, Austria, 2009.

[Crome et al., 1996]

F. H. J. Crome, M. R. Thomas, and L. A. Moore. A novel Bayesian approach to assessing impacts of rain forest logging. Ecological Applications, 6:1104–1123, 1996.

[Davis, 1991]

Charles S Davis. Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials. Statistics in Medicine, 10(12):1959–1980, December 1991. (doi:10.1002/sim.4780101210)

[Dezeure et al., 2015]

Ruben Dezeure, Peter Bühlmann, Lukas Meier, and Nicolai Meinshausen. High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi. Statistical Science, 30(4):533–558, November 2015. (doi:10.1214/15-STS527)

[Dobson and Barnett, 2008]

Annette J. Dobson and Adrian Barnett. An Introduction to Generalized Linear Models, Third Edition. Chapman and Hall/CRC, 3 edition, May 2008.

[Dorie, 2011]

Vincent Dorie. blme: Bayesian Linear Mixed-Effects models, 2011. R package version 0.01-4.

[Dormann et al., 2007]

Carsten F. Dormann, Jana M. McPherson, Miguel B. Araújo, Roger Bivand, Janine Bolliger, Gudrun Carl, Richard G. Davies, Alexandre Hirzel, Walter Jetz, W. Daniel Kissling, Ingolf Kühn, Ralf Ohlemüller, Pedro R. Peres-Neto, Björn Reineking, Boris Schröder, Frank M. Schurr, and Robert Wilson. Methods to account for spatial autocorrelation in the analysis of species distributional data: a review. Ecography, 30(5):609–628, 2007. (doi:10.1111/j.2007.0906-7590.05171.x)

[Dushoff et al., 2006]

Jonathan Dushoff, Joshua B. Plotkin, Cecile Viboud, David J. D. Earn, and Lone Simonsen. Mortality due to Influenza in the United States—An Annualized Regression Approach Using Multiple-Cause Mortality Data. American Journal of Epidemiology, 163(2):181–187, January 2006. (doi:10.1093/aje/kwj024)

[Eager and Roy, 2017]

Christopher Eager and Joseph Roy. Mixed Effects Models are Sometimes Terrible. arXiv preprint arXiv:1701.04858, 2017.

[Ebbes et al., 2004]

P. Ebbes, U. Böckenholt, and M. Wedel. Regressor and random-effects dependencies in multilevel models. Statistica Neerlandica, 58(2):161–178, 2004.

[Efron, 1986]

B. Efron. Why isn't everyone a Bayesian?. The American Statistician, 40(1):1–5, February 1986. Publisher: Taylor & Francis _eprint: https://www.tandfonline.com/doi/pdf/10.1080/00031305.1986.10475342. (doi:10.1080/00031305.1986.10475342)

[Elston et al., 2001]

D. A. Elston, R. Moss, T. Boulinier, C. Arrowsmith, and X. Lambin. Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks. Parasitology, 122(5):563–569, 2001.

[Faraway, 2006]

Julian J. Faraway. Extending Linear Models with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman & Hall/CRC, 2006.

[Faraway, 2016]

Julian J. Faraway. Extending Linear Models with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman & Hall/CRC, 2 edition, 2016.

[Fears et al., 1996]

Thomas R. Fears, Jacques Benichou, and Mitchell H. Gail. A reminder of the fallibility of the Wald statistic. The American Statistician, 50(3):226–227, August 1996. (doi:10.2307/2684659)

[Feng et al., 2004]

Ziding Feng, Thomas Braun, and Charles McCulloch. Small sample inference for clustered data. In D. Y. Lin and P. J. Heagerty, editors, Proceedings of the Second Seattle Symposium in Biostatistics, volume 179, pages 71–87. Springer, New York, NY, 2004.

[Field and Welsh, 2007]

C. A. Field and A. H. Welsh. Bootstrapping clustered data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 69(3):369–390, June 2007. (doi:10.1111/j.1467-9868.2007.00593.x)

[Firth, 1993]

David Firth. Bias reduction of maximum likelihood estimates. Biometrika, 80(1):27–38, March 1993. (doi:10.1093/biomet/80.1.27)

[Fournier et al., 2011]

David A. Fournier, Hans J. Skaug, Johnoel Ancheta, James Ianelli, Arni Magnusson, Mark N. Maunder, Anders Nielsen, and John Sibert. AD model builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optimization Methods and Software, pages 1–17, 2011. (doi:10.1080/10556788.2011.597854)

[Freeman and Modarres, 2006]

Jade Freeman and Reza Modarres. Inverse Box-Cox: The power-normal distribution. Statistics & Probability Letters, 76(8):764–772, April 2006. (doi:10.1016/j.spl.2005.10.036)

[Freitas et al., 2016]

Carla Freitas, Esben M. Olsen, Halvor Knutsen, Jon Albretsen, and Even Moland. Temperature-associated habitat selection in a cold-water marine fish. Journal of Animal Ecology, 85(3):628–637, 2016. (doi:10.1111/1365-2656.12458)

[Friendly and Kwan, 2003]

Michael Friendly and Ernest Kwan. Effect ordering for data displays. Computational Statistics and Data Analysis, 43(4):509–539, August 2003. (doi:10.1016/S0167-9473(02)00290-6)

[Gao and Owen, 2017]

K. Gao and A. B. Owen. Estimation and Inference for Very Large Linear Mixed Effects Models. arXiv:1610.08088 [stat], May 2017. arXiv: 1610.08088.

[Gao and Owen, 2017]

Katelyn Gao and Art Owen. Efficient moment calculations for variance components in large unbalanced crossed random effects models. Electronic Journal of Statistics, 11(1):1235–1296, 2017. (doi:10.1214/17-EJS1236)

[Gao and Owen, 2020]

Katelyn Gao and Art B. Owen. Estimation and Inference for Very Large Linear Mixed Effects Models. Statistica Sinica, 30(4):1741–1771, 2020. Publisher: Institute of Statistical Science, Academia Sinica.

[Gelman and Hill, 2006]

Andrew Gelman and Jennifer Hill. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge, England, 2006.

[Gelman and Loken, 2014]

Andrew Gelman and Eric Loken. The Statistical Crisis in Science. American Scientist, 102(6):460–465, 2014.

[Gelman and Pardoe, 2006]

Andrew Gelman and Iain Pardoe. Bayesian measures of explained variance and pooling in multilevel (hierarchical) models. Technometrics, 48(2):241–251, 2006.

[Gelman and Stern, 2006]

Andrew Gelman and Hal Stern. The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant. The American Statistician, 60(4):328–331, November 2006. (doi:10.1198/000313006X152649)

[Gelman et al., 2002]

Andrew Gelman, Cristian Pasarica, and Rahul Dodhia. Let's practice what we preach: Turning tables into graphs. The American Statistician, 56(2):121–130, May 2002.

[Gelman et al., 2013]

Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. Bayesian Data Analysis. CRC Texts in Statistical Science. Chapman & Hall, 3 edition, 2013.

[Gelman, 2005]

Andrew Gelman. Analysis of variance: why it is more important than ever. Annals of Statistics, 33(1):1–53, 2005. (doi:10.1214/009053604000001048)

[Gelman, 2006]

Andrew Gelman. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1(3):515–533, 2006.

[Gelman, 2008]

Andrew Gelman. Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine, 27(15):2865–2873, July 2008. (doi:10.1002/sim.3107)

[Gelman, 2008]

Andrew Gelman. Objections to Bayesian statistics. Bayesian Analysis, 3:445–450, 2008. (doi:10.1214/08-BA318)

[Ghandwani et al., 2023]

Disha Ghandwani, Swarnadip Ghosh, Trevor Hastie, and Art B. Owen. Scalable solution to crossed random effects model with random slopes, September 2023. arXiv:2307.12378 [stat]. (doi:10.48550/arXiv.2307.12378)

[Ghosh et al., 2022]

Swarnadip Ghosh, Trevor Hastie, and Art B. Owen. Scalable logistic regression with crossed random effects. Electronic Journal of Statistics, 16(2):4604–4635, January 2022. Publisher: Institute of Mathematical Statistics and Bernoulli Society. (doi:10.1214/22-EJS2047)

[Ghosh et al., 2022]

Swarnadip Ghosh, Trevor Hastie, and Art B. Owen. Backfitting for large scale crossed random effects regressions. The Annals of Statistics, 50(1):560–583, February 2022. Publisher: Institute of Mathematical Statistics. (doi:10.1214/21-AOS2121)

[Goldman and Whelan, 2000]

Nick Goldman and Simon Whelan. Statistical tests of gamma-distributed rate heterogeneity in models of sequence evolution in phylogenetics. Molecular Biology and Evolution, 17(6):975–978, 2000.

[Gonzales-Barron and Butler, 2011]

Ursula Gonzales-Barron and Francis Butler. A comparison between the discrete Poisson-gamma and Poisson-lognormal distributions to characterise microbial counts in foods. Food Control, 22(8):1279–1286, August 2011. (doi:10.1016/j.foodcont.2011.01.029)

[Gotelli and Ellison, 2004]

Nicholas J. Gotelli and Aaron M. Ellison. A Primer of Ecological Statistics. Sinauer, Sunderland, MA, 2004.

[Greenland and Mansournia, 2015]

Sander Greenland and Mohammad Ali Mansournia. Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions. Statistics in Medicine, 34(23):3133–3143, October 2015. (doi:10.1002/sim.6537)

[Greven and Kneib, 2010]

Sonja Greven and Thomas Kneib. On the behaviour of marginal and conditional Akaike information criteria in linear mixed models. Biometrika, 97(4):773–789, 2010.

[Greven, 2008]

Sonja Greven. Non-Standard Problems in Inference for Additive and Linear Mixed Models. Cuvillier Verlag, Göttingen, Germany, 2008.

[Griewank and Walther, 2003]

Andreas Griewank and Andrea Walther. Introduction to Automatic Differentiation. Proc. Appl. Math. Mech, 2(1):45–49, 2003. (doi:10.1002/pamm.200310012)

[Hadfield, 2010]

Jarrod D. Hadfield. MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R package. Journal of Statistical Software, 33(2):1–22, 2 2010.

[Halekoh and Højsgaard, 2013]

Ulrich Halekoh and Søren Højsgaard. pbkrtest: Parametric bootstrap and Kenward Roger based methods for mixed model comparison, 2013. R package version 0.3-7.

[Hardin and Hilbe, 2007]

James William Hardin and Joseph Hilbe. Generalized linear models and extensions. Stata Press, February 2007.

[Harrell, 2001]

Frank Harrell. Regression Modeling Strategies. Springer, 2001.

[Harrison, 2014]

Xavier A. Harrison. Using observation-level random effects to model overdispersion in count data in ecology and evolution. PeerJ, 2:e616, October 2014. (doi:10.7717/peerj.616)

[Harrison, 2015]

Xavier A. Harrison. A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology and evolution. PeerJ, 3:e1114, July 2015. (doi:10.7717/peerj.1114)

[Hartig, 2018]

Florian Hartig. DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models, 2018. R package version 0.2.0.

[He et al., 2019]

Hua He, Hui Zhang, Peng Ye, and Wan Tang. A test of inflated zeros for Poisson regression models. Statistical methods in medical research, 28(4):1157–1169, April 2019. (doi:10.1177/0962280217749991)

[Hedeker et al., 2018]

Donald Hedeker, Stephen H. C. du Toit, Hakan Demirtas, and Robert D. Gibbons. A note on marginalization of regression parameters from mixed models of binary outcomes. Biometrics, 74(1):354–361, 2018. (doi:10.1111/biom.12707)

[Heiling et al., 2024]

Hillary M Heiling, Naim U Rashid, Quefeng Li, Xianlu L Peng, Jen Jen Yeh, and Joseph G Ibrahim. Efficient computation of high-dimensional penalized generalized linear mixed models by latent factor modeling of the random effects. Biometrics, 80(1):ujae016, March 2024. (doi:10.1093/biomtc/ujae016)

[Heiling et al., 2024]

Hillary M. Heiling, Naim U. Rashid, Quefeng Li, and Joseph G. Ibrahim. glmmPen: High Dimensional Penalized Generalized Linear Mixed Models, April 2024. arXiv:2305.08204 [stat]. (doi:10.48550/arXiv.2305.08204)

[Heisterkamp et al., 2017]

Simon H. Heisterkamp, Engelbertus van Willigen, Paul-Matthias Diderichsen, and John Maringwa. Update of the nlme Package to Allow a Fixed Standard Deviation of the Residual Error. The R Journal, 9(1):239–251, 2017.

[Hinde, 1982]

John Hinde. Compound Poisson regression models. In R. Gilchrist, editor, GLIM82: Proc. Int. Conf. on GLMs, pages 109–121. Springer, 1982.

[Hoaglin, 1980]

David C. Hoaglin. A Poissonness plot. The American Statistician, 34(3):146–149, 1980. (doi:10.2307/2683871)

[Hodges, 2016]

James S. Hodges. Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects. Chapman and Hall/CRC, April 2016.

[Hosmer et al., 1997]

D. W. Hosmer, T. Hosmer, S. Le Cessie, and S. Lemeshow. A Comparison of Goodness-of-Fit Tests for the Logistic Regression Model. Statistics in Medicine, 16(9):965–980, May 1997. (doi:10.1002/(SICI)1097-0258(19970515)16:9<965::AID-SIM509>3.0.CO;2-O)

[Huang, 2009]

Xianzheng Huang. Diagnosis of random-effect model misspecification in generalized linear mixed models for binary response. Biometrics, 65(2):361–368, June 2009. (doi:10.1111/j.1541-0420.2008.01103.x)

[Hughes and King, 2003]

A. Hughes and M. King. Model selection using AIC in the presence of one-sided information. Journal of Statistical Planning and Inference, 115:497–411, 2003.

[Hurlbert, 1984]

S. Hurlbert. Pseudoreplication and the design of ecological field experiments. Ecological Monographs, 54:187–211, 1984.

[Hurvich and Tsai, 1989]

Clifford M. Hurvich and Chih-Ling Tsai. Regression and time series model selection in small samples. Biometrika, 76(2):297 –307, June 1989. (doi:10.1093/biomet/76.2.297)

[Ibrahim et al., 2011]

Joseph G. Ibrahim, Hongtu Zhu, Ramon I. Garcia, and Ruixin Guo. Fixed and random effects selection in mixed effects models. Biometrics, 67(2):495–503, June 2011. WOS:000292504000017. (doi:10.1111/j.1541-0420.2010.01463.x)

[Ives and Helmus, 2011]

Anthony R. Ives and Matthew R. Helmus. Generalized linear mixed models for phylogenetic analyses of community structure. Ecological Monographs, 81(3):511–525, January 2011. (doi:10.1890/10-1264.1)

[Ives and Zhu, 2006]

Anthony R. Ives and Jun Zhu. Statistics for correlated data: phylogenies, space, and time. Ecological Applications, 16(1):20–32, 2006.

[Jaeger et al., 2017]

Byron C. Jaeger, Lloyd J. Edwards, Kalyan Das, and Pranab K. Sen. An R2 statistic for fixed effects in the generalized linear mixed model. Journal of Applied Statistics, 44(6):1086–1105, April 2017. (doi:10.1080/02664763.2016.1193725)

[James et al., 2013]

Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An introduction to statistical learning, volume 112. Springer, 2013.

[Jiang, 2008]

Jiming Jiang. Fence methods for mixed model selection. The Annals of Statistics, 36(4):1669–1692, August 2008. (doi:10.1214/07-AOS517)

[Jin and Lee, 2021]

Shaobo Jin and Youngjo Lee. A review of h-likelihood and hierarchical generalized linear model. WIREs Computational Statistics, 13(5):e1527, 2021. (doi:10.1002/wics.1527)

[Joe, 2008]

Harry Joe. Accuracy of Laplace approximation for discrete response mixed models. Computational Statistics & Data Analysis, 52(12):5066–5074, August 2008. (doi:10.1016/j.csda.2008.05.002)

[Johnson and Raven, 1973]

Michael P. Johnson and Peter H. Raven. Species number and endemism: The Galápagos archipelago revisited. Science, 179(4076):893–895, 1973. (doi:10.1126/science.179.4076.893)

[Johnson et al., 2015]

Paul C. D. Johnson, Sarah J. E. Barry, Heather M. Ferguson, and Pie Müller. Power analysis for generalized linear mixed models in ecology and evolution. Methods in Ecology and Evolution, 6(2):133–142, February 2015. (doi:10.1111/2041-210X.12306)

[Johnson, 2014]

Paul C.D. Johnson. Extension of Nakagawa & Schielzeth's R2glmm to random slopes models. Methods in Ecology and Evolution, 5(9):944–946, September 2014. (doi:10.1111/2041-210X.12225)

[Kain et al., 2015]

Morgan P. Kain, Ben M. Bolker, and Michael W. McCoy. A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects. PeerJ, 3:e1226, September 2015. (doi:10.7717/peerj.1226)

[Kampstra, 2008]

Peter Kampstra. Code snippet: Beanplot: A boxplot alternative for visual comparison of distributions. Journal of Statistical Software, 28(CS-1):??–??, November 2008.

[Kenward and Roger, 1997]

M. G Kenward and J. H Roger. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53(3):983–997, 1997.

[Kindsvater et al., 2013]

Holly K. Kindsvater, Suzanne E. Simpson, Gil G. Rosenthal, and Suzanne H. Alonzo. Male diet, female experience, and female size influence maternal investment in swordtails. Behavioral Ecology, 24(3):691–697, December 2013. (doi:10.1093/beheco/ars213)

[Knudson et al., 2021]

Christina Knudson, Sydney Benson, Charles Geyer, and Galin Jones. Likelihood-based inference for generalized linear mixed models: Inference with the R package glmm. Stat, 10(1):e339, 2021. (doi:10.1002/sta4.339)

[Kéry, 2010]

Marc Kéry. Introduction to WinBUGS for ecologists: Bayesian approach to regression, ANOVA, mixed models and related analyses. Elsevier, Boston, 2010.

[Laird and Ware, 1982]

Nan M. Laird and James H. Ware. Random-Effects Models for Longitudinal Data. Biometrics, 38(4):963–974, 1982. (doi:10.2307/2529876)

[Latimer et al., 2009]

A. M. Latimer, S. Banerjee, H. Sang Jr, E. S. Mosher, and J. A. Silander Jr. Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern united states. Ecology Letters, 12(2):144–154, 2009.

[Lawson et al., 1999]

A. Lawson, A. Biggeri, D. Bohning, E. LeSaffre, J. F. Viel, and R. Bertollini, editors. Disease Mapping and Risk Assessment for Public Health. Wiley, New York, 1999.

[le Cessie and van Houwelingen, 1991]

S. le Cessie and J. C. van Houwelingen. A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics, 47(4):1267–1282, December 1991. (doi:10.2307/2532385)

[Leamer, 2010]

Edward E Leamer. Tantalus on the road to asymptopia. Journal of Economic Perspectives, 24(2):31–46, 2010. (doi:10.1257/jep.24.2.31)

[Lee et al., 2017]

Jarod Y. L. Lee, Peter J. Green, and Louise M. Ryan. On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models. arXiv:1707.08538 [stat], July 2017. arXiv: 1707.08538.

[Lee et al., 2017]

Youngjo Lee, John A. Nelder, and Yudi Pawitan. Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood, Second Edition. Chapman and Hall/CRC, Boca Raton, Florida, 2 edition edition, August 2017.

[Lee et al., 2020]

Jarod Y. L. Lee, Peter J. Green, and Louise M. Ryan. Analysis of grouped data using conjugate generalized linear mixed models. Biometrika, 107(1):231–237, March 2020. Publisher: Oxford Academic. (doi:10.1093/biomet/asz053)

[Leek et al., 2012]

Jeff Leek, Roger Peng, and Rafa Irizarry. A deterministic statistical machine, August 2012.

[Leek et al., 2013]

Jeff Leek, Roger Peng, and Rafa Irizarry. The researcher degrees of freedom - recipe tradeoff in data analysis, July 2013.

[Leemis and McQueston, 2008]

Lawrence M Leemis and Jacquelyn T McQueston. Univariate Distribution Relationships. The American Statistician, 62(1):45–53, February 2008. (doi:10.1198/000313008X270448)

[Leemis et al., 2012]

Lawrence M. Leemis, Daniel J. Luckett, Austin G. Powell, and Peter E. Vermeer. Univariate Probability Distributions. Journal of Statistics Education, 20(3):null, November 2012. (doi:10.1080/10691898.2012.11889648)

[Lesnoff et al., 2004]

Matthieu Lesnoff, Géraud Laval, Pascal Bonnet, Sintayehu Abdicho, Asseguid Workalemahu, Daniel Kifle, Armelle Peyraud, Renaud Lancelot, and François Thiaucourt. Within-herd spread of contagious bovine pleuropneumonia in Ethiopian highlands. Preventive Veterinary Medicine, 64(1):27–40, June 2004. (doi:10.1016/j.prevetmed.2004.03.005)

[Lewandowski et al., 2009]

Daniel Lewandowski, Dorota Kurowicka, and Harry Joe. Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis, 100(9):1989–2001, October 2009. (doi:10.1016/j.jmva.2009.04.008)

[Lindsey, 1997]

James K. Lindsey. Applying Generalized Linear Models. Springer, 1997.

[Littell et al., 2006]

Ramon C. Littell, George A. Milliken, Walter W. Stroup, Russell D. Wolfinger, and Oliver Schabenberger. SAS for Mixed Models, Second Edition. SAS Publishing, 2006.

[Lo and Andrews, 2015]

Steson Lo and Sally Andrews. To transform or not to transform: using generalized linear mixed models to analyse reaction time data. Frontiers in Psychology, 6, 2015. (doi:10.3389/fpsyg.2015.01171)

[Lynch et al., 2014]

Heather J. Lynch, James T. Thorson, and Andrew Olaf Shelton. Dealing with under- and over-dispersed count data in life history, spatial, and community ecology. Ecology, 95(11):3173–3180, 2014.

[Madar, 2015]

Vered Madar. Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix. Statistics & Probability Letters, 103:142–147, August 2015. (doi:10.1016/j.spl.2015.03.014)

[Madsen and Thyregod, 2011]

Henrik Madsen and Poul Thyregod. Introduction to General and Generalized Linear Models. CRC Press, 2011.

[Maindonald and Braun, 2010]

J. Maindonald and J. Braun. Data Analysis and Graphics Using R, An Example-Based Approach. Cambridge University Press, 3 edition, 2010.

[Marschner, 2011]

Ian C. Marschner. glm2: Fitting generalized linear models with convergence problems. The R Journal, 3(2):12–15, December 2011.

[Martin et al., 2005]

Tara G. Martin, Brendan A. Wintle, Jonathan R. Rhodes, Petra M. Kuhnert, Scott A. Field, Samantha J. Low-Choy, Andrew J. Tyre, and Hugh P. Possingham. Zero tolerance ecology: improving ecological inference by modelling the source of zero observations: Modelling excess zeros in ecology. Ecology Letters, 8(11):1235–1246, November 2005. (doi:10.1111/j.1461-0248.2005.00826.x)

[Matuschek et al., 2017]

Hannes Matuschek, Reinhold Kliegl, Shravan Vasishth, Harald Baayen, and Douglas Bates. Balancing type I error and power in linear mixed models. Journal of Memory and Language, 94:305–315, 2017. (doi:10.1016/j.jml.2017.01.001)

[McCarthy, 2007]

M. McCarthy. Bayesian methods for ecology. Cambridge University Press, Cambridge, England, 2007.

[McCullagh and Nelder, 1989]

P. McCullagh and J. A. Nelder. Generalized Linear Models. Chapman and Hall, London, 1989.

[McCulloch and Neuhaus, 2011]

Charles E. McCulloch and John M. Neuhaus. Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter. Statistical Science, 26(3):388–402, August 2011. (doi:10.1214/11-STS361)

[McElreath, 2015]

Richard McElreath. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Chapman and Hall/CRC, Boca Raton, December 2015.

[McKeon et al., 2012]

C. Seabird McKeon, Adrian Stier, Shelby McIlroy, and Benjamin Bolker. Multiple defender effects: synergistic coral defense by mutualist crustaceans. Oecologia, 169(4):1095–1103, 2012. (doi:10.1007/s00442-012-2275-2)

[Meng, 2009]

Xiao-Li Meng. Decoding the H-likelihood. Statistical Science, 24(3), August 2009. (doi:10.1214/09-STS277C)

[Meng, 2011]

Xiao-Li Meng. What's the H in H-likelihood: A Holy Grail or an Achilles' Heel? In José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West, editors, Bayesian Statistics 9, page 0. Oxford University Press, October 2011. (doi:10.1093/acprof:oso/9780199694587.003.0016)

[Millar, 2011]

Russell B. Millar. Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB. John Wiley & Sons, July 2011.

[Molenberghs and Verbeke, 2007]

Geert Molenberghs and Geert Verbeke. Likelihood ratio, score, and Wald tests in a constrained parameter space. The American Statistician, 61(1):22–27, 2007. (doi:10.1198/000313007X171322)

[Moritz et al., 2023]

Max A. Moritz, Enric Batllori, and Benjamin M. Bolker. The role of fire in terrestrial vertebrate richness patterns. Ecology Letters, 26(4):563–574, 2023. _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1111/ele.14177. (doi:10.1111/ele.14177)

[Muff Stefanie et al., 2016]

Muff Stefanie, Held Leonhard, Keller Lukas F., and Matthiopoulos Jason. Marginal or conditional regression models for correlated non‐normal data?. Methods in Ecology and Evolution, 7(12):1514–1524, August 2016. (doi:10.1111/2041-210X.12623)

[Murtaugh, 2007]

Paul A Murtaugh. Simplicity and complexity in ecological data analysis. Ecology, 88(1):56–62, 2007.

[Myers et al., 2010]

Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, and Timothy J. Robinson. Appendix A.6: Computational details for GLMs for a noncanonical link. In Generalized Linear Models, pages 481–483. John Wiley & Sons, Inc., 2010.

[Müller et al., 2013]

Samuel Müller, J. L. Scealy, and A. H. Welsh. Model selection in linear mixed models. Statistical Science, 28(2):135–167, May 2013. (doi:10.1214/12-STS410)

[Nakagawa and Schielzeth, 2010]

Shinichi Nakagawa and Holger Schielzeth. Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists. Biological Reviews, 85(4):935–956, November 2010. (doi:10.1111/j.1469-185X.2010.00141.x)

[Nakagawa and Schielzeth, 2013]

Shinichi Nakagawa and Holger Schielzeth. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2):133–142, February 2013. (doi:10.1111/j.2041-210x.2012.00261.x)

[Nakagawa et al., 2017]

Shinichi Nakagawa, Paul C. D. Johnson, and Holger Schielzeth. The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of The Royal Society Interface, 14(134):20170213, September 2017. (doi:10.1098/rsif.2017.0213)

[Nelder, 1954]

J. A. Nelder. The interpretation of negative components of variance. Biometrika, 41:544–548, 1954.

[Oberpriller et al., 2021]

Johannes Oberpriller, Melina de Souza Leite, and Maximilian Pichler. Fixed or random? On the reliability of mixed-effects models for a small number of levels in grouping variables. bioRxiv, page 2021.05.03.442487, June 2021. Publisher: Cold Spring Harbor Laboratory Section: New Results. (doi:10.1101/2021.05.03.442487)

[O'Hara and Kotze, 2010]

Robert B. O'Hara and D. Johan Kotze. Do not log-transform count data. Methods in Ecology and Evolution, 1(2):118–122, June 2010. (doi:10.1111/j.2041-210X.2010.00021.x)

[O'Hara, 2007]

Bob O'Hara. Focus on DIC, December 2007.

[O'Hara, 2009]

Robert B. O'Hara. How to make models add up: A primer on GLMMs. Annales Zoologici Fennici, 46(2):124–137, April 2009. (doi:10.5735/086.046.0205)

[Ozgul et al., 2009]

Arpat Ozgul, Madan K Oli, Benjamin M Bolker, and Carolina Perez-Heydrich. Upper respiratory tract disease, force of infection, and effects on survival of gopher tortoises. Ecological Applications, 19(3):786–798, April 2009.

[Pasch et al., 2013]

Bret Pasch, Benjamin M. Bolker, and Steven M. Phelps. Interspecific dominance via vocal interactions mediates altitudinal zonation in neotropical singing mice. The American Naturalist, 182(5):E161–E173, November 2013. (doi:10.1086/673263)

[Pawitan, 2000]

Yudi Pawitan. A reminder of the fallibility of the Wald statistic: Likelihood explanation. The American Statistician, 54(1):54–56, February 2000. (doi:10.2307/2685612)

[Peng and Lu, 2012]

Heng Peng and Ying Lu. Model selection in linear mixed effect models. Journal of Multivariate Analysis, 109:109–129, August 2012. (doi:10.1016/j.jmva.2012.02.005)

[Phelps, 1982]

K. Phelps. Use of the complementary log-log function to describe dose-response relationships in insecticide evluation field trials. In R. Gilchrist, editor, GLIM.82: Proceedings of the International Conference on Generalized Linear Models, number 14 in Lecture Notes in Statistics. Springer, 1982.

[Pinheiro and Bates, 1996]

José C. Pinheiro and Douglas M. Bates. Unconstrained parametrizations for variance-covariance matrices. Statistics and Computing, 6(3):289–296, 1996. (doi:10.1007/BF00140873)

[Pinheiro and Bates, 2000]

José C. Pinheiro and Douglas M. Bates. Mixed-effects models in S and S-PLUS. Springer, New York, 2000.

[Plummer, 2003]

Martyn Plummer. JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling, 2003.

[Ponciano et al., 2009]

José Miguel Ponciano, Mark L. Taper, Brian Dennis, and Subhash R. Lele. Hierarchical models in ecology: Confidence intervals, hypothesis testing, and model selection using data cloning. Ecology, 90(2):356–362, February 2009.

[Pregibon, 1980]

Daryl Pregibon. Goodness of link tests for generalized linear models. Journal of the Royal Statistical Society. Series C (Applied Statistics), 29(1):15–14, January 1980. (doi:10.2307/2346405)

[Pryseley et al., 2011]

A. Pryseley, C. Tchonlafi, G. Verbeke, and G. Molenberghs. Estimating negative variance components from Gaussian and non-Gaussian data: A mixed models approach. Computational Statistics & Data Analysis, 55:1071–1085, 2011.

[Quinn and Keough, 2002]

Gerry P. Quinn and Michael J. Keough. Experimental Design and Data Analysis for Biologists. Cambridge University Press, Cambridge, England, 2002.

[Quiñones and Wcislo, 2015]

A. E. Quiñones and W. T. Wcislo. Cryptic extended brood care in the facultatively eusocial sweat bee Megalopta genalis. Insectes Sociaux, 62(3):307–313, August 2015. (doi:10.1007/s00040-015-0409-3)

[R Development Core Team, 2009]

R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2009. ISBN 3-900051-07-0.

[Rabe-Hesketh and Skrondal, 2008]

Sophia Rabe-Hesketh and Anders Skrondal. Multilevel and Longitudinal Modeling Using Stata. Stata Press, 2 edition, 2008.

[Richards, 2005]

Shane A. Richards. Testing ecological theory using the information-theoretic approach: examples and cautionary results. Ecology, 86(10):2805–2814, 2005. (doi:10.1890/05-0074)

[Rights and Sterba, 2018]

Jason D. Rights and Sonya K. Sterba. Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 2018. (doi:10.1037%2Fmet0000184)

[Robinson, 1991]

G. K. Robinson. That BLUP is a good thing: The estimation of random effects. Statistical Science, 6(1):15–32, February 1991.

[Roulin and Bersier, 2007]

Alexandre Roulin and Louis-Felix Bersier. Nestling barn owls beg more intensely in the presence of their mother than in the presence of their father. Animal Behaviour, 74(4):1099–1106, October 2007. (doi:10.1016/j.anbehav.2007.01.027)

[Rousset and Ferdy, 2014]

François Rousset and Jean-Baptiste Ferdy. Testing environmental and genetic effects in the presence of spatial autocorrelation. Ecography, page no–no, 2014. (doi:10.1111/ecog.00566)

[Rue et al., 2009]

H. Rue, S. Martino, and N. Chopin. Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71(2):319–392, 2009.

[Schaalje et al., 2002]

G. Schaalje, J. McBride, and G. Fellingham. Adequacy of approximations to distributions of test statistics in complex mixed linear models. Journal of Agricultural, Biological & Environmental Statistics, 7(14):512–524, 2002.

[Schabenberger and Pierce, 2001]

Oliver Schabenberger and Francis J. Pierce. Contemporary Statistical Models for the Plant and Soil Sciences. CRC Press, Boca Raton, FL, 2001.

[Schabenberger, 2007]

Oliver Schabenberger. Growing up fast: SAS® 9.2 enhancements to the GLIMMIX procedure. Orlando, Florida, 2007.

[Schad et al., 2018]

Daniel J. Schad, Sven Hohenstein, Shravan Vasishth, and Reinhold Kliegl. How to capitalize on a priori contrasts in linear (mixed) models: A tutorial. arXiv:1807.10451 [stat], July 2018. arXiv: 1807.10451.

[Scheipl et al., 2008]

Fabian Scheipl, Sonja Greven, and Helmut Kuechenhoff. Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models. Computational Statistics & Data Analysis, 52(7):3283–3299, 2008.

[Schelldorfer and Bühlmann, 2011]

J. Schelldorfer and P. Bühlmann. GLMMLasso: an algorithm for High-Dimensional generalized linear mixed models using L1-Penalization. Arxiv preprint arXiv:1109.4003, 2011.

[Schielzeth and Forstmeier, 2009]

Holger Schielzeth and Wolfgang Forstmeier. Conclusions beyond support: overconfident estimates in mixed models. Behavioral Ecology, 20(2):416–420, March 2009. (doi:10.1093/beheco/arn145)

[Schielzeth, 2010]

Holger Schielzeth. Simple means to improve the interpretability of regression coefficients. Methods in Ecology and Evolution, 1:103–113, 2010. (doi:10.1111/j.2041-210X.2010.00012.x)

[Schoener, 1970]

Thomas W. Schoener. Nonsynchronous Spatial Overlap of Lizards in Patchy Habitats. Ecology, 51(3):408–418, May 1970. (doi:10.2307/1935376)

[Self and Liang, 1987]

Steven G. Self and Kung-Yee Liang. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82(398):605–610, June 1987. (doi:10.1080/01621459.1987.10478472)

[Shang and Cavanaugh, 2008]

Junfeng Shang and Joseph E. Cavanaugh. Bootstrap variants of the Akaike information criterion for mixed model selection. Computational Statistics & Data Analysis, 52(4):2004–2021, January 2008. (doi:10.1016/j.csda.2007.06.019)

[Simmons et al., 2011]

Joseph P. Simmons, Leif D. Nelson, and Uri Simonsohn. False-positive psychology undisclosed flexibility in data collection and analysis allows presenting anything as significant. Psychological Science, 22(11):1359–1366, November 2011. (doi:10.1177/0956797611417632)

[Singmann, 2018]

Henrik Singmann. Compute effect sizes for mixed() objects, July 2018.

[Skaug and Fournier, 2006]

Hans J. Skaug and David A. Fournier. Automatic approximation of the marginal likelihood in non-gaussian hierarchical models. Computational Statistics & Data Analysis, 51(2):699–709, 2006.

[Skaug, 2002]

Hans J. Skaug. Automatic differentiation to facilitate maximum likelihood estimation in nonlinear random effects models. Journal of Computational and Graphical Statistics, 11(2):458–470, 2002. (doi:10.1198/106186002760180617)

[Smithson and Verkuilen, 2006]

Michael Smithson and Jay Verkuilen. A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological Methods, 11(1):54–71, March 2006. (doi:10.1037/1082-989X.11.1.54)

[Snijders and Bosker, 1993]

Tom A. B. Snijders and Roel J. Bosker. Standard Errors and Sample Sizes for Two-Level Research. Journal of Educational Statistics, 18(3):237, 1993. (doi:10.2307/1165134)

[Sólymos, 2010]

Péter Sólymos. dclone: Data cloning in R. The R Journal, 2(2):29–37, 2010.

[Spiegelhalter et al., 2002]

D. J. Spiegelhalter, N. Best, B. P. Carlin, and A. Van der Linde. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society B, 64:583–640, 2002.

[Steele et al., 1996]

F. Steele, I. Diamond, and S. Amin. Immunization uptake in rural Bangladesh: a multilevel analysis. Journal of the Royal Statistical Society A, 159:289–299, 1996.

[Stram and Lee, 1994]

Daniel O Stram and Jae Won Lee. Variance components testing in the longitudinal fixed effects model. Biometrics, 50(4):1171–1177, 1994.

[Stroup, 2013]

W. W. Stroup. Non-normal data in agricultural experiments. Kansas State University, 2013.

[Stroup, 2014]

Walter W. Stroup. Rethinking the analysis of non-normal data in plant and soil science. Agronomy Journal, 106:1–17, 2014. (doi:10.2134/agronj2013.0342)

[Sung and Geyer, 2007]

Yun Ju Sung and Charles J. Geyer. Monte Carlo likelihood inference for missing data models. The Annals of Statistics, 35(3):990–1011, July 2007. (doi:10.1214/009053606000001389)

[Sweetser, 2017]

Timothy Sweetser. diamond: Python solver for mixed-effects models, November 2017. original-date: 2017-08-07T19:06:10Z.

[Tanaka and Hui, 2019]

Emi Tanaka and Francis K. C. Hui. Symbolic Formulae for Linear Mixed Models. In Hien Nguyen, editor, Statistics and Data Science, Communications in Computer and Information Science, pages 3–21, Singapore, 2019. Springer. (doi:10.1007/978-981-15-1960-4_1)

[Tiwari et al., 2006]

Manjula Tiwari, Karen A. Bjorndal, Alan B. Bolten, and Benjamin M. Bolker. Evaluation of density-dependent processes and green turtle Chelonia mydas hatchling production at Tortuguero, Costa Rica. Marine Ecology Progress Series, 326:283–293, 2006.

[Uriarte and Yackulic, 2009]

Maria Uriarte and Charles B Yackulic. Preaching to the unconverted. Ecological Applications, 19(3):592–596, 2009.

[Vaida and Blanchard, 2005]

Florin Vaida and Suzette Blanchard. Conditional Akaike information for mixed-effects models. Biometrika, 92(2):351–370, June 2005. (doi:10.1093/biomet/92.2.351)

[van de Pol and Wright, 2009]

M. van de Pol and J. Wright. A simple method for distinguishing within-versus between-subject effects using mixed models. Animal Behaviour, 77(3):753–758, 2009.

[Vats and Knudson, 2018]

Dootika Vats and Christina Knudson. Revisiting the Gelman-Rubin Diagnostic. arXiv:1812.09384 [stat], December 2018. arXiv: 1812.09384.

[Venables and Ripley, 2002]

W. Venables and Brian D. Ripley. Modern Applied Statistics with S. Springer, New York, 4th edition, 2002.

[Venables, 1998]

W. N Venables. Exegeses on linear models. In 1998 International S-PLUS User Conference, Washington, DC, 1998.

[Verbeke and Lesaffre, 1997]

Geert Verbeke and Emmanuel Lesaffre. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Computational Statistics & Data Analysis, 23(4):541–556, February 1997. (doi:10.1016/S0167-9473(96)00047-3)

[Vuong, 1989]

Quang H. Vuong. Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses. Econometrica, 57(2):307–333, March 1989. (doi:10.2307/1912557)

[Wainer, 2001]

Howard Wainer. Visual revelations. Chance, 14(2):43–46, March 2001. (doi:10.1080/09332480.2001.10542269)

[Wang et al., 1992]

C. S. Wang, B. S. Yandell, and J. J. Rutledge. The dilemma of negative analysis of variance estimators of intraclass correlation. Theoretical and Applied Genetics, 85:79–88, 1992.

[Warton and Hui, 2011]

David I. Warton and Francis K. C. Hui. The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92:3–10, January 2011. (doi:10.1890/10-0340.1)

[Warton, 2005]

David I. Warton. Many zeros does not mean zero inflation: comparing the goodness-of-fit of parametric models to multivariate abundance data. Environmetrics, 16(3):275–289, 2005. (doi:10.1002/env.702)

[Whittingham et al., 2006]

Mark J. Whittingham, Philip A. Stephens, Richard B. Bradbury, and Robert P. Freckleton. Why do we still use stepwise modelling in ecology and behaviour? Journal of Animal Ecology, 75(5):1182–1189, 2006.

[Wickham, 2009]

Hadley Wickham. ggplot2: elegant graphics for data analysis. Springer New York, 2009.

[Wicklin, 2018]

Rick Wicklin. Fast simulation of multivariate normal data with an AR(1) correlation structure, October 2018.

[Wilkinson and Rogers, 1973]

G. N. Wilkinson and C. E. Rogers. Symbolic description of factorial models for analysis of variance. Applied Statistics, 22(3):392–399, 1973. (doi:10.2307/2346786)

[Wilkinson, 1999]

Leland Wilkinson. The grammar of graphics. Springer, New York, 1999.

[Wilson, 2015]

Paul Wilson. The misuse of the Vuong test for non-nested models to test for zero-inflation. Economics Letters, 127:51–53, February 2015. (doi:10.1016/j.econlet.2014.12.029)

[Wolfinger and O'Connell, 1993]

Russ Wolfinger and Michael O'Connell. Generalized linear mixed models a pseudo-likelihood approach. Journal of Statistical Computation and Simulation, 48(3-4):233–243, December 1993. (doi:10.1080/00949659308811554)

[Wood, 2017]

Simon Wood. Generalized Additive Models: An Introduction with R. CRC Texts in Statistical Science. Chapman & Hall, 2d edition, 2017.

[Xu et al., 2015]

Lizhen Xu, Andrew D. Paterson, Williams Turpin, and Wei Xu. Assessment and Selection of Competing Models for Zero-Inflated Microbiome Data. PLOS ONE, 10(7):e0129606, July 2015. (doi:10.1371/journal.pone.0129606)

[Xu, 2003]

R. Xu. Measuring explained variation in linear mixed effects models. Statist. Med., 22:3527–3541, 2003.

[Yu and Yau, 2012]

Dalei Yu and Kelvin K. W. Yau. Conditional akaike information criterion for generalized linear mixed models. Computational Statistics & Data Analysis, 56(3):629–644, March 2012. WOS:000298122600015. (doi:10.1016/j.csda.2011.09.012)

[Zhang et al., 2011]

Hui Zhang, Naiji Lu, Chanyong Feng, Sally W. Thurston, Yinglin Xia, Liang Zhu, and Xin M Tu. On fitting generalized linear mixed-effects models for binary responses using different statistical packages. Statistics in Medicine, 2011. (doi:10.1002/sim.4265)

[Zuur et al., 2009]

Alain F. Zuur, Elena N. Ieno, Neil J. Walker, Anatoly A. Saveliev, and Graham M. Smith. Mixed Effects Models and Extensions in Ecology with R. Springer, March 2009.

[Zuur et al., 2009]

Alain F. Zuur, Elena N. Ieno, Neil J. Walker, Anatoly A. Saveliev, and Graham M. Smith. Zero-Truncated and Zero-Inflated Models for Count Data. In Mixed effects models and extensions in ecology with R, pages 261–293. Springer New York, New York, NY, 2009.