  We use a principal components analysis of radio-selected (3CRR, 6CE and 7CRS)
AGN datasets to define two parameters related to low-frequency (151 MHz) radio
luminosity L_151 and [OIII] luminosity L_[OIII]: a parameter alpha encoding the
L_151 - L_[OIII] correlation and a parameter beta encoding scatter about this
correlation. We describe methods for constructing generalized luminosity
functions (GLFs) based on alpha, beta, redshift and schemes for unifying
quasars and radio galaxies.
  Luminosity-dependent unified schemes (e.g. a receding-torus scheme) have been
invoked to explain the low quasar to radio galaxy fraction at low alpha and the
differences in emission-line luminosities of radio quasars and radio galaxies.
With the constraints of the 3CRR, 6CE and 7CRS datasets and radio source
counts, our GLF approach was used to determine whether a receding-torus-like
scheme is required if there are two populations of radio sources: one at low
alpha, consisting of 'starved AGN'; the other at high alpha consisting of
'Eddington-tuned AGN'. Because of the overlap between these two populations and
the effects of the beta parameter, schemes with or without a receding torus can
produce a low quasar fraction at low alpha and differences in [OIII] luminosity
between radio galaxies and quasars. The receding torus may be a physical
process important in one or more populations of radio sources, but this is not
yet proved either by the quasar fraction or the emission-line properties of
radio-selected samples.
