  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.
