Anova¶

car::Anova()-style ANOVA table for a fitted linear mixed model. Produces per-term F- or chi-square statistics with Satterthwaite denominator degrees of freedom. Mirrors the interface of car::Anova() in R.

Anova(model, type='III', test='F')[source]¶

car::Anova()-style ANOVA table for a fitted LMM.

Parameters:

model – A fitted CrossedLMEResult, or a list of two such results for likelihood-ratio test (LRT) comparison. When a list is supplied, type and test are ignored and the LRT table from interlace.anova() is returned.
type – ANOVA type: 'II' or 'III' (default). Ignored when model is a list.
test – Test statistic: 'F' (default) or 'Chisq'. 'F' returns the same table as anova_type2() / anova_type3(). 'Chisq' converts to Wald chi-square statistics (Chisq = F * df1) and reports chi-square p-values. Ignored when model is a list.

Return type:

Any

Returns:

pandas.DataFrame – For test='F': columns ["term", "df1", "df2", "F", "Pr(>F)"]. For test='Chisq': columns ["term", "df", "Chisq", "Pr(>Chisq)"]. For a list of models: LRT table from interlace.anova().

Raises:

ValueError – If type is not 'II' or 'III', test is not 'F' or 'Chisq', or if a list of REML-fitted models is passed.

Parameters:

model (Any)
type (str)
test (str)

Returned columns¶

`test='F'` (default)¶

Column	Description
`term`	Fixed-effect term name
`df1`	Numerator degrees of freedom (number of columns for this term)
`df2`	Satterthwaite denominator degrees of freedom
`F`	Wald F-statistic
`Pr(>F)`	p-value from the F distribution

`test='Chisq'`¶

Column	Description
`term`	Fixed-effect term name
`df`	Degrees of freedom (`df1`)
`Chisq`	Wald chi-square statistic (`F * df1`)
`Pr(>Chisq)`	p-value from the chi-square distribution

Choosing between Type II and Type III¶

Type	Use when
`type='III'` (default)	Interpreting main effects in the presence of interactions; matches `lmerTest::anova()` Type III output
`type='II'`	Additive models (no interactions), or when you want hierarchical marginal tests; requires ML refit internally

For additive models (no interactions) the two types produce identical results because the hypothesis matrices coincide. The distinction matters only when interactions are present.

Examples¶

Basic Type III F-table¶

import interlace

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

tbl = interlace.Anova(result)
print(tbl)
#        term  df1       df2      F   Pr(>F)
# 0  condition    1   38.2   31.2   0.0000
# 1       load    1   41.5    8.9   0.0048

Type II¶

tbl2 = interlace.Anova(result, type="II")

Chi-square statistics¶

tbl_chisq = interlace.Anova(result, test="Chisq")
#        term  df  Chisq  Pr(>Chisq)
# 0  condition   1   31.2      0.0000
# 1       load   1    8.9      0.0028

LRT comparison (two-model form)¶

When a list of two models is passed, Anova() delegates to the LRT-based anova function (both models must use method="ML"):

m0 = interlace.fit("rt ~ 1",         data=df, groups=["subject", "item"], method="ML")
m1 = interlace.fit("rt ~ condition", data=df, groups=["subject", "item"], method="ML")

interlace.Anova([m0, m1])   # LRT table, same as interlace.anova(m0, m1)