Symbolic formulae for linear mixed models

Emi Tanaka; Francis K. C. Hui

doi:10.1007/978-981-15-1960-4_1

Symbolic formulae for linear mixed models

Emi Tanaka, Francis K. C. Hui

Econometrics & Business Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

2 Citations (Scopus)

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.

Original language	English
Title of host publication	Statistics and Data Science
Subtitle of host publication	Research School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings
Editors	Hien Nguyen
Place of Publication	Singapore Singapore
Publisher	Springer
Pages	3-21
Number of pages	19
Edition	1st
ISBN (Electronic)	9789811519604
ISBN (Print)	9789811519598
DOIs	https://doi.org/10.1007/978-981-15-1960-4_1
Publication status	Published - 2019
Event	Research School on Statistics and Data Science, RSSDS 2019 - La Trobe University, Melbourne, Australia Duration: 24 Jul 2019 → 26 Jul 2019 Conference number: 3rd https://sites.google.com/view/rssds2019/home

Publication series

Name	Communications in Computer and Information Science
Volume	1150
ISSN (Print)	1865-0929
ISSN (Electronic)	1865-0937

Conference

Conference	Research School on Statistics and Data Science, RSSDS 2019
Abbreviated title	RSSDS 2019
Country/Territory	Australia
City	Melbourne
Period	24/07/19 → 26/07/19
Internet address	https://sites.google.com/view/rssds2019/home

Keywords

Fixed effects
Hierarchical model
Model API
Model formulae
Model specification
Multi-level model
Random effects

Access to Document

10.1007/978-981-15-1960-4_1

Cite this

Tanaka, E., & Hui, F. K. C. (2019). Symbolic formulae for linear mixed models. In H. Nguyen (Ed.), Statistics and Data Science: Research School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings (1st ed., pp. 3-21). (Communications in Computer and Information Science; Vol. 1150). Springer. https://doi.org/10.1007/978-981-15-1960-4_1

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title = "Symbolic formulae for linear mixed models",

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.",

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Tanaka, E & Hui, FKC 2019, Symbolic formulae for linear mixed models. in H Nguyen (ed.), Statistics and Data Science: Research School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings. 1st edn, Communications in Computer and Information Science, vol. 1150, Springer, Singapore Singapore, pp. 3-21, Research School on Statistics and Data Science, RSSDS 2019, Melbourne, Australia, 24/07/19. https://doi.org/10.1007/978-981-15-1960-4_1

Symbolic formulae for linear mixed models. / Tanaka, Emi; Hui, Francis K. C.
Statistics and Data Science: Research School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings. ed. / Hien Nguyen. 1st. ed. Singapore Singapore: Springer, 2019. p. 3-21 (Communications in Computer and Information Science; Vol. 1150).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

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AU - Tanaka, Emi

AU - Hui, Francis K. C.

N1 - Conference code: 3rd

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Fixed effects

KW - Hierarchical model

KW - Model API

KW - Model formulae

KW - Model specification

KW - Multi-level model

KW - Random effects

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PB - Springer

CY - Singapore Singapore

T2 - Research School on Statistics and Data Science, RSSDS 2019

Y2 - 24 July 2019 through 26 July 2019

ER -

Tanaka E, Hui FKC. Symbolic formulae for linear mixed models. In Nguyen H, editor, Statistics and Data Science: Research School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings. 1st ed. Singapore Singapore: Springer. 2019. p. 3-21. (Communications in Computer and Information Science). doi: 10.1007/978-981-15-1960-4_1

Symbolic formulae for linear mixed models

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Keywords

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