  We consider the spin $k/2$ XXZ model in the antiferomagnetic regime using the
free field realization of the quantum affine algebra $\uqa$ of level $k$. We
give a free field realization of the type II $q$-vertex operator, which
describes creation and annihilation of physical particles in the model. By
taking a trace of the type I and the type II $q$-vertex operators over the
irreducible highest weight representation of $\uqa$, we also derive an integral
formula for form factors in this model. Investigating the structure of poles,
we obtain a residue formula for form factors, which is a lattice analog of the
higher spin extension of the Smirnov's formula in the massive integrable
quantum field theory. This result as well as the quantum deformation of the
Knizhnik-Zamolodchikov equation for form factors shows a deep connection in the
mathematical structure of the integrable lattice models and the massive
integrable quantum field theory.
