README.md

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

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

Companion R package to the methodological paper:

Nakamura, D. (2026). The denominator chooses the estimand: A target-population true-score framework for standardized mean differences. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000875

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 (Simulation D, Section 5.3) | | 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 6 examples from the companion paper.

Reproducing the empirical illustrations

The three empirical illustrations in Section 6 of the paper use:

1. Example 1: Ottmar et al. (2025) open mathematics-learning data (Journal of Open Psychology Data, https://doi.org/10.5334/jopd.139).
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 on OSF (https://doi.org/10.17605/OSF.IO/KW9R6); see also the data availability statement in the companion paper. 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. (2026). The denominator chooses the estimand: A target-population true-score framework for standardized mean differences. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000875

In R, citation("ltgsmd") returns this reference, together with a citation for the package itself, in text and BibTeX form. Volume and page details will be added once the article is assigned to an issue.

License

MIT. See the LICENSE file.

Dependencies

• R (≥ 4.1.0)
• stats (base)
• boot (suggested; required for bootstrap confidence intervals)
• metafor (suggested; required for multisite_ltg_smd())
• psych (suggested; an alternative reliability estimator)
• testthat (suggested; for unit tests)
• knitr, rmarkdown (suggested; for building the vignette)

Status

This is version 0.2.3. The companion paper has been published in Psychological Methods (advance online publication, 2026), and the API is stable.

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