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glmm.bib
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glmm.bib
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@article{roulin_nestling_2007,
title = {Nestling barn owls beg more intensely in the presence of their mother than in the presence of their father},
volume = {74},
issn = {0003-3472},
url = {http://www.sciencedirect.com/science/article/B6W9W-4PK8B6H-8/2/e43cfbaad4dc0bb2207adfc54a460c89},
doi = {10.1016/j.anbehav.2007.01.027},
abstract = {Nestling begging behaviour may be an honest signal of need used by parents to adjust optimally both feeding rate and within-brood food allocation. Although several studies showed that mothers and fathers can be differentially responsive to nestling begging behaviour with one parent showing a stronger tendency to feed the offspring that beg the most, little information is yet available on whether offspring beg for food at different intensities from the mother than father. In the present study, we investigated in nestling barn owls whether the intensity of vocal begging behaviour in the presence of the mother and in the presence of the father is different. A difference is expected because reproductive tasks are divided between the sexes with fathers bringing more food items to the nest than mothers. The results show that although mothers transfer their prey item to one of the offspring more rapidly than fathers once in their nestbox, nestlings begged more intensely in the presence of their mother than in the presence of their father. To our knowledge, this is the first empirical evidence that offspring vocalize to different levels in the presence of their mother than in the presence of their father.},
number = {4},
journal = {Animal Behaviour},
author = {Alexandre Roulin and {Louis-Felix} Bersier},
month = oct,
year = {2007},
keywords = {barn owl, begging, parental care, parent-offspring conflict, sexual conflict, sibling negotiation, Tyto alba},
pages = {1099--1106}
}
@book{zuur_mixed_2009,
title = {Mixed Effects Models and Extensions in Ecology with {R}},
isbn = {0387874577},
publisher = {Springer},
author = {Alain F. Zuur and Elena N. Ieno and Neil J. Walker and Anatoly A. Saveliev and Graham M. Smith},
month = mar,
year = {2009}
}
@article{vaida_conditional_2005,
title = {Conditional {Akaike} information for mixed-effects models},
volume = {92},
url = {http://biomet.oxfordjournals.org/cgi/content/abstract/92/2/351},
doi = {10.1093/biomet/92.2.351},
abstract = {This paper focuses on the Akaike information criterion, {AIC,} for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the {AIC} in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional {AIC,} {cAIC.} The penalty term in {cAIC} is related to the effective degrees of freedom {rho} for a linear mixed model proposed by Hodges \& Sargent (2001); {rho} reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The {cAIC} is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data application is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional {AIC} in model selection. },
number = {2},
journal = {Biometrika},
author = {Florin Vaida and Suzette Blanchard},
month = jun,
year = {2005},
pages = {351--370}
}
@incollection{breslow_whither_2004,
title = {Whither {PQL?}},
isbn = {0387208623},
booktitle = {Proceedings of the second {Seattle} symposium in biostatistics: Analysis of correlated data},
publisher = {Springer},
author = {N. E. Breslow},
editor = {Danyu Y. Lin and P. J. Heagerty},
year = {2004},
pages = {1--22}
}
@article{molenberghs_likelihood_2007,
title = {Likelihood Ratio, Score, and {Wald} Tests in a Constrained Parameter Space},
volume = {61},
doi = {10.1198/000313007X171322},
number = {1},
journal = {The American Statistician},
author = {Geert Molenberghs and Geert Verbeke},
year = {2007},
pages = {22--27}
}
@book{pinheiro_mixed-effects_2000,
address = {New York},
title = {Mixed-effects models in {S} and {S-PLUS}},
isbn = {0-387-98957-9},
publisher = {Springer},
author = {José C. Pinheiro and Douglas M. Bates},
year = {2000}
}
@book{venables_modern_2002,
address = {New York},
edition = {4th},
title = {Modern Applied Statistics with S},
publisher = {Springer},
author = {W. Venables and Brian D. Ripley},
year = {2002}
}
@book{littell_sas_2006,
title = {{SAS} for Mixed Models, Second Edition},
isbn = {1590475003},
publisher = {{SAS} Publishing},
author = {Ramon C. Littell and George A. Milliken and Walter W. Stroup and Russell D. Wolfinger and Oliver Schabenberger},
year = {2006}
}
@article{fears_reminder_1996,
title = {A Reminder of the Fallibility of the {Wald} Statistic},
volume = {50},
issn = {00031305},
url = {http://www.jstor.org/stable/2684659},
doi = {10.2307/2684659},
abstract = {Computer programs often produce a parameter estimate θ̂ and estimated variance \${\textbackslash}widehat{var}({\textbackslash}hat{{\textbackslash}theta})\$ . Thus it is easy to compute a Wald statistic \$({\textbackslash}hat{{\textbackslash}theta} - {\textbackslash}theta\_0){\textbackslash}{{\textbackslash}widehat{var} ({\textbackslash}hat{{\textbackslash}theta}){\textbackslash}}{\textasciicircum}{-1/2}\$ to test the null hypothesis θ = θ0. Hauck and Donner and Vaeth have identified situations in which the Wald statistic has poor power. We consider another example that is not in the classes discussed by those authors. We present data from a balanced one-way random effects analysis of variance {(ANOVA)} that illustrate the poor power of the Wald statistic compared to the usual F test. In this example the parameter of interest is the variance of the random effect. The power of the Wald test depends on the parameterization used, however, and a whole family of Wald statistics with p values ranging from 0 to 1 can be generated with power transformations of the random effect parameter.},
number = {3},
journal = {The American Statistician},
author = {Thomas R. Fears and Jacques Benichou and Mitchell H. Gail},
month = aug,
year = {1996},
pages = {226--227}
}
@article{elston_analysis_2001,
title = {Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks},
volume = {122},
number = {5},
journal = {Parasitology},
author = {D. A. Elston and R. Moss and T. Boulinier and C. Arrowsmith and X. Lambin},
year = {2001},
pages = {563--569}
}
@inproceedings{schabenberger_growing_2007,
address = {Orlando, Florida},
title = {Growing Up Fast: {SAS®} 9.2 Enhancements to the {GLIMMIX} Procedure},
url = {http://www2. sas.com/proceedings/forum2007/177-2007.pdf},
abstract = {The {GLIMMIX} procedure was first released as a Web download add-on procedure to {SAS/STAT®} in {SAS}
9.1 in the 32-bit Windows operating environment. It was subsequently released as a Web download for
{SAS} 9.1.3 in {UNIX} and Linux environments. This paper describes the key changes and enhancements to
{PROC} {GLIMMIX} between the {SAS} 9.1 and {SAS} 9.2 releases.
Enhancements fall into several categories: statistical estimation, model building, post-processing, and mis-
cellaneous other features. For example, new estimation methods and covariance structures enable parame-
ter estimation with reduced bias in more flexible generalized linear mixed models. A new statement provides
a comprehensive facility to test hypotheses about covariance parameters. New multiplicity corrections offer
more ways to adjust inferences.
The goal of this paper is to highlight the new estimation and inference techniques and to demonstrate their
usage with examples.},
author = {Oliver Schabenberger},
year = {2007}
}
@article{pawitan_reminder_2000,
title = {A Reminder of the Fallibility of the {Wald} Statistic: Likelihood Explanation},
volume = {54},
issn = {00031305},
url = {http://www.jstor.org/stable/2685612},
doi = {10.2307/2685612},
abstract = {The Wald statistic is one of the most commonly used tools in applied statistics, so it is sobering to read Fears, Benichou, and Gail's recent reminder of its fallibility. What makes their example particularly relevant is the fact that the problem is manifest in a simple normal random effects model on a balanced dataset for a seemingly harmless parameter, while, in practice, one tends to rely on the Wald test in complicated or nonnormal models where there are no exact tests to serve as a gold standard. This article explains the failure of the Wald test via the profile likelihood functions, which graphically look decidedly nonnormal. The methodology used to derive the profile likelihood and the discussion of this example could be instructive for a senior or beginning graduate class in theory of statistics.},
number = {1},
journal = {The American Statistician},
author = {Yudi Pawitan},
month = feb,
year = {2000},
jstornote = {{ArticleType:} primary\_article / Full publication date: Feb., 2000 / Copyright © 2000 American Statistical Association},
pages = {54--56}
}
@article{skaug_automatic_2006,
title = {Automatic approximation of the marginal likelihood in non-gaussian hierarchical models},
volume = {51},
number = {2},
journal = {Computational Statistics \& Data Analysis},
author = {Skaug, Hans J. and Fournier, David A.},
year = {2006},
pages = {699--709}
}
@article{skaug_automatic_2002,
title = {Automatic Differentiation to Facilitate Maximum
Likelihood Estimation in Nonlinear Random Effects
Models},
volume = {11},
issn = {1061-8600},
url =
{http://pubs.amstat.org/doi/abs/10.1198/106186002760180617},
doi = {10.1198/106186002760180617},
number = {2},
journal = {Journal of Computational and Graphical Statistics},
author = {Hans J. Skaug},
year = {2002},
pages = {458--470}
}
@article{gelman_prior_2006,
title = {Prior distributions for variance parameters in hierarchical models},
volume = {1},
url = {http://ba.stat.cmu.edu/journal/2006/vol01/issue03/gelman.pdf},
abstract = {Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-t family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors in this family. We use an example to illustrate serious problems with the inverse-gamma family of “noninformative” prior distributions. We suggest instead to use a uniform prior on the hierarchical standard deviation, using the half-t family when the number of groups is small and in other settings where a weakly informative prior is desired. We also illustrate the use of the half-t family for hierarchical modeling of multiple variance parameters such as arise in the analysis of variance. Keywords: Bayesian inference, conditional conjugacy, folded-noncentral-t distribution, half-t distribution, hierarchical model, multilevel model, noninformative prior distribution, weakly informative prior distribution},
number = {3},
journal = {Bayesian Analysis},
author = {Andrew Gelman},
year = {2006},
pages = {515--533}
}
@Manual{lme4,
title = {lme4: Linear mixed-effects models using S4 classes},
author = {Douglas Bates and Martin Maechler},
year = {2010},
note = {R package version 0.999375-33},
url = {http://CRAN.R-project.org/package=lme4},
}
@Manual{R,
title = {R: A Language and Environment for Statistical Computing},
author = {{R Development Core Team}},
organization = {R Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2009},
note = {{ISBN} 3-900051-07-0},
url = {http://www.R-project.org},
}
@BOOK{McCullaghNelder1989,
title = {Generalized Linear Models},
publisher = {Chapman and Hall},
year = {1989},
author = {P. McCullagh and J. A. Nelder},
address = {London}
}
@article{ozgul_upper_2009,
title = {Upper respiratory tract disease, force of infection, and effects on survival of gopher tortoises},
volume = {19},
issn = {1051-0761},
url = {http://www.ncbi.nlm.nih.gov/pubmed/19425439},
abstract = {Upper respiratory tract disease {(URTD)} caused by Mycoplasma agassizii has been hypothesized to contribute to the decline of some wild populations of gopher tortoises {(Gopherus} polyphemus). However, the force of infection {(FOI)} and the effect of {URTD} on survival in free-ranging tortoise populations remain unknown. Using four years (2003-2006) of mark-recapture and epidemiological data collected from 10 populations of gopher tortoises in central Florida, {USA,} we estimated the {FOI} (probability per year of a susceptible tortoise becoming infected) and the effect of {URTD} (i.e., seropositivity to M. agassizii) on apparent survival rates. Sites with high ({\textgreater} or = 25\%) seroprevalence had substantially higher {FOI} (0.22 +/- 0.03; mean +/- {SE)} than low ({\textless} 25\%) seroprevalence sites (0.04 +/- 0.01). Our results provide the first quantitative evidence that the rate of transmission of M. agassizii is directly related to the seroprevalence of the population. Seropositive tortoises had higher apparent survival (0.99 +/- 0.0001) than seronegatives (0.88 +/- 0.03), possibly because seropositive tortoises represent individuals that survived the initial infection, developed chronic disease, and experienced lower mortality during the four-year span of our study. However, two lines of evidence suggested possible effects of mycoplasmal {URTD} on tortoise survival. First, one plausible model suggested that susceptible (seronegative) tortoises in high seroprevalence sites had lower apparent survival rates than did susceptible tortoises in low seroprevalence sites, indicating a possible acute effect of infection. Second, the number of dead tortoise remains detected during annual site surveys increased significantly with increasing site seroprevalence, from approximately 1 to approximately 5 shell remains per 100 individuals. If (as our results suggest) {URTD} in fact reduces adult survival, it could adversely influence the population dynamics and persistence of this late- maturing, long-lived species.},
number = {3},
journal = {Ecological Applications},
author = {Arpat Ozgul and Madan K Oli and Benjamin M Bolker and Carolina {Perez-Heydrich}},
month = apr,
year = {2009},
keywords = {Animals, Environment, Female, Florida, Longevity, Male, Mycoplasma, Mycoplasma Infections, Population Density, Population Dynamics, Respiratory Tract Infections, Seroepidemiologic Studies, Sex Factors, Time Factors, Turtles},
pages = {786--798}
}
@article{gelman_analysis_2005,
title = {Analysis of variance: why it is more important than ever},
volume = {33},
doi = {doi:10.1214/009053604000001048},
number = {1},
journal = {Annals of Statistics},
author = {Andrew Gelman},
year = {2005},
pages = {1--53}
}
@article{Hadfield:2009:JSSOBK:v33i02,
author = "Jarrod D. Hadfield",
title = "{MCMC} Methods for Multi-Response Generalized Linear Mixed Models: The {MCMCglmm} {R} Package",
journal = "Journal of Statistical Software",
volume = "33",
number = "2",
pages = "1--22",
day = "2",
month = "2",
year = "2010",
CODEN = "JSSOBK",
ISSN = "1548-7660",
bibdate = "2009-12-21",
URL = "http://www.jstatsoft.org/v33/i02",
accepted = "2009-12-21",
acknowledgement = "",
keywords = "",
submitted = "2009-02-18",
}
@article{kenward_small_1997,
title = {Small sample inference for fixed effects from restricted maximum likelihood},
volume = {53},
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.},
number = {3},
journal = {Biometrics},
author = {M. G Kenward and J. H Roger},
year = {1997},
pages = {983--997}
}
@article{schaalje_adequacy_2002,
title = {Adequacy of Approximations to Distributions of Test Statistics in Complex Mixed Linear Models},
volume = {7},
url = {http://www.ingentaconnect.com/content/asa/jabes/2002/00000007/00000004/art00004},
abstract = {A recent study of lady beetle antennae was a small sample repeated measures design involving a complex covariance structure. Distributions of test statistics based on mixed models fitted to such data are unknown, but two recently developed methods for approximating the distributions of test statistics in mixed linear models have been included as options in the latest release of the {MIXED} procedure of {SAS{\textregistered}.} One method {(FC,} from Fai and Cornelius) computes degrees of freedom of an approximating F distribution for the test statistic using spectral decomposition of the hypothesis matrix together with repeated application of a method for single-degree-of-freedom tests. The other method {(KR,} from Kenward and Roger) adjusts the estimated covariance matrix of the parameter estimates, computes a scale adjustment to the test statistic, and computes the degrees of freedom of an approximating F distribution. Using the two methods, p values for a hypothesis of interest in the lady beetle study were quite different. Simulation studies on the Proc {MIXED} implementation of these methods showed that Type I error rates of both methods are affected by covariance structure complexity, sample size, and imbalance. Nonetheless, the {KR} method performs well in situations with fairly complicated covariance structures when sample sizes are moderate to small and the design is reasonably balanced. The {KR} method should be used in preference to the {FC} method, although it had inflated Type I error rates for complex covariance structures combined with small sample sizes.},
number = {14},
journal = {Journal of Agricultural, Biological \& Environmental Statistics},
author = {G. Schaalje and J. {McBride} and G. Fellingham},
year = {2002},
keywords = {kenward-roger},
pages = {512--524}
}
@article{cordeiro_improved_1994,
title = {Improved Likelihood Ratio Tests for Dispersion Models},
volume = {62},
issn = {03067734},
url = {http://www.jstor.org/stable/1403512},
doi = {10.2307/1403512},
abstract = {In this paper we discuss improved likelihood ratio tests for both the parameters in the systematic component and the dispersion parameter in the class of dispersion models {(J?rgensen,} 1987a). General formulae for the expected likelihood ratio statistic are obtained explicitly in dispersion models, which generalize previous results by Cordeiro (1983, 1985, 1987) and Cordeiro \& Paula (1989a). The practical use of the formulae is that we can derive closed-form Bartlett corrections for these models when the information matrix has a closed-form. Various Bartlett corrections are given for special models. The formulae have advantages for numerical purposes because they require only simple operations on matrices. Algebraically, they may be handled within computer systems such as {REDUCE.} Some numerical examples involving real data clarify the use of these formulae. /// Dans cet article nous \'{e}tudions des crit\`{e}res am\'{e}lior\'{e}s du rapport de vraisemblance aussi bien pour les param\`{e}tres dans la composante syst\'{e}matique que pour le param\`{e}tre de dispersion dans la classe des mod\`{e}les de dispersion {(J?rgensen,} 1987a). Des formules g\'{e}n\'{e}rales pour la statistique du rapport de vraisemblance prevue sont obtenues explicitement, dans des mod\`{e}les de dispersion, qui g\'{e}n\'{e}ralisent des r\'{e}sultats anterieurs de Cordeiro (1983, 1985, 1987) et Cordeiro \& Paula (1989a). L'utilisation pratique des formules vient de ce qu'on peut d\'{e}river des corrections de Bartlett en forme ferm\'{e}e por ces mod\`{e}les quand la matrice d'information a forme ferm\'{e}e. On donne plusieurs corrections de Bartlett pour des mod\`{e}les particuliers. Les formules ont des avantages pour les calculs num\'{e}riques parce qu'ils n'exigent que des op\'{e}rations simples sur les matrices. Elles peuvent \^{e}tre trait\'{e}es alg\'{e}briquement dans des syst\`{e}mes d'ordinnateurs comme {REDUCE.} Quelques exemples num\'{e}riques, avec des donn\'{e}es r\'{e}elles, illustrent l'usage de ces formules.},
number = {2},
journal = {International Statistical Review / Revue Internationale de Statistique},
author = {Gauss M. Cordeiro and Gilberto A. Paula and Denise A. Botter},
year = {1994},
pages = {257--274}
}
@article{cordeiro_note_1998,
title = {A note on {Bartlett}-type correction for the first few moments of test statistics},
volume = {71},
issn = {0378-3758},
url = {http://www.sciencedirect.com/science/article/B6V0M-3V5CVRT-M/2/190f68a684dd08c569a7836ff59568e4},
doi = {10.1016/S0378-3758(98)00005-6},
abstract = {The purpose of this paper is to propose a simple method for obtaining Bartlett-type corrections for the first few moments of test statistics which are asymptotically distributed as chi-squared. The method proposed here only requires knowledge of the terms of the expansions to such moments. Some applications of our main result are considered.},
number = {1-2},
journal = {Journal of Statistical Planning and Inference},
author = {Gauss M. Cordeiro and Silvia L. P. Ferrari},
month = aug,
year = {1998},
keywords = {Bartlett correction, Bartlett-type correction, Chi-squared distribution, Method of moments, Score statistics},
pages = {261--269}
}
@ARTICLE{GoldmanWhelan2000,
author = {Goldman, Nick and Whelan, Simon},
title = {Statistical Tests of Gamma-Distributed Rate Heterogeneity in Models
of Sequence Evolution in Phylogenetics},
journal = {Molecular Biology and Evolution},
year = {2000},
volume = {17},
pages = {975-978},
number = {6},
owner = {ben},
timestamp = {2006.12.06}
}
@article{leamer_tantalus_2010,
title = {Tantalus on the Road to Asymptopia},
volume = {24},
issn = {0895-3309},
url = {http://www.aeaweb.org/articles.php?doi=10.1257/jep.24.2.31},
doi = {10.1257/jep.24.2.31},
number = {2},
journal = {Journal of Economic Perspectives},
author = {Edward E Leamer},
year = {2010},
pages = {31--46}
}
@article{hurvich_regression_1989,
title = {Regression and time series model selection in small samples},
volume = {76},
url = {http://biomet.oxfordjournals.org/content/76/2/297.abstract},
doi = {10.1093/biomet/76.2.297},
abstract = {A bias correction to the Akaike information criterion, {AIC,} is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called {AICC,} is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, {AICC} is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.},
number = {2},
journal = {Biometrika},
author = {Clifford M. Hurvich and Chih-Ling Tsai},
month = jun,
year = {1989},
pages = {297 --307}
}
@article{richards_testing_2005,
title = {Testing ecological theory using the information-theoretic approach: examples and cautionary results},
volume = {86},
doi = {10.1890/05-0074},
number = {10},
journal = {Ecology},
author = {Shane A. Richards},
year = {2005},
pages = {2805--2814}
}
@book{greven_non-standard_2008,
address = {G\"{o}ttingen, Germany},
title = {{Non-Standard} Problems in Inference for Additive and Linear Mixed Models},
isbn = {3867274916},
url = {http://www.cuvillier.de/flycms/en/html/30/-UickI3zKPS,3cEY=/Buchdetails.html?SID=wVZnpL8f0fbc},
publisher = {Cuvillier Verlag},
author = {Sonja Greven},
year = {2008}
},
@article{greven_behaviour_2010,
title = {On the Behaviour of Marginal and Conditional {Akaike} Information Criteria in Linear Mixed Models},
volume = {97},
url = {http://www.bepress.com/jhubiostat/paper202/},
abstract = {In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion {(AIC)} have been
used, based either on the marginal or on the conditional distribution. We show that the marginal {AIC} is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional {AIC,} we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the
selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional {AIC,} which avoids
the high computational cost and imprecision of available numerical approximations.
An implementation in an R package is provided. All theoretical results are
illustrated in simulation studies, and their impact in practice is investigated in an
analysis of childhood malnutrition in Zambia.},
number = {4},
journal = {Biometrika},
author = {Sonja Greven and Thomas Kneib},
year = {2010},
pages = {773--789}
}
@article{spiegelhalter_bayesian_2002,
title = {Bayesian measures of model complexity and fit},
volume = {64},
journal = {Journal of the Royal Statistical Society B},
author = {D. J. Spiegelhalter and N. Best and B. P. Carlin and A. Van der Linde},
year = {2002},
pages = {583--640}
}
@article{jiang_fence_2008,
title = {Fence methods for mixed model selection},
volume = {36},
issn = {0090-5364},
url = {http://projecteuclid.org/euclid.aos/1216237296},
doi = {10.1214/07-AOS517},
abstract = {Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and {ARMA} time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.},
number = {4},
journal = {The Annals of Statistics},
author = {Jiming Jiang},
month = aug,
year = {2008},
pages = {1669--1692}
}
@article{sung_monte_2007,
title = {Monte {Carlo} likelihood inference for missing data models},
volume = {35},
issn = {0090-5364},
url = {http://projecteuclid.org/euclid.aos/1185303995},
doi = {10.1214/009053606000001389},
abstract = {We describe a Monte Carlo method to approximate the maximum likelihood estimate {(MLE)}, when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the {MLE} is a consistent and asymptotically normal estimate of the minimizer θ* of the {Kullback–Leibler} information, as both Monte Carlo and observed data sample sizes go to infinity simultaneously. Plug-in estimates of the asymptotic variance are provided for constructing confidence regions for θ*. We give {Logit–Normal} generalized linear mixed model examples, calculated using an R package.},
number = {3},
journal = {The Annals of Statistics},
author = {Sung, Yun Ju and Geyer, Charles J.},
month = jul,
year = {2007},
pages = {990--1011}
}
@article{booth_maximizing_1999,
title = {Maximizing Generalized Linear Mixed Model Likelihoods with an Automated {Monte} {Carlo} {EM} Algorithm},
volume = {61},
url = {http://links.jstor.org/sici?sici=1369-7412(1999)61%3A1%3C265%3AMGLMML%3E2.0.CO%3B2-C},
doi = {10.1111/1467-9868.00176},
number = {1},
journal = {Journal of the Royal Statistical Society. Series B},
author = {Booth, James G. and Hobert, James P.},
year = {1999},
keywords = {glmm},
pages = {265--285}
},
@article{booth_negative_2003,
title = {Negative binomial loglinear mixed models},
volume = {3},
url = {http://dx.doi.org/10.1191/1471082x03st058oa},
number = {3},
journal = {Statistical Modelling},
author = {Booth, James and Casella, George and Friedl, Herwig and Hobert, James},
year = {2003},
keywords = {glmm},
pages = {179--191}
}
@Article{Rue+2009,
author = {H. Rue and S. Martino and N. Chopin},
title = {Gaussian models using integrated nested {Laplace} approximations (with discussion)},
journal = {Journal of the Royal
Statistical Society, Series B},
year = {2009},
volume = {71},
number = {2},
pages = {319-392}
}
@article{schielzeth_simple_2010,
title = {Simple means to improve the interpretability of regression coefficients},
url = {http://dx.doi.org/10.1111/j.2041-210X.2010.00012.x},
doi = {10.1111/j.2041-210X.2010.00012.x},
abstract = {1. Linear regression models are an important statistical tool in evolutionary and ecological studies. Unfortunately, these models often yield some uninterpretable estimates and hypothesis tests, especially when models contain interactions or polynomial terms. Furthermore, the standard errors for treatment groups, although often of interest for including in a publication, are not directly available in a standard linear model. 2. Centring and standardization of input variables are simple means to improve the interpretability of regression coefficients. Further, refitting the model with a slightly modified model structure allows extracting the appropriate standard errors for treatment groups directly from the model. 3. Centring will make main effects biologically interpretable even when involved in interactions and thus avoids the potential misinterpretation of main effects. This also applies to the estimation of linear effects in the presence of polynomials. Categorical input variables can also be centred and this sometimes assists interpretation. 4. Standardization (z-transformation) of input variables results in the estimation of standardized slopes or standardized partial regression coefficients. Standardized slopes are comparable in magnitude within models as well as between studies. They have some advantages over partial correlation coefficients and are often the more interesting standardized effect size. 5. The thoughtful removal of intercepts or main effects allows extracting treatment means or treatment slopes and their appropriate standard errors directly from a linear model. This provides a simple alternative to the more complicated calculation of standard errors from contrasts and main effects. 6. The simple methods presented here put the focus on parameter estimation (point estimates as well as confidence intervals) rather than on significance thresholds. They allow fitting complex, but meaningful models that can be concisely presented and interpreted. The presented methods can also be applied to generalised linear models {(GLM)} and linear mixed models.},
volume = {1},
pages = {103-113},
journal = {Methods in Ecology and Evolution},
author = {Schielzeth, Holger},
year = {2010}
}
@inproceedings{venables_exegeses_1998,
address = {Washington, {DC}},
booktitle = {1998 International {S-PLUS} User Conference},
title = {Exegeses on Linear Models},
url = {http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf},
author = {Venables, W. N},
year = {1998}
}
@article{whittingham_why_2006,
title = {Why do we still use stepwise modelling in ecology and behaviour?},
volume = {75},
number = {5},
journal = {Journal of Animal Ecology},
author = {Whittingham, Mark J. and Stephens, Philip A. and Bradbury, Richard B. and Freckleton, Robert P.},
year = {2006},
pages = {1182--1189}
}
@book{harrell_regression_2001,
title = {Regression Modeling Strategies},
isbn = {0387952322},
publisher = {Springer},
author = {Harrell, Frank},
year = {2001}
}
@book{hardin_generalized_2007,
title = {Generalized linear models and extensions},
isbn = {9781597180146},
publisher = {Stata Press},
author = {Hardin, James William and Hilbe, Joseph},
month = feb,
year = {2007}
}
@article{robinson_that_1991,
title = {That {BLUP} is a Good Thing: The Estimation of Random Effects},
volume = {6},
issn = {0883-4237},
shorttitle = {That {BLUP} is a Good Thing},
url = {http://www.jstor.org/stable/2245695},
abstract = {In animal breeding, Best Linear Unbiased Prediction, or {BLUP}, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the theory of {BLUP}, some examples of its application and its relevance to the foundations of statistics. Understanding of procedures for estimating random effects should help people to understand some complicated and controversial issues about fixed and random effects models and also help to bridge the apparent gulf between the Bayesian and Classical schools of thought.},
number = {1},
journal = {Statistical Science},
author = {Robinson, G. K.},
month = feb,
year = {1991},
pages = {15--32}
}
@BOOK{GotelliEllison2004,
title = {A Primer of Ecological Statistics},
publisher = {Sinauer},
year = {2004},
author = {Nicholas J. Gotelli and Aaron M. Ellison},
address = {Sunderland, MA}
}
@article{bolker_generalized_2009,
title = {Generalized linear mixed models: a practical guide for ecology and evolution},
volume = {24},
issn = {0169-5347},
shorttitle = {Generalized linear mixed models},
url = {http://www.sciencedirect.com/science/article/B6VJ1-4VGKHJP-1/2/35970065c78c14ad30bf71bd1d5b452e},
doi = {10.1016/j.tree.2008.10.008},
abstract = {How should ecologists and evolutionary biologists analyze nonnormal data that involve random effects? Nonnormal data such as counts or proportions often defy classical statistical procedures. Generalized linear mixed models {(GLMMs)} provide a more flexible approach for analyzing nonnormal data when random effects are present. The explosion of research on {GLMMs} in the last decade has generated considerable uncertainty for practitioners in ecology and evolution. Despite the availability of accurate techniques for estimating {GLMM} parameters in simple cases, complex {GLMMs} are challenging to fit and statistical inference such as hypothesis testing remains difficult. We review the use (and misuse) of {GLMMs} in ecology and evolution, discuss estimation and inference and summarize [`]best-practice' data analysis procedures for scientists facing this challenge.},
journal = {Trends in Ecology \& Evolution},
author = {Bolker, Benjamin M. and Brooks, Mollie E. and Clark, Connie J. and Geange, Shane W. and Poulsen, John R. and Stevens, M. Henry H. and White, {Jada-Simone} S.},
year = {2009},
pages = {127--135}
}
@article{latimer_hierarchical_2009,
title = {Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern United States},
volume = {12},
shorttitle = {Hierarchical models facilitate spatial analysis of large data sets},
number = {2},
journal = {Ecology Letters},
author = {Latimer, A. M. and Banerjee, S. and Sang Jr, H. and Mosher, E. S. and Silander Jr, J. A.},
year = {2009},
pages = {144-154}
}
@article{van2009simple,
title={A simple method for distinguishing within-versus between-subject effects using mixed models},
author={van de Pol, M. and Wright, J.},
journal={Animal Behaviour},
volume={77},
number={3},
pages={753--758},
year={2009},
publisher={Elsevier}
}
@article{ohara_not_2010,
title = {Do not log-transform count data},
volume = {1},
issn = {{2041-210X}},
url = {http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2010.00021.x/abstract},
doi = {10.1111/j.2041-210X.2010.00021.x},
abstract = {1. Ecological count data (e.g. number of individuals or species) are often log-transformed to satisfy parametric test assumptions.},
number = {2},
journal = {Methods in Ecology and Evolution},
author = {{O'Hara}, Robert B. and Kotze, D. Johan},
month = jun,
year = {2010},
keywords = {generalized linear models, Linear Models, overdispersion, Poisson, transformation},
pages = {118--122}
}
@article{warton_arcsine_2011,
title = {The arcsine is asinine: the analysis of proportions in ecology},
volume = {92},
issn = {0012-9658},
shorttitle = {The arcsine is asinine},
url = {http://www.esajournals.org/doi/full/10.1890/10-0340.1},
doi = {10.1890/10-0340.1},
journal = {Ecology},
author = {Warton, David I. and Hui, Francis K. C.},
month = jan,
year = {2011},
pages = {3--10}
}
@Article{WilkinsonRogers1973,
author = {G. N. Wilkinson and C. E. Rogers},
title = {Symbolic Description of Factorial Models for Analysis of Variance},
journal = {Applied Statistics},
year = {1973},
volume = {22},
number = {3},
pages = {392-399},
doi = {10.2307/2346786}
}
@book{gelman_data_2006,
address = {Cambridge, England},
title = {Data Analysis Using Regression and {Multilevel/Hierarchical} Models},
url = {http://www.stat.columbia.edu/~gelman/arm/},
publisher = {Cambridge University Press},
author = {Gelman, Andrew and Hill, Jennifer},
year = {2006},
keywords = {uploaded}
}
@BOOK{Crawley2002,
title = {Statistical Computing: An Introduction to Data Analysis using {S-PLUS}},
publisher = {John Wiley \& Sons},
year = {2002},
author = {Michael J. Crawley},
isbn = {0-471-56040-5}
}
@article{banta_comprehensive_2010,
title = {A comprehensive test of the 'limiting resources' framework applied to plant tolerance to apical meristem damage},
volume = {119},
issn = {1600-0706},
url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0706.2009.17726.x/abstract},
doi = {10.1111/j.1600-0706.2009.17726.x},
abstract = {Tolerance to apical meristem damage {(AMD)} is a form of plant defense against herbivory. Theoretical models come to different conclusions about the effects of inorganic soil nutrient levels on tolerance to {AMD}, and different plants have shown different relationships between these variables. To assign some order to these disparate patterns and to resolve conflicts among the models, the ‘limiting resources model’ {(LRM)} was developed. However, we believe that the {LRM} is actually comprised of several different models, which we describe. Our study marks the first comprehensive and simultaneous test of the entire {LRM} framework, treating it explicitly as separate models, which also evaluates the models’ underlying assumptions. We studied tolerance to {AMD} in laboratory-reared natural populations of Arabidopsis thaliana from three different regions of Europe, spanning a wide latitudinal gradient. We show that, in different populations of this species, basic responses to nutrients and damage are best described by different models, which are based on different assumptions and make different predictions. This demonstrates the need for complexity in our explanations, and suggests that no one existing model can account for all relationships between tolerance to {AMD} and nutrients. Our results also demonstrate that fruit production can provide a misleading approximation of fitness in A. thaliana, contrary to the common assumption in the literature.},
number = {2},
journal = {Oikos},
author = {Banta, Joshua A. and Stevens, Martin H. H. and Pigliucci, Massimo},
month = feb,
year = {2010},
pages = {359--369}
}
@Article{JohnsonRaven1973,
author = {Michael P. Johnson and Peter H. Raven},
title = {Species Number and Endemism: The {Gal{\'a}pagos} Archipelago Revisited},
journal = {Science},
year = {1973},
volume = {179},
number = {4076},
pages = {893-895},
doi = {10.1126/science.179.4076.893},
url = {http://www.sciencemag.org/content/179/4076/893.short}
}
@article{pregibon_goodness_1980,
title = {Goodness of Link Tests for Generalized Linear Models},
volume = {29},
issn = {0035-9254},
url = {http://www.jstor.org/stable/2346405},
doi = {10.2307/2346405},
abstract = {Data analytic procedures are proposed to examine the adequacy of the hypothesized link used in fitting a generalized linear model. Through model expansion and linearization, tests and estimation techniques are provided. These procedures, along with the release of {GLIM3}, enable the user to examine routinely and objectively the fit of an hypothesized model. Examples are presented to illustrate the testing and fitting procedure.},
number = {1},
journal = {Journal of the Royal Statistical Society. Series C {(Applied} Statistics)},
author = {Pregibon, Daryl},
month = jan,
year = {1980},
pages = {15--14}
}
@ARTICLE{Tiwari+2006,
author = {Tiwari, Manjula and Bjorndal, Karen A. and Bolten, Alan B. and Bolker,
Benjamin M.},
title = {Evaluation of density-dependent processes and green turtle \emph{Chelonia mydas} hatchling production at {Tortuguero}, {Costa Rica}},
journal = {Marine Ecology Progress Series},
year = {2006},
volume = {326},
pages = {283-293}
}
@article{schelldorfer_glmmlasso:_2011,
title = {{GLMMLasso:} An Algorithm for {High-Dimensional} Generalized Linear Mixed Models Using {L1-Penalization}},
shorttitle = {{GLMMLasso}},
journal = {Arxiv preprint {arXiv:1109.4003}},
author = {Schelldorfer, J. and Bühlmann, P.},
year = {2011},
url = {http://arxiv.org/abs/1109.4003}
}
@article{zhang_fitting_2011,
title = {On fitting generalized linear mixed-effects models for binary responses using different statistical packages},
issn = {1097-0258},
url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.4265/abstract},
doi = {10.1002/sim.4265},
year = {2011},
abstract = {The generalized linear mixed-effects model {(GLMM)} is a popular paradigm to extend models for cross-sectional data to a longitudinal setting. When applied to modeling binary responses, different software packages and even different procedures within a package may give quite different results. In this report, we describe the statistical approaches that underlie these different procedures and discuss their strengths and weaknesses when applied to fit correlated binary responses. We then illustrate these considerations by applying these procedures implemented in some popular software packages to simulated and real study data. Our simulation results indicate a lack of reliability for most of the procedures considered, which carries significant implications for applying such popular software packages in practice. Copyright © 2011 John Wiley \& Sons, Ltd.},
journal = {Statistics in Medicine},
author = {Hui Zhang and Naiji Lu and Chanyong Feng and Sally W. Thurston and Xia, Yinglin and Zhu, Liang and Tu, Xin M},
keywords = {{GLIMMIX}, integral approximation, linearization, lme4, {NLMIXED}, R, {SAS}, {ZELIG}}
}
@article{self_asymptotic_1987,
title = {Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions},
volume = {82},
issn = {0162-1459, 1537-{274X}},
url = {http://amstat.tandfonline.com/doi/abs/10.1080/01621459.1987.10478472#.UpNeOVQ9sVI},
doi = {10.1080/01621459.1987.10478472},
number = {398},
urldate = {2013-11-25},
journal = {Journal of the American Statistical Association},
author = {Self, Steven G. and Liang, Kung-Yee},
month = jun,
year = {1987},
pages = {605--610}
}
@article{davis_semiparametric_1991,
title = {Semi-parametric and non-parametric methods for the analysis of repeated measurements with applications to clinical trials},
volume = {10},
issn = {1097-0258},
url = {http://onlinelibrary.wiley.com/doi/10.1002/sim.4780101210/abstract},
doi = {10.1002/sim.4780101210},
abstract = {Techniques applicable for the analysis of longitudinal data when the response variable is non-normal are not nearly as comprehensive as for normally-distributed outcomes. However, there have been several recent developments. Semi-parametric and non-parametric methodology for the analysis of repeated measurements is reviewed. The commonly encountered design in which, for each subject, one assesses a univariate response variable at multiple fixed time points, is considered. The types of outcomes considered include binary, ordered categorical, and continuous (but extremely non-normal) response variables. All of the methods considered allow for incomplete data due to the occurrence of missing observations. In addition, discrete and/or continuous covariates, which may be time-dependent, are accommodated by some of the approaches. The methods are demonstrated using data from three clinical trials.},
number = {12},
journal = {Statistics in Medicine},
author = {Davis, Charles S},
month = dec,
year = {1991},
pages = {1959--1980}
}
@article{fournier_ad_2011,
title = {{AD} Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models},
issn = {1055-6788},
shorttitle = {{AD} Model Builder},
url = {http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.597854},
doi = {10.1080/10556788.2011.597854},
abstract = {Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder {(ADMB)} is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using {AD} are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of {ADMB}, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which {ADMB} has been used, and discuss future development of {ADMB} as an open source project. Overall, the main advantages of {ADMB} are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder {(ADMB)} is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using {AD} are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of {ADMB}, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which {ADMB} has been used, and discuss future development of {ADMB} as an open source project. Overall, the main advantages of {ADMB} are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.},
journal = {Optimization Methods and Software},
author = {Fournier, David A. and Skaug, Hans J. and Ancheta, Johnoel and Ianelli, James and Magnusson, Arni and Maunder, Mark N. and Nielsen, Anders and Sibert, John},
year = {2011},
pages = {1--17}
}
@misc{plummer_jags:_2003,
title = {{JAGS:} A program for analysis of {Bayesian} graphical models using {Gibbs} sampling},
shorttitle = {{JAGS}},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.3406},
author = {Plummer, Martyn},
year = {2003}
}
@Manual{blme,
title = {blme: Bayesian Linear Mixed-Effects models},
author = {Vincent Dorie},
year = {2011},
note = {R package version 0.01-4},
url = {http://CRAN.R-project.org/package=blme},
}
@BOOK{Wilkinson1999,
title = {The grammar of graphics},
publisher = {Springer},
year = {1999},
author = {Leland Wilkinson},
address = {New York}
}
@Book{wickham2009,
author = {Hadley Wickham},
title = {{ggplot2}: elegant graphics for data analysis},
publisher = {Springer New York},
year = {2009},
isbn = {978-0-387-98140-6},
url = {http://had.co.nz/ggplot2/book},
}
@article{murtaugh_simplicity_2007,
title = {Simplicity and Complexity in Ecological Data Analysis},
volume = {88},
url = {http://www.esajournals.org/doi/abs/10.1890/0012-9658%282007%2988%5B56%3ASACIED%5D2.0.CO%3B2},
number = {1},
journal = {Ecology},
author = {Murtaugh, Paul A},
year = {2007},
pages = {56--62}
}
@article{dormann_methods_2007,
title = {Methods to account for spatial autocorrelation in the analysis of species distributional data: a review},
volume = {30},
url = {http://dx.doi.org/10.1111/j.2007.0906-7590.05171.x},
doi = {10.1111/j.2007.0906-7590.05171.x},
abstract = {Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species' distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.},
number = {5},
journal = {Ecography},
author = {Dormann, Carsten F. and Jana M. {McPherson} and {{Miguel} B. Araújo} and Roger Bivand and Janine Bolliger and Gudrun Carl and Richard G. Davies and Alexandre Hirzel and Walter Jetz and W. Daniel Kissling and Ingolf Kühn and Ralf Ohlemüller and Pedro R. Peres-Neto and Björn Reineking and Boris Schröder and Frank M. Schurr and Robert Wilson},
year = {2007},
pages = {609--628}
}
@article{ponciano_hierarchical_2009,
title = {Hierarchical Models in Ecology: Confidence Intervals, Hypothesis Testing, and Model Selection Using Data Cloning},
volume = {90},
issn = {0012-9658},
shorttitle = {Hierarchical Models in Ecology},
url = {http://www.jstor.org/stable/27650990},
abstract = {Hierarchical statistical models are increasingly being used to describe complex ecological processes. The data cloning ({DC)} method is a new general technique that uses Markov chain Monte Carlo ({MCMC)} algorithms to compute maximum likelihood ({ML)} estimates along with their asymptotic variance estimates for hierarchical models. Despite its generality, the method has two inferential limitations. First, it only provides Wald-type confidence intervals, known to be inaccurate in small samples. Second, it only yields {ML} parameter estimates, but not the maximized likelihood values used for profile likelihood intervals, likelihood ratio hypothesis tests, and information-theoretic model selection. Here we describe how to overcome these inferential limitations with a computationally efficient method for calculating likelihood ratios via data cloning. The ability to calculate likelihood ratios allows one to do hypothesis tests, construct accurate confidence intervals and undertake information-based model selection with hierarchical models in a frequentist context. To demonstrate the use of these tools with complex ecological models, we reanalyze part of Gause's classic Paramecium data with state—space population models containing both environmental noise and sampling error. The analysis results include improved confidence intervals for parameters, a hypothesis test of laboratory replication, and a comparison of the Beverton-Holt and the Ricker growth forms based on a model selection index.},
number = {2},
urldate = {2012-02-03},
journal = {Ecology},
author = {Ponciano, José Miguel and Taper, Mark L. and Dennis, Brian and Lele, Subhash R.},
month = feb,
year = {2009},
pages = {356--362},
}
@article{pinheiro_unconstrained_1996,
title = {Unconstrained parametrizations for variance-covariance matrices},
volume = {6},
url = {http://dx.doi.org/10.1007/BF00140873},
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{stram_variance_1994,
title = {Variance Components Testing in the Longitudinal Fixed Effects Model},
volume = {50},
url = {http://links.jstor.org/sici?sici=0006-341X%28199412%2950%3A4%3C1171%3AVCTITL%3E2.0.CO%3B2-H},
number = {4},
journal = {Biometrics},
author = {Stram, Daniel O and Lee, Jae Won},
year = {1994},
pages = {1171--1177}
}
@article{mckeon_multiple_2012,
title = {Multiple defender effects: synergistic coral defense by mutualist crustaceans},
volume = {169},
issn = {0029-8549},
shorttitle = {Multiple defender effects},
url = {http://www.springerlink.com/content/nm20758r6557v448/abstract/},
doi = {10.1007/s00442-012-2275-2},
abstract = {The majority of our understanding of mutualisms comes from studies of pairwise interactions. However, many hosts support mutualist guilds, and interactions among mutualists make the prediction of aggregate effects difficult. Here, we apply a factorial experiment to interactions of ‘guard’ crustaceans that defend their coral host from seastar predators. Predation was reduced by the presence of mutualists (15\% reduction in predation frequency and 45\% in volume of coral consumed). The frequency of attacks with both mutualists was lower than with a single species, but it did not differ significantly from the expected frequency of independent effects. In contrast, the combined defensive efficacy of both mutualist species reduced the volume of coral tissue lost by 73\%, significantly more than the 38\% reduction expected from independent defensive efforts, suggesting the existence of a cooperative synergy in defensive behaviors of ‘guard’ crustaceans. These emergent ‘multiple defender effects’ are statistically and ecologically analogous to the emergent concept of ‘multiple predator effects’ known from the predation literature.},
number = {4},
urldate = {2012-10-18},
journal = {Oecologia},
author = {McKeon, C. Seabird and Stier, Adrian and McIlroy, Shelby and Bolker, Benjamin},
year = {2012},
keywords = {Biomedical and Life Sciences},
pages = {1095--1103},
}
@book{dobson_introduction_2008,
edition = {3},
title = {An Introduction to Generalized Linear Models, Third Edition},
isbn = {1584889500},
publisher = {Chapman and {Hall/CRC}},
author = {Dobson, Annette J. and Barnett, Adrian},
month = may,
year = {2008}
}
@incollection{myers_appendix_2010,
title = {Appendix {A.6}: Computational Details for {GLMs} for a Noncanonical Link},
copyright = {Copyright © 2010 John Wiley \& Sons, Inc. All rights reserved.},
isbn = {9780470556986},
shorttitle = {Appendix A.6},
url = {http://onlinelibrary.wiley.com/doi/10.1002/9780470556986.app6/summary},
language = {en},
urldate = {2013-09-25},
booktitle = {Generalized Linear Models},
publisher = {John Wiley \& Sons, Inc.},
author = {Myers, Raymond H. and Montgomery, Douglas C. and Vining, G. Geoffrey and Robinson, Timothy J.},
year = {2010},
pages = {481-483}
}
@article{marschner_glm2:_2011,
title = {glm2: Fitting Generalized Linear Models with Convergence Problems},
volume = {3},
url = {http://journal.r-project.org/archive/2011-2/RJournal_2011-2_Marschner.pdf},
number = {2},
journal = {The R Journal},
author = {Marschner, Ian C.},
month = dec,
year = {2011},
pages = {12–15}
}
@Article{Kampstra:2008:CSB,
author = "Peter Kampstra",
title = "Code Snippet: {{\tt Beanplot}}: {A} Boxplot
Alternative for Visual Comparison of Distributions",
journal = {Journal of Statistical Software},
volume = "28",
number = "CS-1",
pages = "??--??",
month = nov,
year = "2008",
CODEN = "JSSOBK",
ISSN = "1548-7660",
bibdate = "Wed Aug 25 09:57:41 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jstatsoft.bib",
URL = "http://www.jstatsoft.org/v28/c01",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Software",
pubdates = "Submitted 2008-09-19; Accepted 2008-10-28",
}
@article{augustin_quantile_2012,
title = {On quantile quantile plots for generalized linear models},
volume = {56},
issn = {01679473},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167947312000692},
doi = {10.1016/j.csda.2012.01.026},
number = {8},
urldate = {2013-07-01},
journal = {Computational Statistics \& Data Analysis},
author = {Augustin, Nicole H. and Sauleau, Erik-André and Wood, Simon N.},
month = aug,
year = {2012},
pages = {2404--2409}
}
@article{hoaglin_poissonness_1980,
title = {A {Poissonness} Plot},
volume = {34},
issn = {0003-1305},
url = {http://www.jstor.org/stable/2683871},
doi = {10.2307/2683871},