Decompose Variables into Within-Group and Between-Group Components

This function performs a multilevel decomposition of variables by computing:

Grand mean centered scores (deviations from overall mean)
Between-group scores (group means)
Within-group scores (deviations from group means)

Usage

decompose_within_between(
  data,
  group,
  vars,
  components = c("gmc", "between", "within"),
  gmc_pattern = "{col}_grand_mean_centered",
  between_pattern = "{col}_between_{group}",
  within_pattern = "{col}_within_{group}"
)

Arguments

data: A data frame containing the variables to decompose.
group: A character string specifying the name of the grouping variable.
vars: A character vector specifying the names of variables to decompose.
components: A character vector specifying which components to compute. Any subset of c("gmc", "between", "within") (default: all three). "gmc" = grand mean centering, "between" = group means, "within" = within-group deviations. If "within" is requested without "between", the between component is computed internally as an intermediate step and not included in the output.
gmc_pattern: A glue-style naming pattern for grand-mean-centered columns. Use {col} for the variable name. Default: "{col}_grand_mean_centered".
between_pattern: A glue-style naming pattern for between-group (group mean) columns. Use {col} for the variable name and {group} for the grouping variable name. Default: "{col}_between_{group}".
within_pattern: A glue-style naming pattern for within-group deviation columns. Use {col} for the variable name and {group} for the grouping variable name. Default: "{col}_within_{group}".

Value

A data frame containing:

All original variables from data
Grand mean centered versions (named by gmc_pattern), if "gmc" in components
Between-group means (named by between_pattern), if "between" in components
Within-group deviations (named by within_pattern), if "within" in components

Details

This decomposition is commonly used in multilevel modeling to separate within-group and between-group variance components (Enders & Tofighi, 2007). The decomposed variables are particularly useful for Random Effects Within-Between (REWB) models (Bell et al., 2019), which allow the estimation of distinct within-group and between-group effects.

The function performs three centering operations:

1. Grand mean centering: Each value is expressed as a deviation from the overall sample mean. This centers the entire distribution at zero.

2. Between-group component: For each observation, this equals the mean of their group. These values are constant within groups and vary between groups. In REWB models, this represents the between-group effect of the predictor.

3. Within-group component: Each value is expressed as a deviation from their group mean. This removes all between-group variance and represents the within-group effect of the predictor in REWB models.

References

Bell, A., Fairbrother, M., & Jones, K. (2019). Fixed and random effects models: making an informed choice. Quality & Quantity, 53(2), 1051-1074.

Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121-138.

Examples

data("media_diary")

# Decompose all three components (default)
result <- decompose_within_between(
  data = media_diary,
  group = "person",
  vars = c("stress", "screen_time")
)

# Only between and within (no grand mean centering)
result_wb <- decompose_within_between(
  data = media_diary,
  group = "person",
  vars = c("stress", "screen_time"),
  components = c("between", "within")
)

# Custom column naming: flat suffixes without the group name
result_flat <- decompose_within_between(
  data = media_diary,
  group = "person",
  vars = c("stress", "screen_time"),
  components = c("between", "within"),
  between_pattern = "{col}_between",
  within_pattern = "{col}_within"
)