  We report the origin of a high-energy kink structure of heavily
electron-doped nonsuperconducting Li$_{1+x}$FeAs observed by three-dimensional
angle-resolved photoemission spectroscopy. The $d_{xy}$ orbital at the center
of the Brillouin zone is strongly renormalized, indicating stronger electron
correlation, exceeding that of stoichiometric LiFeAs despite the fact that the
orbital characters of all bands remain unchanged. Two types of kink structure
on the $d_{yz}$ band were identified: an isotropic kink at the binding energy
of 20 meV, and another kink located at 100 meV observed only in the (110)
direction. The higher-energy kink is considered to originate from a magnetic
interaction, because the peak energy is consistent with that of a spin
excitation.
