  We construct a compactification of the moduli of toric pairs by using ideas
from mirror symmetry. The secondary fan $\Sigma(Q)$ is used in [Ale02] to
parametrize degenerations of toric pairs. It is also used in [CLS11] to control
the variation of GIT. We verify the prediction of mirror symmetry that
$\Sigma(Q)$ for the moduli of toric pairs is equal to the Mori fan of the
relative minimal models of the mirror family. As a result, we give an explicit
construction of the compactification $\mathscr{T}_Q$ of the moduli of toric
pairs which is the normalization of the compactification in [Ale02] and
[Ols08].
