Top

Published in:

2019 | OriginalPaper | Chapter

Symbolic Formulae for Linear Mixed Models

Authors : Emi Tanaka, Francis K. C. Hui

Published in: Statistics and Data Science

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in many disciplines e.g. agriculture, ecology, econometrics, psychology. Mixed models, also commonly known as multi-level, nested, hierarchical or panel data models, incorporate a combination of fixed and random effects, with LMMs being a special case. The inclusion of random effects in particular gives LMMs considerable flexibility in accounting for many types of complex correlated structures often found in data. This flexibility, however, has given rise to a number of ways by which an end-user can specify the precise form of the LMM that they wish to fit in statistical software. In this paper, we review the software design for specification of the LMM (and its special case, the linear model), focusing in particular on the use of high-level symbolic model formulae and two popular but contrasting R-packages in lme4 and asreml.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

next chapter code::proof: Prepare for Most Weather Conditions

Aitkin, M., Dorothy, A., Francis, B., Hinde, J.: Statistical Modelling in GLIM. Oxford University Press, Oxford (1989)MATH

Bates, D., Machler, M., Bolker, B., Walker, S.: Fitting linear mixed-effects models using lme4. J. Stat. Softw. 67(1) (2015). https://doi.org/10.18637/jss.v067.i01

Buitinck, L., et al.: API design for machine learning software: experiences from the scikit-learn project. In: ECML PKDD Workshop: Languages for Data Mining and Machine Learning, pp. 108–122 (2013)

Butler, D.G., Cullis, B.R., Gilmour, A.R., Gogel, B.J.: Mixed models for s language environments ASReml-R reference manual (2009)

Butler, D.G., Gogel, B.J., Cullis, B.R., Thompson, R.: Navigating from ASReml-R version 3 to 4 (2018)

Bürkner, P.-C.: brms: an R package for Bayesian multilevel models using Stan. J. Stat. Softw. 80(1), 1–28 (2017)CrossRef

Bürkner, P.-C.: Advanced Bayesian multilevel modeling with the R package brms. R J. 10(1), 395–411 (2018). https://doi.org/10.32614/RJ-2018-017CrossRef

CAIGE: Caige project (2016). http://www.caigeproject.org.au

Chambers, J.M., Hastie, T.: Statistical models in S. Wadsworth & Brooks/Cole Computer Science Series. Wadsworth & Brooks/Cole Advanced Books & Software (1992). ISBN 9780534167646. http://books.google.fr/books?id=uyfvAAAAMAAJ

Crowder, M., Hand, D.: Analysis of Repeated Measures. Chapman and Hall, London (1990). http://www.python.orgMATH

Csárdi, G.: cranlogs: download logs from the ‘RStudio’ ‘CRAN’ mirror (2019). https://CRAN.R-project.org/package=cranlogs. R package version 2.1.1

Cullis, B.R., Smith, A.B., Coombes, N.E.: On the design of early generation variety trials with correlated data. J. Agric. Biol. Environ. Stat. 11(4), 381–393 (2006). https://doi.org/10.1198/108571106X154443. ISSN 1085–7117CrossRef

Gilmour, A.R., Cullis, B.R., Verbyla, A.P.: Accounting for natural and extraneous variation in the analysis of field experiments. J. Agric. Biol. Environ. Stat. 2(3), 269–293 (1997). https://doi.org/10.2307/1400446MathSciNetCrossRef

Gilmour, A.R., Gogel, B.J., Cullis, B.R., Thompson, R.: ASReml user guide release 3.0 (2009)

Kuhn, M.: parsnip: a common API to modeling and analysis functions (2018). https://topepo.github.io/parsnip. R package version 0.0.0.9003

Mrode, R.A.: Linear Models for the Prediction of Animal Breeding Values, 3rd edn. CABI, Wallingford (2014). https://doi.org/10.1017/CBO9781107415324.004. ISBN 1780643918, 9781780643915CrossRef

Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetMATH

Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., R Core Team: Nlme: linear and nonlinear mixed effects models (2019). https://CRAN.R-project.org/package=nlme. R package version 3.1-140

R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2018). https://www.R-project.org/

Ryan, T.A., Joiner, B.L., Ryan, B.F.: The Minitab Student Handbook. Duxbury Press, London (1976)

Seabold, S., Perktold, J.: Statsmodels: econometric and statistical modeling with python. In: 9th Python in Science Conference (2010)

Smith, N.J., et al.: pydata/patsy: v0.5.1, October 2018. https://doi.org/10.5281/zenodo.1472929

Stan Development Team: RStan: the R interface to Stan (2019). http://mc-stan.org/. R package version 2.19.2

Van Rossum, G., Drake Jr, F.L.: Python tutorial. Centrum voor Wiskunde en Informatica Amsterdam, The Netherlands (1995). http://www.python.org

Vazquez, A.I., Bates, D.M., Rosa, G.J.M., Gianola, D., Weigel, K.A.: Technical note: an R package for fitting generalized linear mixed models in animal breeding. J. Anim. Sci. 88, 497–504 (2010)CrossRef

VSN International: Genstat for Windows 19th Edition. VSN International, Hemel Hempstead, UK (2017). Genstat.co.uk

Welham, S.J., Gezan, S.A., Clark, S.J., Mead, A.: Statistical Methods in Biology: Design and Analysis of Experiments and Regression. Chapman and Hall, London (2015)

Wickham, H., FranÃğois, R., Henry, L., MÃijller, K.: dplyr: a grammar of data manipulation (2019). https://CRAN.R-project.org/package=dplyr. R package version 0.8.3

Wilkinson, G.N., Rogers, C.E.: Symbolic description of factorial models for analysis of variance. J. Roy. Stat. Soc.: Ser. C (Appl. Stat.) 22(3), 392–399 (1973)

Wright, K.: agridat: agricultural datasets (2018). https://CRAN.R-project.org/package=agridat. R package version 1.16

Xie, Y., Allaire, J.J., Grolemund, G.: R Markdown: The Definitive Guide. Chapman and Hall/CRC, Boca Raton (2018). ISBN 9781138359338. https://bookdown.org/yihui/rmarkdownCrossRef

Title: Symbolic Formulae for Linear Mixed Models
Authors: Emi Tanaka
Francis K. C. Hui
Publisher: Springer Singapore
Book: Statistics and Data Science
Print ISBN: 978-981-15-1959-8

Electronic ISBN: 978-981-15-1960-4

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-981-15-1960-4_1

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner