Partial Eta-Squared for Crossed, Nested, and Mixed Linear Mixed Models.

pecanr

pecanr computes partial eta-squared (eta2p) effect sizes for fixed effects in linear mixed models fitted with lme4. It correctly handles crossed, nested, and mixed (crossed-and-nested) random effects structures – including random slopes – using a variance decomposition approach that translates slope variances to the outcome scale.

Why pecanr?

pecanr accounts for:

• Crossed designs – any number of grouping factors (subjects, items, raters, etc.)
• Nested designs – hierarchical structures with automatic level detection
• Mixed designs – grouping factors that are simultaneously nested within some variables and crossed with others (e.g., photos nested within models, but both crossed with participants)
• Random slopes – translated to the outcome scale via sigma^2_slope x sigma^2_X
• Operative effect sizes – excluding variance components that don’t contribute to the standard error of the tested effect

Installation

You can install the development version of pecanr from GitHub:

# install.packages("pak")
pak::pak("bcohen0901/pecanr")

Once on CRAN:

install.packages("pecanr")

Usage

Crossed design (subjects x items)

library(lme4)
library(pecanr)

model <- lmer(y ~ condition + (1 | subject) + (1 | item), data = my_data)
eta2p(model, effect = "condition", data = my_data,
      design     = "crossed",
      cross_vars = c("subject", "item"))

Three crossed factors

model3 <- lmer(y ~ condition + (1 | subject) + (1 | item) + (1 | rater),
               data = my_data)
eta2p(model3, effect = "condition", data = my_data,
      design     = "crossed",
      cross_vars = c("subject", "item", "rater"))

Nested design

model_nested <- lmer(y ~ treatment + (1 | school/class), data = my_data)
eta2p(model_nested, effect = "treatment", data = my_data,
      design    = "nested",
      nest_vars = c("class", "school"))

Mixed design (nested-and-crossed)

Use design = "mixed" when some grouping factors are nested within others but all levels are crossed with additional factors. A common example is participants viewing multiple photos of each model: photos are nested within models, but both levels are crossed with participants.

model_mixed <- lmer(y ~ x + (1 | participant) + (1 | model) + (1 | photo:model),
                    data = my_data)
eta2p(model_mixed, effect = "x", data = my_data,
      design     = "mixed",
      cross_vars = "participant",
      nest_vars  = c("photo", "model"))

Batch over all effects

batch_eta2p(model, data = my_data,
            design     = "crossed",
            cross_vars = c("subject", "item"))

Operative effect sizes

eta2p(model, effect = "condition", data = my_data,
      design     = "crossed",
      cross_vars = c("subject", "item"),
      operative  = TRUE)

References

Correll, J., Mellinger, C., McClelland, G. H., & Judd, C. M. (2020). Avoid Cohen’s “Small”, “Medium”, and “Large” for Power Analysis. Trends in Cognitive Sciences, 24(3), 200-207.

Correll, J., Mellinger, C., & Pedersen, E. J. (2022). Flexible approaches for estimating partial eta squared in mixed-effects models with crossed random factors. Behavior Research Methods, 54, 1626-1642.

Rights, J. D., & Sterba, S. K. (2019). Quantifying explained variance in multilevel models: An integrative framework for defining R-squared measures. Psychological Methods, 24(3), 309-338.