  In plant breeding the presence of a genotype by environment (GxE) interaction
has a strong impact on cultivation decision making and the introduction of new
crop cultivars. The combination of linear and bilinear terms has been shown to
be very useful in modelling this type of data. A widely-used approach to
identify GxE is the Additive Main Effects and Multiplicative Interaction
Effects (AMMI) model. However, as data frequently can be high-dimensional,
Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible.
In this article, we consider a variational inference approach for such a model.
We derive variational approximations for estimating the parameters and we
compare the approximations to MCMC using both simulated and real data. The new
inferential framework we propose is on average two times faster whilst
maintaining the same predictive performance as MCMC.
