  Studies show that both radio jets from the active galactic nuclei (AGN) and
the star formation (SF) activity in quasar host galaxies contribute to the
quasar radio emission; yet their relative contributions across the population
remain unclear. Here, we present an improved parametric model that allows us to
statistically separate the SF and AGN components in observed quasar radio flux
density distributions, and investigate how their relative contributions evolve
with AGN bolometric luminosity ($L_\mathrm{bol}$) and redshift ($z$) using a
fully Bayesian method. Based on the newest data from LOFAR Two-Metre Sky Survey
Data Release 2, our model gives robust fitting results out to $z\sim4$, showing
a quasar host galaxy SFR evolution that increases with bolometric luminosity
and with redshift out to $z\sim4$. This differs from the global cosmic SFR
density, perhaps due to the importance of galaxy mergers. The prevalence of
radio AGN emissions increases with quasar luminosity, but has little dependence
on redshift. Furthermore, our new methodology and large sample size allow us to
subdivide our dataset to investigate the role of other parameters.
Specifically, in this paper, we explore quasar colour and demonstrate that the
radio excess in red quasars is due to an enhancement in AGN-related emission,
since the host galaxy SF contribution to the total radio emission is
independent of quasar colour. We also find evidence that this radio enhancement
occurs mostly in quasars with weak or intermediate radio power.
