Implements the latent true-score and target-population
anchored geometric standardized mean difference (LTG-SMD) framework
for two-group effect-size analysis. Provides plug-in estimation,
analytic delta-method confidence intervals using a sample
fourth-moment plug-in, bias-corrected and bias-corrected-accelerated
nonparametric bootstrap confidence intervals with study x group
stratification, denominator-sensitivity profiles, and multi-site
meta-analytic wrappers. Includes denominator-diagnostic reporting,
a pluggable reliability estimator interface, and an explicit
interface for specifying the target reference distribution.
Companion software to Nakamura (2026) "The Denominator Chooses the
Estimand: A Target-Population True-Score Framework for Standardized
Mean Differences"
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
# From CRAN:
install.packages("ltgsmd")
# Development version from OSF:
# https://doi.org/10.17605/OSF.IO/KW9R6
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
)
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.
| 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) |
The package vignette vignette("getting-started", package = "ltgsmd") works through the three Section 6 examples from the companion paper.
The three empirical illustrations in Section 6 of the paper use:
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.
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.
MIT. See the LICENSE file.
multisite_ltg_smd())This is version 0.2.3. The companion paper has been published in Psychological Methods (advance online publication, 2026), and the API is stable.