This Scroll article quotes an IDFC Institute 2015 article to discuss the effect of holding simultaneous elections at the Legislative Assembly and the Parliamentary level on election outcomes. The article states:
"A 2015 study by the IDFC Institute found “a 77% chance that the winning political party or alliance will win both the Lok Sabha and Assembly elections in that state when held simultaneously”. If the elections are held six months apart, however, only 61% of the voters choose the same party."
Read the full article here