  We develop a conceptual framework and methodology to study the drivers of the
quenching of galaxies, including the drivers of galactic conformity. The
framework is centred on the statistic $\Delta$, which is defined as the
difference between the observed star-formation state of a galaxy, and a
prediction of its state based on an empirical model of quenching. In
particular, this work uses the average quenching effects of stellar mass and
local density to construct an empirical model of quenching. $\Delta$ is
therefore a residual which reflects the effects of drivers of quenching not
captured by stellar mass and local density, or so-called 'hidden variables'.
Through a toy model, we explore how the statistical properties of $\Delta$ can
be used to learn about the internal and external hidden variables which control
the quenching of a sample of galaxies. We then apply this analysis to a sample
of local galaxies and find that, after accounting for the average quenching
effects of stellar mass and local density, $\Delta$ remains correlated out to
separations of 3 Mpc. Furthermore, we find that external hidden variables
remain important for driving the residual quenching of low-mass galaxies, while
the residual quenching of high-mass galaxies is driven mostly by internal
properties. These results, along with a similar analysis of a semi-analytical
mock catalogue, suggest that it is necessary to consider halo-related
properties as candidates for hidden variables. A preliminary halo-based
analysis indicates that much of the correlation of $\Delta$ can be attributed
to the physics associated with individual haloes.
