Thanks all.
@sakrejda : I double checked everything. model, data and program version are the same.
So I moved to complier flags. Following both @bgoodri 's advices I set
CXXFLAGS" = -O3 -mtune=native -march=native -Wno-unused-variable -Wno-macro-redefined -fno-fast-math
now both times to run CmdStan and the final results are comparable on my machine and on the cluster.
Here are the results on the cluster:
Inference for Stan model: orderedLogistic_model
1 chains: each with iter=(1000); warmup=(0); thin=(1); 1000 iterations saved.
Warmup took (1216) seconds, 20 minutes total
Sampling took (995) seconds, 17 minutes total
Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat
lp__ -7.1e+03 1.4e-01 3.0e+00 -7.1e+03 -7.1e+03 -7.1e+03 447 4.5e-01 1.0e+00
accept_stat__ 9.4e-01 2.7e-03 8.4e-02 7.4e-01 9.7e-01 1.0e+00 1000 1.0e+00 1.0e+00
stepsize__ 1.4e-02 4.9e-17 3.5e-17 1.4e-02 1.4e-02 1.4e-02 0.50 5.0e-04 1.0e+00
treedepth__ 8.0e+00 6.7e-03 2.1e-01 8.0e+00 8.0e+00 8.0e+00 1000 1.0e+00 1.0e+00
n_leapfrog__ 2.6e+02 1.7e+00 5.4e+01 2.6e+02 2.6e+02 2.6e+02 1000 1.0e+00 1.0e+00
divergent__ 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 0.0e+00 1000 1.0e+00 -nan
energy__ 7.1e+03 2.1e-01 4.2e+00 7.1e+03 7.1e+03 7.1e+03 389 3.9e-01 1.0e+00
beta[1] 3.4e-02 1.0e-03 2.6e-02 -7.0e-03 3.5e-02 7.7e-02 634 6.4e-01 1.0e+00
beta[2] -3.9e+00 5.8e-03 1.8e-01 -4.2e+00 -3.9e+00 -3.6e+00 1000 1.0e+00 1.0e+00
beta[3] -2.6e-01 6.2e-03 2.0e-01 -5.8e-01 -2.6e-01 7.5e-02 1000 1.0e+00 1.0e+00
beta[4] 5.8e-02 1.9e-04 6.0e-03 4.8e-02 5.8e-02 6.8e-02 1000 1.0e+00 1.0e+00
beta[5] -1.3e+00 2.0e-02 6.4e-01 -2.3e+00 -1.3e+00 -3.2e-01 1000 1.0e+00 1.0e+00
beta[6] 1.8e-02 6.4e-05 2.0e-03 1.5e-02 1.8e-02 2.1e-02 1000 1.0e+00 1.0e+00
beta[7] -6.3e-03 2.3e-05 7.2e-04 -7.5e-03 -6.3e-03 -5.1e-03 1000 1.0e+00 1.0e+00
beta[8] -1.5e-01 3.7e-02 9.8e-01 -1.8e+00 -1.3e-01 1.4e+00 708 7.1e-01 1.0e+00
beta[9] 5.2e-01 7.1e-03 1.8e-01 2.2e-01 5.1e-01 8.0e-01 653 6.6e-01 1.0e+00
beta[10] 1.7e+00 5.6e-03 1.8e-01 1.4e+00 1.7e+00 2.0e+00 1000 1.0e+00 1.0e+00
beta[11] 9.0e-01 9.7e-04 2.7e-02 8.5e-01 9.0e-01 9.4e-01 753 7.6e-01 1.0e+00
c[1] 4.6e+00 5.3e-02 1.2e+00 2.5e+00 4.6e+00 6.5e+00 538 5.4e-01 1.0e+00
c[2] 6.8e+00 5.3e-02 1.2e+00 4.7e+00 6.8e+00 8.7e+00 533 5.4e-01 1.0e+00
c[3] 1.0e+01 5.3e-02 1.2e+00 7.8e+00 1.0e+01 1.2e+01 529 5.3e-01 1.0e+00
c[4] 1.3e+01 5.4e-02 1.2e+00 1.0e+01 1.3e+01 1.4e+01 526 5.3e-01 1.0e+00
c[5] 1.5e+01 5.4e-02 1.2e+00 1.3e+01 1.5e+01 1.7e+01 526 5.3e-01 1.0e+00
c[6] 1.9e+01 5.5e-02 1.3e+00 1.7e+01 1.9e+01 2.1e+01 547 5.5e-01 1.0e+00