To reveal dynamical property of a guest ion in type-I clathrate compound, n-and p-type clathrates Ba8Ga16Ge30 have been investigated by Raman scattering. It is found that the guest ion in a 6d-site cage (6d-cage) rotationally moves for both n-and p-type since the additional guest mode Eg(A) has been observed regardless of its carrier. The potential-energy difference between [100] and [110] directions in the 6d-cage is proportional to the off-center distance of the guest-ion position from the cage center and this off-center distance for p-type is much larger than that for n-type Ba8Ga16Ge30. In addition, the Raman intensity of the cage vibration at a 6c site for p-type is weaker than that for n-type. Thus, the amplitude of the vibration at the 6c site becomes small for p-type, and this small amplitude induces a large movable space for the guest ion, i.e., this vibrational amplitude of the 6c-site atom works as the barrier for the off-center position. For both systems, the guest ion in the 6d-cage shows an anharmonic vibration, judging from the anomalous energy decrease in the guest ion with decreasing temperature. The energy difference between T-2g and T-1u [T. Mori et al., Phys. Rev. B 79, 212301 (2009)] of the guest mode clearly supports the theoretical prediction of an interacting dipoles picture that explains the glasslike properties of the off-centered clathrate. It is concluded that the off-center rattling plays an important role to suppress a lattice thermal conductivity.