  We show that every subshift factor of a ($-\beta$)-shift is intrinsically
ergodic, when $\beta\geq \frac{1+\sqrt{5}}{2}$ and the ($-\beta$)-expansion of
$1$ is not periodic with odd period. Moreover, the unique measure of maximal
entropy satisfies a certain Gibbs property. This is an application of the
technique established by Climenhaga and Thompson to prove intrinsic ergodicity
beyond specification. We also prove that there exists a subshift factor of a
($-\beta$)-shift which is not intrinsically ergodic in the cases other than the
above.
