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@InCollection{Chambers:1993,
  author = 	 {John M. Chambers},
  title = 	 {Linear Models},
  booktitle = 	 {Statistical Models in \proglang{S}},
  publisher =	 {Chapman \& Hall},
  year =	 1993,
  editor = 	 {John M. Chambers and Trevor J. Hastie},
  chapter =	 4,
  pages = {95--144},
}

@book{Rauden:Bryk:2002,
	Author = {Stephen W. Raudenbush and Anthony S. Bryk},
	Edition = {2nd},
	Isbn = {0-7619-1904-X},
	Publisher = {Sage},
	Title = {Hierarchical Linear Models: Applications and Data Analysis Methods},
	Year = 2002
}

@book{MLwiNUser:2000,
	Address = {London},
	Author = {J. Rasbash and W. Browne and H. Goldstein and M. Yang and I. Plewis},
	Publisher = {Multilevel Models Project, Institute of Education, University of London},
	Title = {A User's Guide to \pkg{MLwiN}},
	Year = 2000}

                  @Book{davis06:csparse_book,
  address =	 {Philadelphia, PA},
  author =	 {Tim Davis},
  publisher =	 {SIAM},
  title =	 {Direct Methods for Sparse Linear Systems},
  year =	 2006,
  doi =		 {10.1137/1.9780898718881},
}

@Article{laird_ware_1982,
  author =	 {Nan M. Laird and James H. Ware},
  journal =	 {Biometrics},
  pages =	 {963--974},
  title =	 {Random-Effects Models for Longitudinal Data},
  volume =	 38,
  number =	 4,
  year =	 1982,
  doi =		 {10.2307/2529876},
}

@Book{bateswatts88:_nonlin,
  address =	 {Hoboken, NJ},
  author =	 {Douglas M. Bates and Donald G. Watts},
  publisher =	 {John Wiley \& Sons},
  title =	 {Nonlinear Regression Analysis and Its Applications},
  year =	 1988,
  doi =		 {10.1002/9780470316757},
}

@book{R:Pinheiro+Bates:2000,
  Author =	 {Jose C. Pinheiro and Douglas M. Bates},
  Title =	 {Mixed-Effects Models in \proglang{S} and \proglang{S-PLUS}},
  Year =	 2000,
  Orderinfo =	 {springer.txt},
  ISBN =	 {0-387-98957-0},
  Publisher =	 {Springer-Verlag},
  Abstract =	 {A comprehensive guide to the use of the `nlme' package
                  for linear and nonlinear mixed-effects models.},
}

@article{bates04:_linear,
	Author = {Douglas M. Bates and Saikat DebRoy},
	Journal = {Journal of Multivariate Analysis},
	doi = {10.1016/j.jmva.2004.04.013},
	Number = 1,
	Pages = {1--17},
	Title = {Linear Mixed Models and Penalized Least Squares},
	Volume = 91,
	Year = 2004}

@article{gelman2005analysis,
  title = {Analysis of Variance --- Why it is More Important than Ever},
  author = {Gelman, Andrew},
  journal = {The Annals of Statistics},
  volume = 33,
  number = 1,
  pages = {1--53},
  year = 2005,
  doi = {10.1214/009053604000001048},
  publisher =	 {Institute of Mathematical Statistics}
}

@ARTICLE{1977EfronAndMorris,
   author = {{Efron}, B. and {Morris}, C.},
    title = "{Stein's Paradox in Statistics}",
  journal = {Scientific American},
     year = 1977,
    month = may,
   volume = 236,
    pages = {119-127},
      doi = {10.1038/scientificamerican0577-119},
   adsurl = {http://adsabs.harvard.edu/abs/1977SciAm.236e.119E},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{henderson_1982,
  author =	 {Charles R. {Henderson Jr.}},
  Title =	 {Analysis of Covariance in the Mixed Model: Higher-Level,
                  Nonhomogeneous, and Random Regressions},
  Journal =	 {Biometrics},
  Year =	 1982,
  Volume =	 38,
  Number =	 3,
  Pages =	 {623--640},
  Language =	 {English},
  Publisher =	 {International Biometric Society},
  Url =		 {http://www.jstor.org/stable/2530044},
}

@article{golub_pereyra_1973,
  Author =	 {Golub, G. H. and Pereyra, V.},
  Title =	 {The Differentiation of Pseudo-Inverses and Nonlinear
                  Least Squares Problems Whose Variables Separate},
  Year =	 1973,
  Journal =	 {SIAM Journal on Numerical Analysis},
  Volume =	 10,
  Number =	 2,
  Pages =	 {413--432},
  doi =		 {10.1137/0710036},
}

@article{sleepstudy,
	Author = {Gregory Belenky and Nancy J. Wesensten and David R. Thorne and Maria L. Thomas and Helen C. Sing and Daniel P. Redmond and Michael B. Russo and Thomas J. Balkin},
	Date-Modified = {2014-02-14 21:07:17 +0000},
	Journal = {Journal of Sleep Research},
	Pages = {1--12},
	Title = {Patterns of Performance Degradation and Restoration During Sleep Restriction and Subsequent Recovery: A Sleep Dose-Response Study},
	Volume = 12,
	Year = 2003,
 doi = {10.1046/j.1365-2869.2003.00337.x},
}

@article{Chen:2008:ACS:1391989.1391995,
 author = {Chen, Yanqing and Davis, Timothy A. and Hager, William W. and Rajamanickam, Sivasankaran},
 title = {Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate},
 journal = {ACM Trans. Math. Softw.},
 year = 2008,
 volume = 35,
 number = 3,
 month = oct,
 issn = {0098-3500},
 pages = {22:1--22:14},
 articleno = 22,
 doi = {10.1145/1391989.1391995},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {Cholesky factorization, linear equations, sparse matrices},
}


@article{kenward_small_1997,
	author = {M. G Kenward and J. H Roger},
	title = {Small Sample Inference for Fixed Effects from Restricted
                  Maximum Likelihood},
	year = {1997},
	journal = {Biometrics},
	volume = {53},
	number = {3},
	pages = {983--997},
	abstract = {Restricted maximum likelihood {(REML)} is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T\${\textasciicircum}2\$ type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different {REML} analyses and the methods are illustrated using three examples.},
  doi =		 {10.2307/2533558},
}

@Article{Satterthwaite_1946,
  author = 	 {F. E. Satterthwaite},
  title = 	 {An Approximate Distribution of Estimates of Variance Components},
  journal = 	 {Biometrics Bulletin},
  year = 	 1946,
  volume =	 2,
  number =	 6,
  pages =	 {110-114},
 doi =		 {10.2307/3002019},

}

@Manual{gamm4,
  title =	 {\pkg{gamm4}: Generalized Additive Mixed Models Using
                  \pkg{mgcv} and \pkg{lme4}},
  author =	 {Simon Wood and Fabian Scheipl},
  year =	 2014,
  note =	 {\proglang{R} package version 0.2-3},
  url =		 {https://CRAN.R-project.org/package=gamm4},
}

@Manual{blme,
    title = {\pkg{blme}: {Bayesian} Linear Mixed-Effects Models},
    author = {Vincent Dorie},
    year = 2015,
    note = {R package version 1.0-4},
    url = {https://CRAN.R-project.org/package=blme},
  }

@Article{blme2,
  title =	 {A Nondegenerate Penalized Likelihood Estimator for
                  Variance Parameters in Multilevel Models},
  author =	 {Yeojin Chung and Sophia Rabe-Hesketh and Vincent
                  Dorie and Andrew Gelman and Jingchen Liu},
  year =	 2013,
  journal =	 {Psychometrika},
  volume =	 78,
  number =	 4,
  pages =	 {685--709},
}

@article{doran2007estimating,
  author={Doran, Harold and Bates, Douglas and Bliese, Paul and Dowling, Maritza},
  title={Estimating the Multilevel {Rasch} Model: With the \pkg{lme4} Package},
  year=2007,
  journal={Journal of Statistical Software},
  volume=20,
  number=2,
  pages={1--18},
  doi =		 {10.18637/jss.v020.i02},
  publisher={American Statistical Association},
}


@TechReport{Powell_bobyqa,
  author = 	 {M. J. D. Powell},
  title = 	 {The {BOBYQA} Algorithm for Bound Constrained Optimization without Derivatives},
  institution =  {Centre for Mathematical Sciences, University of Cambridge},
  year = 	 {2009},
  number =	 {DAMTP 2009/NA06},
  address =	 {Cambridge, England},
  url =  {http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf}
}


@article{pinheiro_unconstrained_1996,
	title = {Unconstrained Parametrizations for Variance-Covariance Matrices},
	volume = {6},
	doi = {10.1007/BF00140873},
	abstract = {The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We compare the parametrizations based on their computational efficiency and statistical interpretability. The results described here are particularly useful in maximum likelihood and restricted maximum likelihood estimation in linear and non-linear mixed-effects models, but are also applicable to other areas of statistics.},
	number = {3},
	urldate = {2010-01-05},
	journal = {Statistics and Computing},
	author = {Pinheiro, José C. and Bates, Douglas M.},
	year = {1996},
	pages = {289--296}
}

@article{bolker_strategies_2013,
  title =	 {Strategies for Fitting Nonlinear Ecological Models
                  in \proglang{R}, \pkg{AD Model Builder}, and
                  \proglang{BUGS}},
	volume = 4,
	doi = {10.1111/2041-210X.12044},
	number = 6,
	urldate = {2013-06-11},
	journal = {Methods in Ecology and Evolution},
	author = {Bolker, Benjamin M. and Gardner, Beth and Maunder, Mark and Berg, Casper W. and Brooks, Mollie and Comita, Liza and Crone, Elizabeth and Cubaynes, Sarah and Davies, Trevor and de Valpine, Perry and Ford, Jessica and Gimenez, Olivier and Kéry, Marc and Kim, Eun Jung and Lennert-Cody, Cleridy and Magnusson, Arni and Martell, Steve and Nash, John and Nielsen, Anders and Regetz, Jim and Skaug, Hans and Zipkin, Elise},
	editor = {Ramula, Satu},
	month = jun,
	year = 2013,
	pages = {501--512},
        pdf={bbpapers/bolker_strategies_2013.pdf}
}


@Article{Klein_nelder_2013,
  author = 	 {Kyle Klein and Julian Neira},
  title = 	 {{Nelder-Mead} Simplex Optimization Routine for Large-Scale Problems: A Distributed Memory Implementation},
  journal = 	 {Computational Economics},
  year = 	 2013,
doi =  {10.1007/s10614-013-9377-8}
}

@Misc{merBoot,
  author =	 {José A. Sánchez-Espigares and Jordi Ocaña},
  title =	 {An \proglang{R} Implementation of Bootstrap Procedures for Mixed Models},
  howpublished = {Conference presentation, useR!},
  month =	 {July},
  year =	 {2009},
  note =	 {accessed 25 May 2014},
  url = {https://www.r-project.org/conferences/useR-2009/slides/SanchezEspigares+Ocana.pdf}
}



@book{gelman_data_2006,
	address = {Cambridge, England},
	title = {Data Analysis Using Regression and {Multilevel/Hierarchical} Models},
	url = {https://sites.stat.columbia.edu/gelman/arm/},
	publisher = {Cambridge University Press},
	author = {Gelman, Andrew and Hill, Jennifer},
	year = {2006},
	keywords = {uploaded}
}

@article{khatri1968solutions,
  title={Solutions to Some Functional Equations and their Applications to Characterization of Probability Distributions},
  author={Khatri, CG and Rao, C Radhakrishna},
  journal={Sankhy{\=a}: The Indian Journal of Statistics A},
  pages={167--180},
  volume =	 30,
  number =	 2,
  year =	 1968,
}

@incollection{zhang2006schur,
   year={2005},
   booktitle={The Schur Complement and its Applications},
   volume={4},
   series={Numerical Methods and Algorithms},
   editor={Zhang, Fuzhen},
   title={Basic Properties of the Schur Complement},
  doi =		 {10.1007/0-387-24273-2_2},
   publisher={Springer-Verlag},
   author={Horn, RogerA. and Zhang, Fuzhen},
   pages={17--46}
}

@book{gelman2013bayesian,
  title={Bayesian Data Analysis},
  author={Gelman, Andrew and Carlin, John B and Stern, Hal S and Dunson, David B and Vehtari, Aki and Rubin, Donald B},
  year={2013},
  publisher={CRC press}
}

@Manual{Matrix_pkg,
    title = {\pkg{Matrix}: Sparse and Dense Matrix Classes and Methods},
    author = {Douglas Bates and Martin Maechler},
    year = 2015,
    note = {\proglang{R} package version 1.2-2},
    url = {https://CRAN.R-project.org/package=Matrix},
  }

@Manual{minqa_pkg,
    title = {\pkg{minqa}: Derivative-Free Optimization Algorithms by
                  Quadratic Approximation},
    author = {Douglas Bates and Katharine M. Mullen and John C. Nash and Ravi Varadhan},
    year = {2014},
    note = {\proglang{R} package version 1.2.4},
    url = {https://CRAN.R-project.org/package=minqa},
  }

@Article{optimx_pkg,
    author = {John C. Nash and Ravi Varadhan},
    title = {Unifying Optimization Algorithms to Aid Software System Users: \pkg{optimx} for \proglang{R}},
    journal = {Journal of Statistical Software},
    year = 2011,
    volume = 43,
    number = 9,
    pages = {1--14},
    doi = {10.18637/jss.v043.i09},
    url = {https://www.jstatsoft.org/v43/i09/},
  }


@Misc{NLopt,
  author =	 {Steven G. Johnson},
  title =	 {The \pkg{NLopt} Nonlinear-Optimization Package},
  year = {2014},
  url = { https://nlopt.readthedocs.io/en/latest/}
}

@Manual{nlme_pkg,
  title =	 {\pkg{nlme}: Linear and Nonlinear Mixed Effects Models},
  author =	 {Jose Pinheiro and Douglas Bates and Saikat DebRoy and
                  Deepayan Sarkar and {\proglang{R} Core Team}},
  year =	 2014,
  note =	 {\proglang{R} package version 3.1-117},
  url =		 {https://CRAN.R-project.org/package=nlme},
}

@Article{HLMdiag_pkg,
    title = {\pkg{HLMdiag}: A Suite of Diagnostics for Hierarchical Linear Models in \proglang{R}},
    author = {Adam Loy and Heike Hofmann},
    journal = {Journal of Statistical Software},
    year = 2014,
    volume = 56,
    number = 5,
    pages = {1--28},
    doi = {10.18637/jss.v056.i05},
    url = {https://www.jstatsoft.org/v56/i05/},
}

@Article{influenceME_pkg,
    title = {\proglang{Influence.ME}: Tools for Detecting Influential Data in Mixed Effects Models},
    author = {Rense Nieuwenhuis and Manfred {Te Grotenhuis} and Ben Pelzer},
    year = 2012,
    journal = {R Journal},
    volume = 4,
    number = 2,
    pages = {38-47},
  }


@Manual{boot_pkg,
  author = {Angelo Canty and Brian Ripley},
   year = 2015,
   title = { \pkg{boot}: Bootstrap \proglang{R} (\proglang{S-PLUS}) Functions},
    note = {\proglang{R} package version 1.3-17},
    url = {https://CRAN.R-project.org/package=boot}
}


@Book{DavisonHinkley1997,
  author = 	 {A. C. Davison and D. V. Hinkley},
  title = 	 {Bootstrap Methods and Their Applications},
  year = 	 1997,
  publisher = 	 {Cambridge University Press},
  ISBN = {0-521-57391-2},
  address = {Cambridge, England}
}

@article{vaida2005conditional,
  title={Conditional Akaike Information for Mixed-Effects Models},
  author={Vaida, Florin and Blanchard, Suzette},
  journal={Biometrika},
  volume={92},
  number={2},
  pages={351--370},
  year={2005},
  doi =		 {10.1093/biomet/92.2.351},
  publisher={Biometrika Trust}
}

@book{cook1982residuals,
  title={Residuals and Influence in Regression},
  author={Cook, R Dennis and Weisberg, Sanford},
  year={1982},
  publisher={New York: Chapman and Hall}
}

%% -------- Software manuals, mostly R and R packages ---------


@Manual{lme4,
  title =	 {\pkg{lme4}: Linear Mixed-Effects Models Using
                  \pkg{Eigen} and \proglang{S}4},
  author =	 {Douglas Bates and Martin Maechler and Ben Bolker and
                  Steven Walker},
  year =	 2014,
  note =	 {\proglang{R} package version 1.1-7},
  url =		 {https://CRAN.R-project.org/package=lme4},
}

@Manual{R,
  title =	 {\proglang{R}: A Language and Environment for
                  Statistical Computing},
  author =	 {{\proglang{R} Core Team}},
  organization = {\proglang{R} Foundation for Statistical Computing},
  address =	 {Vienna, Austria},
  year =	 2015,
  url =		 {https://www.R-project.org/},
}

@Unpublished{Julia,
  title =	 {\proglang{Julia}: A Fast Dynamic Language for
                  Technical Computing},
  author =	 {Jeff Bezanson and Stefan Karpinski and Viral B. Shah
                  and Alan Edelman},
  year =	 2012,
  url =		 {https://arxiv.org/abs/1209.5145},
  note =	 {{arXiv}:1209.5145 [cs.PL]},
}

@Manual{MixedModels,
  title =	 {\pkg{MixedModels}: A \proglang{Julia} Package for
                  Fitting (Statistical) Mixed-Effects Models},
  author =	 {Douglas Bates},
  year =	 2015,
  note =	 {\proglang{Julia} package version 0.3-22},
  url =		 {https://github.com/JuliaStats/MixedModels.jl},
}

@Manual{lme4pureR,
  title =	 {\pkg{lme4pureR}: \pkg{lme4} in Pure \proglang{R}},
  author =	 {Douglas Bates and Steven Walker},
  year =	 2013,
  note =	 {\proglang{R} package version 0.1-0},
  url =		 {https://github.com/lme4/lme4pureR},
}

@Manual{Eigen,
  title =	 {\pkg{Eigen}3},
  author =	 {G Guennebaud and B Jacob and {and others}},
  year =	 2015,
  url =		 {https://libeigen.gitlab.io/}
}

@Manual{SuiteSparse,
  title =	 {\pkg{SuiteSparse}: A Suite of Sparse Matrix
                  Software},
  author =	 {Timothy A. Davis and others},
  year =	 2015,
  note =	 {Version 4.4-5},
  url =		 {https://aldenmath.com}
}

@Book{lattice,
  title =	 {\pkg{lattice}: Multivariate Data Visualization with
                  \proglang{R}},
  author =	 {Deepayan Sarkar},
  publisher =	 {Springer-Verlag},
  address =	 {New York},
  year =	 2008,
  url =		 {http://lmdvr.R-Forge.R-project.org},
}

@Article{Bates_JSS,
    title = {Fitting Linear Mixed-Effects Models Using {lme4}},
    author = {Douglas Bates and Martin M{\"a}chler and Ben Bolker and Steve Walker},
    journal = {Journal of Statistical Software},
    year = {2015},
    volume = {67},
    number = {1},
    pages = {1--48},
    doi = {10.18637/jss.v067.i01},
  }
