Symbolic Formulae for Linear Mixed Models

Emi Tanaka*, Francis K.C. Hui

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

    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 - Research School on Statistics and Data Science, RSSDS 2019, Proceedings
    EditorsHien Nguyen
    Number of pages19
    ISBN (Print)9789811519598
    Publication statusPublished - 2019
    Event3rd Research School on Statistics and Data Science, RSSDS 2019 - Melbourne, Australia
    Duration: 24 Jul 201926 Jul 2019

    Publication series

    NameCommunications in Computer and Information Science
    Volume1150 CCIS
    ISSN (Print)1865-0929
    ISSN (Electronic)1865-0937


    Conference3rd Research School on Statistics and Data Science, RSSDS 2019


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