Title:	Partial Eta-Squared for Crossed and Nested Linear Mixed Models
Version:	0.1.2
Description:	Computes partial eta-squared effect sizes for fixed effects in linear mixed models fitted with the 'lme4' package. Supports crossed and nested random effects structures with any number of grouping factors. Random slope variances are translated to the outcome scale using a variance decomposition approach, correctly accounting for predictor scaling and interaction terms. Both general and operative effect sizes are provided. Methods are based on Correll, Mellinger, McClelland, and Judd (2020) <doi:10.1016/j.tics.2019.12.009>, Correll, Mellinger, and Pedersen (2022) <doi:10.3758/s13428-021-01687-2>, and Rights and Sterba (2019) <doi:10.1037/met0000184>.
License:	MIT + file LICENSE
URL:	https://github.com/bcohen0901/pecanr
BugReports:	https://github.com/bcohen0901/pecanr/issues
Encoding:	UTF-8
RoxygenNote:	7.3.3
Imports:	lme4
Suggests:	spelling, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Language:	en-US
NeedsCompilation:	no
Packaged:	2026-03-04 00:51:44 UTC; brandoncohen
Author:	Brandon Cohen [aut, cre], Joshua Correll [aut, ths]
Maintainer:	Brandon Cohen <brandon.cohen-1@colorado.edu>
Repository:	CRAN
Date/Publication:	2026-03-17 18:00:08 UTC

pecanr: Partial Eta-Squared for Crossed and Nested Linear Mixed Models

Description

Computes partial eta-squared effect sizes for fixed effects in linear mixed models fitted with the 'lme4' package. Supports crossed and nested random effects structures with any number of grouping factors. Random slope variances are translated to the outcome scale using a variance decomposition approach, correctly accounting for predictor scaling and interaction terms. Both general and operative effect sizes are provided. Methods are based on Correll, Mellinger, McClelland, and Judd (2020) doi:10.1016/j.tics.2019.12.009, Correll, Mellinger, and Pedersen (2022) doi:10.3758/s13428-021-01687-2, and Rights and Sterba (2019) doi:10.1037/met0000184.

Author(s)

Maintainer: Brandon Cohen brandon.cohen-1@colorado.edu (ORCID)

Authors:

• Joshua Correll joshua.correll@colorado.edu (ORCID) [thesis advisor]

See Also

Useful links:

• https://github.com/bcohen0901/pecanr

• Report bugs at https://github.com/bcohen0901/pecanr/issues

Batch Calculate Partial Eta-Squared for Multiple Effects

Description

Calculates partial eta-squared for all fixed effects in a model.

Usage

batch_eta2p(
  model,
  data,
  design = c("crossed", "nested"),
  subj_var = NULL,
  item_var = NULL,
  cross_vars = NULL,
  nest_vars = NULL,
  operative = FALSE,
  verbose = FALSE
)

Arguments

Value

A data frame with one row per effect containing eta-squared values and variance components.

Partial Eta-Squared for Linear Mixed Models

Description

Calculates partial eta-squared effect sizes for fixed effects in linear mixed models with crossed or nested random effects.

Usage

eta2p(
  model,
  effect,
  data,
  design = c("crossed", "nested"),
  subj_var = NULL,
  item_var = NULL,
  cross_vars = NULL,
  nest_vars = NULL,
  effect_level = NULL,
  var_x = NULL,
  operative = FALSE,
  verbose = TRUE
)

Arguments

Details

The function implements a variance decomposition approach for computing partial eta-squared in mixed models. Random slope variances are translated to the outcome scale using the formula:

\sigma^2_{slope}(Y) = \sigma^2_b \times \sigma^2_X

For interaction effects, the variance of the predictor is calculated as the variance of the actual product term (e.g., var(X1 * X2)), not the product of individual variances. This correctly accounts for centering, scaling, and correlation between predictors. The var_x argument allows bypassing this computation when the variance is known a priori.

For general effect sizes (default), all variance components are included in the denominator. For operative effect sizes (operative = TRUE), only variance components that contribute to the standard error of the effect are included.

Crossed designs support any number of grouping factors via cross_vars. The two-argument form (subj_var + item_var) is retained for backward compatibility and is equivalent to cross_vars = c(subj_var, item_var).

Value

An object of class "eta2p_lmm" containing:

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. doi:10.1016/j.tics.2019.12.009

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. doi:10.3758/s13428-021-01687-2

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. doi:10.1037/met0000184

Examples

library(lme4)

# --- Two crossed factors (backward-compatible call) ---
set.seed(42)
crossed_data <- data.frame(
  y         = rnorm(120),
  condition = rep(c(-0.5, 0.5), 60),
  subject   = factor(rep(1:20, each = 6)),
  item      = factor(rep(1:6, 20))
)
model <- lmer(y ~ condition + (1 | subject) + (1 | item),
              data = crossed_data)
eta2p(model, "condition", crossed_data,
      design   = "crossed",
      subj_var = "subject",
      item_var = "item")

# --- Three crossed factors using cross_vars ---
set.seed(42)
three_way_data <- data.frame(
  y         = rnorm(180),
  condition = rep(c(-0.5, 0.5), 90),
  subject   = factor(rep(1:20, each = 9)),
  item      = factor(rep(rep(1:6, each = 3), 10)),
  rater     = factor(rep(1:3, 60))
)
model3 <- lmer(y ~ condition + (1 | subject) + (1 | item) + (1 | rater),
               data = three_way_data)
eta2p(model3, "condition", three_way_data,
      design     = "crossed",
      cross_vars = c("subject", "item", "rater"))

# --- Supply predictor variance directly (var_x) ---
eta2p(model, "condition", crossed_data,
      design     = "crossed",
      cross_vars = c("subject", "item"),
      var_x      = 1)   # +/-1 binary predictor: var = 1 by design