multisite_ltg_smd: Multi-site LTG-SMD analysis with cross-site reference...

In ltgsmd: Latent True-Score and Target-Population Anchored Geometric SMD

Multi-site LTG-SMD analysis with cross-site reference anchoring

Description

Implements the multi-site workflow described in Section 7.3 and illustrated in Example 3 (Section 6.3) of the paper (Many Labs 2 Anderson.1). Each site is treated as a study sample, the cross-site pooled distribution (or an external sample) is treated as the target reference, and site-level Hedges's g and LTG-SMD estimates are returned along with a meta-analytic comparison from metafor::rma().

Usage

multisite_ltg_smd(
  data,
  site_var,
  group_var,
  score_var = NULL,
  items = NULL,
  group_levels = NULL,
  reliability_estimator = "alpha",
  reference_strategy = c("pooled_across_sites", "external"),
  reference_data = NULL,
  min_n_per_group = 50L,
  rho_external = NULL
)

Arguments

data	A data frame with one row per participant containing group, site, item-level, and (optionally) composite-score columns.
site_var	Character. Name of the site grouping variable.
group_var	Character. Name of the experimental-condition variable.
score_var	Optional character. Name of a precomputed composite score column. If NULL, built from items (in both data and, if supplied, reference_data).
items	Optional character vector of item column names.
group_levels	Optional named character vector with names "reference" and "focal".
reliability_estimator	Either "alpha" (default) or a function; see compute_ltg_smd().
reference_strategy	One of "pooled_across_sites" (default; uses all retained sites as the reference) or "external" (requires reference_data).
reference_data	Optional data frame; required when reference_strategy = "external".
min_n_per_group	Integer. Minimum per-group sample size for a site to be retained. Defaults to 50.
rho_external	Optional named numeric vector with names "focal" and "reference" to override item-level reliability estimation.

Details

The site-level standard error for the LTG-SMD is approximated as

\widehat{\mathrm{SE}}_{\mathrm{LTG, site}} = \sqrt{s^2_{1,\text{site}}/n_{1,\text{site}} + s^2_{0,\text{site}}/n_{0,\text{site}}} \,/\, D,

treating the cross-site (or external) reference denominator D as fixed. This approximation is reasonable when the reference sample is large relative to each site, which is typical in coordinated multi-site projects, but it understates uncertainty when the reference is small. For a full reliability-propagated interval at the site level, use ltg_smd_ci() with method = "bootstrap" on each site separately.

Value

An object of class "multisite_ltg_smd" containing:

site_table

Data frame of site-level estimates: site, n_focal, n_reference, hedges_g, ltg_smd, se_hedges, se_ltg.

reference_summary

List of pooled reference quantities (variances, reliabilities, true-score geometric SD).

meta_hedges

Output of metafor::rma() for Hedges's g.

meta_ltg

Output of metafor::rma() for the LTG-SMD.

meta_comparison

Data frame summarizing the two meta-analytic pools side by side.

se_ltg_method

Character. Notes that the site-level SE for the LTG-SMD treats the reference denominator as fixed.

Examples

set.seed(2026)
gen_site <- function(site_name, n_per_cond = 15, shift = 0.3) {
  true_ctrl <- rnorm(n_per_cond)
  true_trt  <- rnorm(n_per_cond)
  ctrl <- data.frame(
    site = site_name, condition = "control",
    item1 = true_ctrl + rnorm(n_per_cond, sd = 0.6),
    item2 = true_ctrl + rnorm(n_per_cond, sd = 0.6),
    item3 = true_ctrl + rnorm(n_per_cond, sd = 0.6),
    item4 = true_ctrl + rnorm(n_per_cond, sd = 0.6)
  )
  trt <- data.frame(
    site = site_name, condition = "treatment",
    item1 = true_trt + rnorm(n_per_cond, sd = 0.6) + shift,
    item2 = true_trt + rnorm(n_per_cond, sd = 0.6) + shift,
    item3 = true_trt + rnorm(n_per_cond, sd = 0.6) + shift,
    item4 = true_trt + rnorm(n_per_cond, sd = 0.6) + shift
  )
  rbind(ctrl, trt)
}
ml_data <- do.call(rbind, lapply(
  c("SiteA", "SiteB", "SiteC", "SiteD"), gen_site
))

result <- multisite_ltg_smd(
  data = ml_data,
  site_var = "site",
  group_var = "condition",
  items = paste0("item", 1:4),
  reference_strategy = "pooled_across_sites",
  min_n_per_group = 10
)
print(result)

ltgsmd documentation built on Sept. 27, 2026, 5:07 p.m.