Using Non-Linear Mixed Models for Agricultural Data.

Non-linear mixed-effects models (NLME) can be thought of an extension of linear
mixed-effects (LME) models or non-linear models. The possibility of specifying
the mean structure of a model as non-linear has the two main advantages of
parsimony (fewer parameters) and interpretability (the parameters are meaningful
biologically). The ability of including random-effects, as in LME, allows for
inference at the level of population and also the individual level. These NLME
have not been extensively used in agricultural research despite their advantages
and the availability of software to fit these models. Here I will present an
introduction to the formulation of NLME, a simple example using barley response
to N fertilizer and a more recent application, in the context of meta-analysis,
modeling growth curves and assesing the effects of planting density and N
fertilizer on miscanthus (a biomass crop). In both examples, the NLME prove easy
to fit and to interpret. Additionally, they are flexible enough to accomodate
population and individual level predictions.