  We investigate the clustering of Lyman-break galaxies (LBGs) at $z\sim4$.
Using the hierarchical galaxy formation model GALFORM, we predict, for the
first time using a semi-analytical model with feedback from active galactic
nuclei (AGN), the angular correlation function (ACF) of LBGs and find agreement
within $3\,\sigma$ with new measurements of the ACF from surveys including the
Hubble eXtreme Deep Field (XDF) and CANDELS field. Our simulations confirm the
conclusion reached using independent models that although the predicted ACFs
reproduce the trend of increased clustering with luminosity, the dependence is
less strong than observed. We find that for the detection limits of the XDF
field central LBGs at $z\sim 4$ predominantly reside in haloes of mass $\sim
10^{11}-10^{12}h^{-1}M_{\rm \odot}$ and that satellites reside in larger haloes
of mass $\sim 10^{12}-10^{13}h^{-1}M_{\rm \odot}$. The model predicts fewer
bright satellite LBGs at $z\sim4$ than is inferred from measurements of the ACF
at small scales. By analysing the halo occupation distribution (HOD) predicted
by the model, we find evidence that AGN feedback affects the HOD of central
LBGs in massive haloes. This is a new high-redshift test of this important
feedback mechanism. We investigate the effect of photometric errors in the
observations on the ACF predictions. We find that the observational uncertainty
in the galaxy luminosity reduces the clustering amplitude and that this effect
increases towards faint galaxies, particularly on small scales. To compare
properties of model with observed LBGs this uncertainty must be considered.
