Why does SLS (REML) give a different intercept than Python statsmodels for the same mixed model?

Question

I fitted:

Y ~ A(Sum) + B(Sum) + C(Sum) + D(Sum) + Subject(&Random)
 
in both JMP SLS (REML) and Python statsmodels MixedLM (REML) on the same data (~14k obs, ~200 levels of A, sparse A×C cross-tabulation, ~120 random subjects).

What I observe:

* All ~200 LS Means for factor A are shifted by a constant ~0.22 (JMP higher)
* Relative effects and rankings are identical (diff std < 0.001)
* LS Means for different factors in JMP have different grand means (A → 78.5, B/D → 73.0), which shouldn't happen with Sum coding
* A different Y on the same X gives essentially no offset (0.006)

What I need help with:

Is there a known reason why JMP's SLS personality (REML) would produce a different intercept than standard GLS β̂ = (X'V⁻¹X)⁻¹X'V⁻¹y? Is SLS using a different algorithm than the Mixed Model personality for computing fixed effects or LS Means?

JMP Pro 17, Windows.

xmq · Answer

Hi @MRB3855 Thanks for your kind help!

MRB3855 · Answer

Hi @xmq : at first I thought it might be a parameterizaton issue for the differences between the intercepts and coefficients for the fixed effects (https://www.jmp.com/support/help/en/15.2/#page/jmp/nominal-factors.shtml#).

But, I'm not so sure since the LSMeans should be unaffected by this, and I'm no Python user so maybe someone else could help here.

xmq · Answer

Hi @MRB3855 Thanks for your reply, here I visualized the difference between Python and JMP results, would it be helpful to identify the reason behind?

image