Symbolic formulae for linear mixed models

Emi Tanaka, Francis K. C. Hui

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther

2 Citations (Scopus)


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 languageEnglish
Title of host publicationStatistics and Data Science
Subtitle of host publicationResearch School on Statistics and Data Science, RSSDS 2019 Melbourne, VIC, Australia, July 24–26, 2019 Proceedings
EditorsHien Nguyen
Place of PublicationSingapore Singapore
Number of pages19
ISBN (Electronic)9789811519604
ISBN (Print)9789811519598
Publication statusPublished - 2019
EventResearch School on Statistics and Data Science, RSSDS 2019 - La Trobe University, Melbourne, Australia
Duration: 24 Jul 201926 Jul 2019
Conference number: 3rd

Publication series

NameCommunications in Computer and Information Science
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937


ConferenceResearch School on Statistics and Data Science, RSSDS 2019
Abbreviated titleRSSDS 2019
Internet address


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

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