ABSTRACT 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 Δ, 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 M* and local density δ to construct an empirical model of quenching. Δ is therefore a residual which reflects the effects of drivers of quenching not captured by M* and δ, or so-called hidden variables. Through a toy model, we explore how the statistical properties of Δ 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 M* and δ, Δ 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 Δ can be attributed to the physics associated with individual haloes.