Factor analytic (FA) models are widely used across a range of disciplines owing to computational advantages from dimension reduction and possible ability to interpret the factors. In plant breeding, FA model provides a natural framework to model the genotype x environment interaction. An FA model is dictated by the number of factors (order of the model). A higher order lends to more parameters in the model and this necessitates the order selection to achieve parsimony. We introduce an order selection method via the ordered factor lasso (OFAL). We illustrate its performance based on a simulation on a real wheat yield multi-environmental trial.