Random subsampling using the extract function

Hi Stan community,

I have a general question about selecting a random subset of sampled parameters using the rstan::extract function.

With 9000 iterations and 4 chains in the rstan’s sampling statement, I found that one parameter’s Rhat value was 1.09 in a specific stan model. I then randomly selected 2000 out of 9000 samples for that specific parameter. The random sample of size 2000 produced the parameter’s Rhat value of about 1.01. I assume it’s acceptable to use the randomly selected 2000 samples instead of 9000. Of course, I used set.seed in R so that those random subsamples could be kept across all four chains. Would this practice be sound?