The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

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

Companion R package to the methodological paper:

Nakamura, D. (in press). The Denominator Chooses the Estimand: A Target-Population True-Score Framework for Standardized Mean Differences. Psychological Methods.

Installation

# From CRAN:
install.packages("ltgsmd")

# Development version from OSF:
# https://doi.org/10.17605/OSF.IO/KW9R6

Quick start

library(ltgsmd)

# Single study with an internal holdout reference
result <- compute_ltg_smd(
  study_data     = study_df,
  reference_data = reference_df,
  group_var      = "condition",
  score_var      = "outcome",
  items          = c("item1", "item2", "item3", "item4"),
  group_levels   = c(reference = "control", focal = "treatment")
)
print(result)

# Confidence intervals
ci <- ltg_smd_ci(result, method = c("analytic", "bootstrap"),
                  B = 2000, seed = 20240501,
                  study_data = study_df, reference_data = reference_df,
                  group_var = "condition", score_var = "outcome",
                  items = c("item1", "item2", "item3", "item4"),
                  group_levels = c(reference = "control", focal = "treatment"))

# Denominator diagnostics (Table F.1 format)
diag <- denominator_diagnostics(result)

# Six-denominator sensitivity profile
sens <- denominator_sensitivity(result)

# Multi-site / meta-analysis
multisite <- multisite_ltg_smd(
  data               = ml_data,
  site_var           = "site",
  group_var          = "condition",
  items              = paste0("item", 1:25),
  reference_strategy = "pooled_across_sites",
  min_n_per_group    = 50
)

What the LTG-SMD is

The latent true-score and target-population anchored geometric standardized mean difference (LTG-SMD) is

\[\delta_{\mathrm{LTG}} = \frac{\mu_{T1} - \mu_{T0}}{(\sigma^2_{T1,R}\,\sigma^2_{T0,R})^{1/4}},\]

a two-group SMD whose denominator is the geometric mean of group-specific true-score standard deviations in an explicitly chosen target reference population \(R\). The framework treats the denominator as an estimand choice, in the spirit of Lundberg, Johnson, and Stewart (2021), rather than as a technical detail.

Functions

Function Purpose
compute_ltg_smd() Plug-in estimator + five SMD comparators (Hedges’s g, Welch, observed geometric, external observed, LTG-SMD)
ltg_smd_ci() Analytic delta-method + BC/BCa bootstrap confidence intervals
denominator_diagnostics() Table F.1 diagnostics for reporting (Section 8.3)
denominator_sensitivity() Profile across six symmetric denominators (Section 7 Simulation D)
sensitivity_reference() Sensitivity to alternative target reference distributions
multisite_ltg_smd() Multi-site wrapper with cross-site reference and meta-analytic pooling
export_supplementary() Bundle diagnostics, CIs, and sensitivity for a supplementary appendix
coef_alpha() Cronbach’s coefficient alpha (internal default reliability estimator)

Vignette

The package vignette vignette("getting-started", package = "ltgsmd") works through the three Section 8 examples from the companion paper.

Reproducing the empirical illustrations

The three empirical illustrations in Section 8 of the paper use:

  1. Example 1: Ottmar et al. (2025) open mathematics-learning data, accessed via the OSF.
  2. Example 2: Open Psychometrics IPIP Big Five 2014 dataset.
  3. Example 3: Many Labs 2 Anderson.1 effect, Slate 1 data from Klein et al. (2018).

R scripts that reproduce each example are archived in the supplementary repository (see the companion paper’s Data and Code Availability statement). The scripts read the public data and call this package’s functions in the order documented in the vignette.

Citation

Please cite the companion paper:

Nakamura, D. (in press). The Denominator Chooses the Estimand: A Target-Population True-Score Framework for Standardized Mean Differences. Psychological Methods.

A CITATION file will be updated with full volume/page details once assigned.

License

MIT. See the LICENSE file.

Dependencies

Status

This is version 0.2.2. The companion paper has been accepted for publication in Psychological Methods, and the API is stable.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.