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Within / between (Mundlak) decomposition for longitudinal data

Source: R/within_between.R
within_between.Rd

For each variable in vars, adds two new columns to data:

Usage

within_between(data, group, vars, suffix = c("_btw", "_wtn"), na.rm = TRUE)

Arguments

data

A data frame.

group

Character name (or character vector of names) identifying the grouping column(s). With multiple names, grouping is by the interaction.

vars

Character vector of numeric columns to decompose. Must all exist in data.

suffix

Length-2 character vector giving the suffixes for the between- and within-group columns. Default c("_btw", "_wtn").

na.rm

Logical; passed to mean() when computing per-group means. Default TRUE.

Value

The input data with 2 * length(vars) new columns appended.

Details

  • <var><suffix[1]> - the per-group mean of var (the between-group component, constant within each group),

  • <var><suffix[2]> - var - <var><suffix[1]> (the within-group deviation, summing to zero within each group).

The decomposition is exact: data[[var]] == data[[btw]] + data[[wtn]]. Including both columns in a regression (~ x_btw + x_wtn) separates the cross-group association from the within-group association without imposing that they be the same coefficient (the random-effects assumption).

Typical use in the MOTIVATE cover-resurvey workflow:

plots <- within_between(plots, group = "plot_id", vars = "year")
fit   <- tobs(~ year_btw + year_wtn + bym2(graph = adj), data = plots,
              family = cover("beta"), y = plots$cover,
              method = "nested_laplace")

year_wtn then carries the within-plot temporal trend; year_btw absorbs across-plot timing heterogeneity (older versus newer baseline plots).

References

Mundlak, Y. (1978). On the pooling of time series and cross section data. Econometrica, 46(1), 69-85.

Bell, A. & Jones, K. (2015). Explaining fixed effects: random effects modeling of time-series cross-sectional and panel data. Political Science Research and Methods, 3(1), 133-153.

Examples

set.seed(1)
plots <- data.frame(
  plot_id = rep(1:5, each = 4),
  year    = rep(2000:2003, times = 5) + rep(c(0, 5, 10, 15, 20), each = 4),
  cover   = stats::runif(20)
)
decomposed <- within_between(plots, group = "plot_id", vars = "year")
head(decomposed)