The guest ion motion has been investigated by Raman scattering for the following caged crystals: La3Pd20X6 (X=Ge, Si), X8Ga16Ge30 (X=Ba, Sr, Eu), and KOs 2O6. The observed Raman peaks have been well assigned by the polarization dependence and the first principles calculation. It has been found that the energy of the guest ion anomalously decreases with decreasing temperature for X8Ga16Ge30, La 3Pd20Ge6, and KOs2O6, where the rattling motion of the guest ion has been reported. However, such anomalous decrease has not been observed in La3Pd20Si 6 (no rattling). The origin of the energy decrease is understood by the existence of the large quartic anharmonic potential. Furthermore, the existence of carriers is important for the rattling mode.