  We investigate the long-term spectral variability in the ultra-luminous X-ray
source Holmberg IX X--1. By analyzing the data from eight {\it Suzaku} and 13
{\it XMM-Newton} observations conducted between 2001 and 2015, we perform a
detailed spectral modeling for all spectra with simple models and complex
physical models. We find that the spectra can be well explained by a disc plus
thermal Comptonization model. Applying this model, we unveil correlations
between the X-ray luminosity ($L_{\rm X}$) and the spectral parameters. Among
the correlations, a particular one is the statistically significant positive
correlation between $L_{\rm X}$ and the photon index ($\Gamma$), while at the
high luminosities of $> 2\times10^{40}\,{\rm~erg\ s}^{-1}$, the source becomes
marginally hard and that results a change in the slope of the $\Gamma - L_{\rm
X}$ correlation. Similar variability behavior is observed in the optical depth
of the source around $L_{\rm X} \sim 2\times10^{40}\,{\rm~erg\ s}^{-1}$ as the
source becomes more optically thick. We consider the scenario that a corona
covers the inner part of the disc, and the correlations can be explained as to
be driven by the variability of seed photons from the disc input into the
corona. On the basis of the disc-corona model, we discuss the physical
processes that are possibly indicated by the variability of the spectral
parameters. Our analysis reveals the complex variability behavior of Holmberg
IX X--1 and the variability mechanism is likely related to the geometry of the
X-ray emitting regions.
