ezANOVA转lme4：模型公式编写及结果差异问题咨询

Hey there, I’ve run into this exact issue before—getting mismatched results between ezANOVA and lmer is super common, but it’s almost always down to two key things: how you specify the random effects structure and how Type III sums of squares (SS) are calculated. Let’s walk through how to align your lmer model with your ezANOVA output.

Why Your Current lmer Model Isn’t Matching #

Your original ezANOVA code handles a mixed design properly:

• Between-subjects factor: Group
• Within-subjects factors: Day, Cue
• It uses Type III SS and explicitly accounts for within-subject variability tied to Subject.

Your initial lmer model only includes a random intercept for Subject ((1|Subject)), which fails to capture the within-subject variation from Day and Cue. Additionally, base anova(lmeModel) doesn’t compute Type III SS by default—this is what ezANOVA uses with type=3.

Step-by-Step Fixes #

1. Set Up Orthogonal Contrasts First #

Type III SS is highly sensitive to factor coding. ezANOVA uses orthogonal contrasts under the hood, so we need to match that in lmer:

# Set orthogonal contrasts for factors (critical for accurate Type III SS)
options(contrasts = c("contr.sum", "contr.poly"))

2. Update the Random Effects Structure #

To properly model within-subject effects, we need to include random slopes for your within-subject factors (Day and Cue) nested within Subject. This tells the model that each subject’s response to Day and Cue can vary independently:

# Full random structure (includes intercept + slopes for Day/Cue per subject)
lmeModel <- lmer(Att ~ Group*Day*Cue + (1 + Day + Cue | Subject), data = SG10Long)

If this model has convergence issues (common with complex random structures), you can simplify it while still capturing key variation:

# Simplified random structure (separate random effects for intercept, Day, and Cue)
lmeModel <- lmer(Att ~ Group*Day*Cue + (1|Subject) + (0+Day|Subject) + (0+Cue|Subject), data = SG10Long)

3. Compute Type III SS with the car Package #

Base anova() for lmer models doesn’t support Type III SS. Use the Anova() function from the car package instead:

library(car)
# Get Type III SS results that match ezANOVA
Anova(lmeModel, type = "III")

Additional Checks #

• Ensure Day and Cue are coded as factors (not numeric). ezANOVA treats them as categorical by default, so convert them first with as.factor() if needed.
• Confirm your Subject variable is a factor too—this ensures random effects are grouped correctly by individual participants.

After making these changes, the Anova() output should align perfectly with the main effects and interactions reported by ezANOVA.

内容的提问来源于stack exchange，提问作者PeterPer