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.
Hi @xmq , and welcome! Can you show the pertinent output from each please? It will help folks here diagnose what might be going on; I have a few thoughts but I don't want us to get ahead of ourselves.
Hi @MRB3855 , thanks for your reply!
Here shares my dataset and JMP/Python scripts and outputs for checking,
For JMP
Fit Model(
Y( :Y1 ),
Effects( :A, :B, :C, :D ),
Random Effects( :Subject ),
NoBounds( 1 ),
Personality( "Standard Least Squares" ),
Method( "REML" ),
Emphasis( "Effect Leverage" ),
Run(
:Y1 << {Summary of Fit( 1 ), Analysis of Variance( 0 ),
Parameter Estimates( 1 ), Scaled Estimates( 0 ),
Plot Actual by Predicted( 0 ), Plot Regression( 0 ),
Plot Residual by Predicted( 0 ), Plot Studentized Residuals( 0 ),
Plot Effect Leverage( 0 ), Plot Residual by Normal Quantiles( 0 ),
{:A << {LSMeans Student's t( 0.05 )}}}
)
);
For Python
def fit_model(df, y_col):
"""Fit Y ~ A(Sum) + B(Sum) + C(Sum) + D(Sum) + (1|Subject) via REML."""
# Note: column "C" conflicts with patsy's C() function,
# so we temporarily rename it for formula construction.
df_tmp = df.rename(columns={'C': '_C_'})
formula = '1 + C(A, Sum) + C(B, Sum) + C(_C_, Sum) + C(D, Sum)'
X_mat = dmatrix(formula, df_tmp)
design_info = X_mat.design_info
X = pd.DataFrame(np.asarray(X_mat), columns=design_info.column_names)
y = df[y_col].values
groups = df['Subject']
model = MixedLM(y, X, groups=groups)
result = model.fit(reml=True, method='powell')
return result, X, design_info, df_tmp
def compute_lsmeans_A(result, X, df_tmp, design_info):
"""Compute LS Means for factor A (Sum coding → intercept + effect)."""
fe = result.fe_params.values
n_fe = len(fe)
col_names = list(X.columns)
target_prefix = 'C(A, Sum)'
target_col_idx = [i for i, c in enumerate(col_names) if target_prefix in c]
base_contrast = np.zeros(n_fe)
base_contrast[0] = 1.0 # intercept
levels = sorted(df_tmp['A'].unique())
lsmeans = {}
for level in levels:
sr = df_tmp.iloc[0:1].copy()
sr['A'] = level
X_single = np.asarray(build_design_matrices([design_info], sr)[0])
c = base_contrast.copy()
for idx in target_col_idx:
c[idx] = X_single[0, idx]
lsmeans[level] = float(c @ fe)
return lsmeans
I'd appreciate any comments/suggestions you might have.
Hi @xmq : Apologies, but it's difficult for me to see the intercept etc especially from the Python output (I don't use Python). Can you show a picture of the JMP output (including intercept, coefficents, ls means, etc) and a picture of the corresponding Python output laid out so they are easily comparable?
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?
imageimageimageimage
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.
Hi @MRB3855 Thanks for your kind help!
