emmeans¶

Estimated marginal means (EMMs) for a fitted linear mixed model. Mirrors R’s emmeans package: for each level combination of the specified factor(s), the marginal mean of the fixed-effects predictor is computed after averaging continuous covariates at their observed means. Standard errors and degrees of freedom use the Satterthwaite approximation.

Reference: Lenth (2016) Least-Squares Means: The R Package lsmeans, J. Stat. Softw. 69(1).

emmeans(model, specs, at=None, level=0.95)[source]¶

Compute estimated marginal means (EMMs) for a fitted LMM.

Parameters:

model – A fitted CrossedLMEResult.
specs – Name of the factor (str) or list of factor names for which to compute marginal means. Each named column must appear in the fixed-effects formula.
at – Optional dict of covariate values to use in the reference grid instead of their training-data means. For example at={"x": 0.0} centres the estimates at x = 0.
level – Nominal CI coverage (default 0.95).

Return type:

Any

Returns:

pandas.DataFrame – One row per level combination of specs, with columns:

<specs columns>, estimate, SE, df, lower, upper, t.ratio, p.value.

Parameters:

model (CrossedLMEResult)
specs (str | list[str])
at (dict[str, Any] | None)
level (float)

Examples

>>> emm = interlace.emmeans(result, specs="treatment")
>>> emm

Returned columns¶

Column	Description
`<specs>`	One column per specs factor showing the level combination
`estimate`	Marginal mean (EMM)
`SE`	Standard error
`df`	Satterthwaite denominator degrees of freedom
`lower`	Lower bound of the confidence interval
`upper`	Upper bound of the confidence interval
`t.ratio`	t-statistic (`estimate / SE`)
`p.value`	Two-tailed p-value

The confidence interval width is controlled by the level parameter (default 0.95).

Examples¶

Single factor¶

import interlace

result = interlace.fit("rt ~ condition", data=df, groups=["subject", "item"])

emm = interlace.emmeans(result, specs="condition")
print(emm)
#   condition  estimate        SE        df      lower      upper  t.ratio  p.value
# 0   control    456.3   12.4  38.2  431.2  481.4    36.8    0.000
# 1      high    502.7   13.1  39.5  476.2  529.2    38.4    0.000

Two-way grid¶

emm2 = interlace.emmeans(result, specs=["condition", "group"])
# One row per condition × group combination

Custom covariate values with `at=`¶

# Centre estimates at x = 0 instead of the training mean
emm_at = interlace.emmeans(result, specs="condition", at={"x": 0.0})

Narrower confidence interval¶

emm_90 = interlace.emmeans(result, specs="condition", level=0.90)