Symbolic Formulae for Linear Mixed Models

TL;DR

This paper reviews the use of high-level symbolic formulae for specifying linear mixed models in statistical software, comparing two popular R packages, lme4 and asreml, to improve model flexibility and usability.

Contribution

It provides a comparative analysis of symbolic model specification methods in lme4 and asreml, highlighting their design and implementation for linear mixed models.

Findings

Highlights differences in software design for LMM specification

Emphasizes the role of symbolic formulae in model flexibility

Provides insights into user-friendly model specification approaches

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.