There is a big difference between triggers and controling factors. Rainfall is the second important trigger. But if you are intrested in factors that controling occurrence of landslides then, the most important factor depends on the size of the landslides in your database. If landslides are smaller than 10^7m^3 then slope is the most important factor that controlls landslides accurrence. But for landslides largar than 10^7m^3 lithology ( type of material and also dip direction of fracture system/beding layer) is the most important factor.
Article Size distribution and controls of landslides in the Zagros m...
The trigger is rainfall, of course. However, anthropogenic activities like un-engineered road expansion and extension in geologically unstable hill slopes lead to multi-fold increase in landslides intensity. So, the most responsible factor depends on the region of intrest in my opinion.