  We present X-ray spectral variability of 24 local active galactic nuclei
(AGN) from the Palomar sample of nearby galaxies, as observed mainly by Swift.
From hardness ratio measurements, we find that 18 AGN with low accretion rates
show hardening with increasing count rate, converse to the softer-when-brighter
behaviour normally observed in AGN with higher accretion rates. Two AGN show
softening with increasing count rate, two show more complex behaviour, and two
do not show any simple relationship.
  Sufficient data were available for the spectra of 13 AGN to be summed in
flux-bins. In 9 of these sources, correlated luminosity-dependent changes in
the photon index ($\Gamma$) of a power-law component are found to be the main
cause of hardness variability. For 6 objects, with a low accretion rate as a
fraction of the Eddington rate (\.m$\mathrm{_{Edd}}$), $\Gamma$ is
anticorrelated with \.m$\mathrm{_{Edd}}$, i.e. `harder-when-brighter' behaviour
is observed. The 3 higher-\.m$\mathrm{_{Edd}}$-rate objects show a positive
correlation between $\Gamma$ and \.m$\mathrm{_{Edd}}$. This transition from
harder-when-brighter at low \.m$\mathrm{_{Edd}}$s to softer-when-brighter at
high \.m$\mathrm{_{Edd}}$s can be explained by a change in the dominant source
of seed-photons for X-ray emission from cyclo-synchrotron emission from the
Comptonising corona itself to thermal seed-photons from the accretion disc.
This transition is also seen in the `hard state' of black hole X-ray binaries
(BHXRBs). The results support the idea that LINERs are analogues of BHXRBs in
the hard state and that Seyferts are analogues of BHXRBs in either the
high-accretion-rate end of the hard state or in the hard-intermediate state.
