ackwards: Bass-Ackwards Hierarchical Structural Analysis

Implements Goldberg's (2006) <doi:10.1016/j.jrp.2006.01.001> bass-ackwards method and modern descendants for hierarchical structural analysis. Extracts solutions from 1 to k factors using principal component analysis (PCA), exploratory factor analysis (EFA), or exploratory structural equation modeling (ESEM) engines. It then describes the hierarchy through the correlations between the factor scores of different levels. It computes them with linear algebra from the scoring weights and the correlation matrix the fit uses, so they are exact for that matrix. Waller (2007) <doi:10.1016/j.jrp.2006.08.005> showed, for principal components, that these correlations follow from the correlation matrix alone. Includes the Forbes (2023) <doi:10.1037/met0000546> extension for redundancy pruning and all-levels cross-correlations.

Version: 0.3.0
Depends: R (≥ 4.1.0)
Imports: cli, generics, psych, rlang, stats, utils
Suggests: covr, EFAtools, future, future.apply, ggplot2, GPArotation, gt, knitr, lavaan (≥ 0.6-13), rmarkdown, testthat (≥ 3.0.0)
Published: 2026-10-19
DOI: 10.32614/CRAN.package.ackwards
Author: Jeffrey M. Girard ORCID iD [aut, cre], Miriam K. Forbes [cph] (Author of the bundled AMH correlation matrix (data/forbes2023.rda), CC-BY 4.0)
Maintainer: Jeffrey M. Girard <me at jmgirard.com>
BugReports: https://github.com/jmgirard/ackwards/issues
License: MIT + file LICENSE
URL: https://jmgirard.github.io/ackwards/, https://github.com/jmgirard/ackwards
NeedsCompilation: no
Citation: ackwards citation info
Materials: README, NEWS
CRAN checks: ackwards results

Documentation:

Reference manual: ackwards.html , ackwards.pdf
Vignettes: Choosing an Engine: PCA, EFA, and ESEM (source)
The Forbes Extension: Skip-Level Connections and Pruning (source)
Reproducing Forbes (2023): The AMH Applied Example (source)
Replicability-Gated Hierarchies: A Recommended Workflow (source)
Interpreting and Labeling Factors (source, R code)
Introduction to Bass-Ackwards Analysis (source)
Ordinal Data: Polychoric Correlations and WLSMV (source)
Choosing k: How Many Factors? (source)
Customizing the Hierarchy Diagram (source)

Downloads:

Package source: ackwards_0.3.0.tar.gz
Windows binaries: r-devel: ackwards_0.2.0.zip, r-release: ackwards_0.2.0.zip, r-oldrel: ackwards_0.2.0.zip
macOS binaries: r-release (arm64): not available, r-oldrel (arm64): not available, r-release (x86_64): not available, r-oldrel (x86_64): not available
Old sources: ackwards archive

Linking:

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