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("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: c("between", "within")). "gmc" = grand mean centering, "between" = group means, "within" = within-group deviations. Grand mean centered scores are not included by default and must be requested explicitly. 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.

Observations with a missing value on group are kept in the output, but their between- and within-group components are set to NA (with a warning): without a known group, no group mean can be assigned. Grand mean centering does not involve the grouping variable and is unaffected.

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 between and within components (default)
result <- decompose_within_between(
  data = media_diary,
  group = "person",
  vars = c("stress", "screen_time")
)

# Include grand mean centered scores as well
result_gmc <- decompose_within_between(
  data = media_diary,
  group = "person",
  vars = c("stress", "screen_time"),
  components = c("gmc", "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"
)