A speakers frequency response will change with SPL, at the lower frequencies the effect of the suspension stiffening and the BL dropping due to the coil leaving the center of the gap will increase the Qt and decrease the sensitivity, also the coil impedance will rise dur to thermal effects.
there is lots of data on this from klippel
the high frequency response can also change with level, I've seen prototypes where the high frequency roll of of a 6" driver changes from 4Khz at 1w(86dB) to 1.5Khz at 80w(102dB)