Semipartial geometries (SPG) were introduced in 1978 by Debroey and Thas. As some of
the examples they provided were embedded in affine space it was a natural question to ask whether it was possible to
classify all SPG embedded in affine space. In $AG(2,q)$ and $AG(3,q)$ a complete classification was obtained. Later on it was shown that if an SPG, with $\alpha>1$, is embedded in affine space it is either a
linear representation or $\mathrm{TQ}(4,2^h)$. In this paper we derive general
restrictions on the parameters of an SPG to have a linear representation and classify the linear representations of SPG
in $AG(4,q)$, hence yielding the complete classification of SPG in $AG(4,q)$, with $\alpha>1$.