We can see that the differences between the second and the first lines and also the third and the second lines are both β1 + β3E which means that the differences between the slopes of the lines are always the same and that the slopes are always ordered from the G = 0 line to the G = 1 line to the G = 2 line. However, there is no theoretical reason to assume that the Y axis differences between the lines should always be the same; in principle they could differ and in practice they will always differ due to sampling error and possibly from genuine non-linear G × E effects. Further, forcing the lines to be ordered (although this may make biological sense because it constrains the model to an additive effect), could lead to inaccurate representation of the data. Essentially it will always predict an ordered effect even when the data do not follow this pattern.
