  This paper presents a study of the redshift evolution of radio-loud active
galactic nuclei (AGN) as a function of the properties of their galaxy hosts in
the Bo\"otes field. To achieve this we match low-frequency radio sources from
deep $150$-MHz LOFAR observations to an $I$-band-selected catalogue of
galaxies, for which we have derived photometric redshifts, stellar masses and
rest-frame colours. We present spectral energy distribution (SED) fitting to
determine the mid-infrared AGN contribution for the radio sources and use this
information to classify them as High- versus Low-Excitation Radio Galaxies
(HERGs and LERGs) or Star-Forming galaxies. Based on these classifications we
construct luminosity functions for the separate redshift ranges going out to $z
= 2$. From the matched radio-optical catalogues, we select a sub-sample of
$624$ high power ($P_{150\mathrm{\,MHz}}>10^{25}$ W Hz$^{-1}$) radio sources
between $0.5 \leq z < 2$. For this sample, we study the fraction of galaxies
hosting HERGs and LERGs as a function of stellar mass and host galaxy colour.
The fraction of HERGs increases with redshift, as does the fraction of sources
in galaxies with lower stellar masses. We find that the fraction of galaxies
that host LERGs is a strong function of stellar mass as it is in the local
Universe. This, combined with the strong negative evolution of the LERG
luminosity functions over this redshift range, is consistent with LERGs being
fuelled by hot gas in quiescent galaxies.
