I have trained at home for well over a decade. Much of lifting heavy/seriously is focus and pacing. Public gyms usually mess with your flow. Some of them don't have the equipment for serious lifting or they do and won't let you...
So, after training at home that long I feel like it does negatively affect my lifting at a commercial gym (usually happens when I'm out of town on vacation/business).
You can't always do the same warmup/prep routine at a comm gym and routine is important for heavier lifts. Also, your overall routine is often screwy...if you travel, your sleep, food, hydration, etc. can all be out of step.
Currently, I train in my garage for the serious stuff and my apartment complexes basic gym for some BS stuff. Since the work I do in the apartment's gym is simple and I made it part of my routine, I don't notice any difference there...
"...strength is built one recovery day at a time..." -OMP
"Do not change shit up during a training cycle." -Sandbox
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