Skip to contents

Changelog

Source: NEWS.md

ackwards (development version)

ackwards 0.3.0

CRAN release: 2026-10-19

Oblique rotation as an option, with partialled edge coefficients and within-level factor correlations in tidy(). Also fixes to the ESEM engine, and documentation rewritten in plain English.

Breaking changes

  • ESEM with cor = "spearman" and missing = "fiml" now stops with an error. Before this fix, the fit ran, but x$r held lavaan’s Pearson FIML matrix while the object reported cor = "spearman". All edges were Pearson under a Spearman label. FIML estimates a multivariate-normal (Pearson) matrix on every engine, so it now requires cor = "pearson" for ESEM, as it already did for PCA and EFA. To keep a Spearman basis, use missing = "pairwise" or "listwise". The warning for ESEM with cor = "spearman" now says that lavaan fits Pearson covariances of the raw data. Before, it said “Pearson-ML model”, which was wrong under WLSMV and ULSMV.

New features

  • Oblique rotation as an option. ackwards() gains a rotation argument. The default stays "varimax", and default numerical output does not change (PCA and EFA factor_cor gain row and column names, see below). With engine = "pca" or "efa", it also accepts "oblimin" and "promax". The GPArotation package (now in Suggests) is needed for "oblimin" with these engines, and for "promax" with engine = "efa". With engine = "esem", it also accepts "oblimin" and "geomin". Under an oblique rotation, each level stores the engine’s factor correlation. The scores keep that correlation: EFA and ESEM use the oblique form of the ten Berge weights, and PCA uses the oblique components. The variance values follow psych’s convention for correlated factors. Each edge r is then a total correlation. Primary parents, sign alignment, and the diagram still use r, and beta in tidy() gives the partialled coefficient. The fit prints a message that says so, and print(), summary(), and autoplot() label it. prune() warns that its thresholds were set for varimax. boot_edges() refits each replicate with the object’s rotation. If that rotation needs GPArotation, it checks for the package first. A PCA level whose oblique rotation fails, or raises an error, ends the hierarchy at the level before it, because PCA rotates once. EFA rotates from several random starts, so its non-convergence warnings are shown and the level is kept. ESEM counts its failed starts, as the first entry under Bug fixes describes. An EFA level whose final rotation step failed still ends the hierarchy. If the installed psych rotates from one start, any EFA rotation warning ends it too. Set seed to reproduce an oblique EFA fit or any ESEM fit exactly. A new test checks the oblique results against Forbes’s reference implementation on her three simulation studies.

  • Within-level factor correlations are carried and shown. Every engine now stores the factor correlation it reports for each level. That matrix is permuted and sign-flipped in step with the loadings, in place of a fixed identity matrix. The new table tidy(x, what = "factor_cor") has one row per pair of factors within a level. Its columns are level, factor_a, factor_b, and cor. The summary() output prints a “Within-level factor correlations” block only when some pair is correlated, which means a within-level correlation above 1e-8 in size. Under the default varimax rotation every within-level correlation is 0, so no number changes and the block is absent.

  • Partialled edge columns. The edge table from tidy() gains beta beside r, and the variance table gains r2. The beta column is the standardized regression weight of the child factor on all factors of the parent level together. It removes the part of r that the other factors at the parent level share. The r2 column is the share of a factor’s score variance that all factors of the level just above account for together. It is NA at level 1. Under varimax beta equals r, and r2 equals the sum of that factor’s squared r values from the level above. The two pairs of quantities come apart only when the factors within a level are correlated. If a level’s within-level score correlation cannot be inverted, both are NA, with a warning.

  • tidy(what = "edges") now warns when the within-level score correlation of a level is nearly singular, meaning its smallest eigenvalue is below 1e-2. The factors at that level are then close to collinear, so the partialled beta for edges from that level is unstable. beta is still reported, and the warning names the level. The package chose this cutoff as a numerical guard. It is not a published rule. tidy(what = "variance") and summary() do not raise this warning.

  • PCA and EFA factor_cor matrices now carry the level’s factor labels as row and column names, as the ESEM ones already did.

Bug fixes

  • ESEM now counts failed rotation starts. At each rotated level, lavaan keeps the best of 30 random starts (its default). In 0.2.0, ESEM showed no rotation warning, and it kept the level even when no start converged. Now a warning gives the count of starts that did not converge (for example, “3 of 30”), and the level is kept. If no start converged, the kept rotation did not converge either. The hierarchy then ends at the level before it with a warning. This holds under every ESEM rotation, varimax included. Fits where at least one start converges keep the same levels and values as before.

  • ESEM with ULSMV on continuous items now fits under the default missing = "pairwise". Before this fix, ackwards() stopped at level 1 with a lavaan error, complete data included. lavaan 0.7.2 efa() fails for ULSMV on continuous items when it uses all available cases. That setting now fits the complete rows, as ML and MLR do, and the edges still come from the pairwise correlation matrix. ULSMV on cor = "polychoric" and WLSMV are unchanged. The help for missing in ackwards() now says which estimators use all available cases. It no longer calls WLSMV and ULSMV ordinal-only, and it names the $meta fields that record the setting. The estimator table in the engines article no longer calls them ordinal-only either.

Documentation

  • Which matrix an edge is exact for. Each between-level edge is implied by the correlation matrix the fit uses, and it is exact for that matrix. The package description, the README, the help for ackwards(), tidy(), and prune(), and five articles now say so. The five articles are the introduction, engines, ordinal, recommended-workflow, and Forbes articles. Scores computed from the observed items do not in general reproduce the edges when that matrix is polychoric or Spearman. The same holds when the matrix comes from incomplete data, by pairwise deletion or by full-information maximum likelihood (FIML). The ackwards() help names the two ESEM settings in which lavaan fits a matrix other than the stored x$r. With cor = "spearman" and missing = "pairwise" or "listwise", lavaan fits Pearson covariances of the raw data. With cor = "pearson" and missing = "pairwise" on data with missing values, ML and MLR fit the complete rows, and WLSMV fits the pairwise covariances. The package description no longer says that edges can come from materialized scores, because no exported function computes them that way. It credits Waller (2007) with the closed-form result for principal components only. No code or result changed.

  • Where the redundancy chase stops, in the prune() help. Under the default redundancy_criterion = "direct", the chase stops at the first ancestor level that fails the criterion. A level further up that passes again does not restart it. The help now says so, and says that this stop follows Forbes’s (2023) reference code, ChaseCorrPaths. To bridge such a gap by your own judgment, pass the factor to drop to manual. A factor that no rule flagged then gets prune_reason = "manual", and manual adds no row to x$prune$chains. A new test shows this on component m7f2 of the forbes2023 example. The behavior and results of prune() did not change.

  • Varimax and oblimin side by side in the engines article. The section on orthogonal and oblique rotation now fits EFA to the BFI-25 twice, with varimax and with oblimin, in place of the simulated example. It shows the oblimin factor correlations within each level. It matches each oblimin factor to a varimax factor by Tucker’s congruence of loadings. After the match, the two primary-parent trees are the same. It lists the secondary edges that reach the display cutoff under oblimin, with r beside beta, and draws both diagrams. No package function or its output changed.

  • Plain-English documentation. The README, the package description, the help pages, and all nine articles were revised so that a reader outside the field can follow them on one read. Sentences are shorter, and each statistical term is explained in plain words where it is first used. No function, argument, default, or example changed. The code in the articles and the results they show did not change either. The settings that reproduce Forbes (2023), the Pearson default with its ordinal-data warning, and the descriptive reading of the hierarchy are stated as before.

ackwards 0.2.0

CRAN release: 2026-07-27

New publication-figure controls for autoplot(), secondary correlation edges in the pruned view, a near-redundant band in prune(), and cleaner layouts for deep hierarchies. Also fixes an error on degenerate hierarchies, and a crash in the package’s own test suite — both of which surfaced only on particular numerical platforms after 0.1.1 was published.

  • Publication-figure controls for autoplot(). Three additions make hand-tuned figures easier. show_items = TRUE lists the salient items (top n_items by |loading|, via the same extraction as top_items()) beneath each deepest-level factor box, so a figure shows what each most-granular factor is made of. node_width / node_height now also accept a named vector keyed by factor ID, sizing individual boxes to fit long manual labels. And order = (also on ba_layout()) fixes the deepest level’s left-to-right order by hand — every factor above stays centred over its primary children, so any arrangement of the hierarchy is reachable from the leaf order. All are opt-in; defaults are unchanged. The visualization vignette demonstrates each.

  • autoplot(drop_pruned = TRUE) can now draw secondary correlation edges. A new show_secondary = TRUE adds the between-level correlations the pruned view otherwise hides — every kept cross-level factor pair with |r| >= cut_show that is not the single strongest-ancestor primary edge, including a factor’s weaker second parents and direct skip-level correlations (a skip-level |r| is its own non-transitive fact). They render in a channel deliberately distinct from the primary edges — dimmed and thinner, drawn beneath them — while still inheriting the sign encoding (sign_by), so the sign color/linetype is never conflated with the secondary channel. Default FALSE leaves the pruned view unchanged. The visualization vignette illustrates the new argument.

  • prune(x, "artifact") now reports a near-redundant band. A new x$prune$near_redundant table flags cross-level factor pairs that sit just below the redundancy thresholds — where prune(x, "redundant") drops full redundancy (|r| >= redundancy_r), the band surfaces the messier candidates a hair under it (e.g. |r| = 0.89 / phi = 0.94), which Forbes (2023) treats as the main use of the artifact flags. A pair is flagged when its direct (skip-level) |r| or its Tucker phi falls within the new near_margin argument (default 0.1) below the corresponding threshold, and the pair is not itself fully redundant. The band is report-only — no factor is dropped on its basis. Under EFA/ESEM, redundancy_phi now auto-resolves in artifact mode too (announced via cli), so the phi band is active; under PCA only the |r| band applies. The Forbes-extension vignette’s artifact example now illustrates a genuinely near-redundant pair rather than one redundancy already drops.

  • Cleaner deep-hierarchy diagrams (k >= 10). ba_layout() now orders each level by a traversal of the primary-parent forest, laying every subtree out as a contiguous block. This drives primary-tree edge crossings to zero in deep hierarchies (the “bent levels” the previous single-pass ordering left behind — e.g. 3 crossings down to 0 on the 155-variable AMH example at k_max = 10), with no change to shallow layouts and the primary-child x-placement unchanged. Separately, autoplot(show_r = TRUE) now dodges overlapping edge-correlation labels apart so dense diagrams stay legible. The layout stays fully deterministic.

  • print() for suggest_k() now renders an aligned criteria table. The per-criterion evidence prints as a column-aligned grid (one row per k, one column per requested criterion) with a header row and a glyph legend, instead of the previous per-k concatenated lines. Numeric columns are right-aligned so the optimal-k star never shifts the decimals, and the “retained” tick is drawn in text presentation so terminals that render it as a wide emoji keep the columns aligned. The returned object and all criteria values are unchanged; only the printed layout is new.

  • Clarified documentation (no behavior change). The ?prune help and the bass-ackward vignette now explain the default redundancy_criterion = "direct" as a star anchored on the chain’s deepest factor — each ancestor correlates directly with that leaf — distinct from adjacent-hop chaining and from an all-pairs screen. The ?ackwards rationale for varimax now states the reason correctly: the between-level edge algebra is exact for any linear scoring, so orthogonality is an interpretive choice (it keeps within-level factors uncorrelated, so between-level edges are not confounded by within-level factor intercorrelation), not a numerical necessity. The artifact-mode discussion now frames automated flags as removing investigator degrees of freedom, leaving only the substantive drop decision to the researcher.

  • Fixed an error when a level of the hierarchy is degenerate. If an extraction produced a factor whose scores carry no variance — reachable when k_max exceeds what the data can identify — ackwards() aborted with an opaque invalid subscript type 'list' message instead of handling it. Such a level is now recorded, warned about, and skipped, with every level above it kept, which is how a non-converged level has always been treated. The failure was platform-dependent: the same fit is merely ill-conditioned under most numerical libraries and fully degenerate under others, so it surfaced only on some check platforms (ATLAS and no-long-double builds). A hierarchy left with fewer than two usable levels now reports that directly.

  • The package’s own tests no longer require two identically seeded boot_edges() runs to agree bit-for-bit. A multi-threaded linear-algebra library may reassociate its reductions between runs, which moves aggregated bootstrap quantities in the last unit of precision (~1e-16, seen on ATLAS builds); the test now allows that while still holding the seed to a far tighter standard than any real reproducibility failure would pass. Nothing user-facing changed.

  • Fixed a crash in the package’s own test suite on macOS. Two tests set a forking parallel plan (future::multicore) to verify that parallel and serial fits agree exactly. Forking does not mix with the multi-threaded numerical libraries R’s linear algebra runs through — ?mclapply warns against the combination — and R segfaulted inside the forked worker on one of CRAN’s macOS check flavours. Both tests now skip macOS and continue to run everywhere else. Nothing user-facing changed: ackwards() and boot_edges() never set a parallel plan themselves — the default plan is sequential, and choosing one is the caller’s business.

ackwards 0.1.1

CRAN release: 2026-07-24

CRAN resubmission of the first release, addressing reviewer feedback on the 0.1.0 submission; also picks up everything added since that submission.

  • Fixed compatibility with lavaan 0.7. lavaan 0.7 renamed its sample-statistics slot argument (breaking the ESEM engine’s multi-level reuse of anchor-level sample statistics — every level beyond k = 1 failed to build) and now requires an explicit ordered = FALSE to use WLSMV/ULSMV with continuous data. The ESEM engine detects the installed lavaan’s argument vocabulary and works with both lavaan >= 0.7 and >= 0.6-13.

  • New vignette: “Reproducing Forbes (2023): The AMH Applied Example” (vignette("ackwards-forbes2023")). A full worked reproduction of the paper’s 155-variable applied example on the bundled forbes2023 dataset: the 10-level hierarchy, skip-level correlations, the redundancy chase (including where the default direct criterion and the adjacent opt-in disagree), and the pruned-factor diagram in the paper’s publication style.

  • Corrected the Forbes (2023) article title in the forbes2023 help page (“bass-ackward method”, per the published title).

  • Corrected the n_obs advisory for PCA on correlation-matrix input. The message (and the n_obs help text) claimed supplying n_obs would enable chi-square/RMSEA/TLI, but the PCA engine’s level fit is eigenvalue-based and never computes them; n_obs is recorded in the result metadata and feeds the N-based sampling-adequacy checks only. The message now says so. No behavior changes.

  • Completed the Goldberg (2006) reference to its full published title (“Doing it all Bass-Ackwards: The development of hierarchical factor structures from the top down”) in the ackwards() help page and four vignettes.

  • Corrected the historical citations for comparability()’s split-half benchmarks. The .90 replication threshold traces to Everett (1983) and to its use in Goldberg’s lexical research program by Saucier (1997) and Saucier, Georgiades, Tsaousis, and Goldberg (2005) — not to Goldberg (1990), which contains no split-half analyses and is no longer cited for this purpose. The .95 reference line is now sourced to Lorenzo-Seva and ten Berge (2006). Affects the roxygen help page, print()/autoplot() footer text, the README, and the replicability-workflow vignette; no behavior changes.

  • Sourced suggest_k()’s k-selection guidance. The consensus-range stance now cites Lim and Jahng (2019) with Achim’s (2021) counterpoint, and the “PA-PC tends to overextract” note cites Saucier (1997) alongside Forbes (2023), in both the help page and the suggest-k vignette; no behavior changes.

  • label_template() now returns its scaffold visibly (behavior change). The named character vector carries class "ackwards_labels", and the editable c(...) literal is rendered by its print() method instead of being written to the console unconditionally. A top-level call looks the same as before; assigning the result (labs <- label_template(x)) or passing it inline (e.g. inside autoplot()) is now silent, per CRAN policy on console output.

  • DESCRIPTION now spells out principal component analysis (PCA), exploratory factor analysis (EFA), and exploratory structural equation modeling (ESEM) per CRAN feedback.

  • New bundled dataset forbes2023. The 155-variable “Assessing Mental Health” Spearman correlation matrix that forms Forbes’s (2023) applied example is now exported, so ackwards(forbes2023, k_max = 10) reproduces her worked hierarchy directly. It joins bfi25 and sim16. The matrix is redistributed under CC-BY 4.0 with attribution to M. K. Forbes (see LICENSE.note).

  • prune("redundant") gains redundancy_criterion, defaulting to "direct" (behavior change). Redundancy chains are now traced by the direct (skip-level) correlation between a factor and each ancestor level — Forbes’s

    1. actual ChaseCorrPaths rule — rather than the previous adjacent-hop walk. Because correlation is non-transitive, the two can differ in deep (many-level) hierarchies: on shallow ones (e.g. the bundled sim16) results are unchanged, but a factor can now be flagged redundant with an ancestor it correlates with directly even if an intermediate step is weak (and vice versa). Pass redundancy_criterion = "adjacent" for the old behavior. This makes prune("redundant") reproduce Forbes’s published applied example exactly. print() and summary() name the active criterion. Note that under "direct", a chain’s r_to_prev column reports the adjacent-level correlation and can sit below redundancy_r (membership is set by the direct skip-level link; see ?prune).

  • Validation. The Forbes (2023) fidelity suite now also reproduces her 155-variable “Assessing Mental Health” applied example (k_max = 10), not just the three simulation studies: between-level correlations match her reference implementation to 1.3e-14 across all 45 level-pairs, loading congruences agree within her two-decimal rounding, and her redundancy chase is reproduced for all 54 components. The published matrix ships as a test fixture under CC-BY 4.0 (see LICENSE.note).

  • suggest_k() now reads Comparison Data (CD) results from EFAtools >= 0.8.0, which restructured CD()’s return value (the per-iteration RMSE matrix moved from the top-level RMSE_eigenvalues field into results[[1]]$rmse_eigenvalues). Without this, the CD criterion and its autoplot() panel silently dropped out when a current EFAtools was installed. Older EFAtools versions still work.

  • Console output consistency. summary()’s per-level fit-index pass/fail mark is now the same terminal-adaptive cli glyph as print()’s convergence mark (a tick/cross that degrades to v/x in a non-UTF-8 console), replacing a hard-coded Unicode ✔/✘. And print()’s cumulative-variance percentages now carry a fixed single decimal (e.g. 20.0%, where a whole-number value previously printed as 20%), matching summary(). Cosmetic only; the reported values are unchanged.

ackwards 0.1.0

First public release. ackwards implements Goldberg’s (2006) bass-ackwards method and its modern extensions: it fits factor solutions at every level from 1 to k and characterizes the hierarchy through the between-level factor-score correlations that connect them. Initial features, roughly in order of importance:

  • ackwards() — fit the hierarchy with a PCA, EFA, or ESEM engine; between-level edges from Waller’s (2007) exact W′RW algebra.
  • suggest_k() — bracket a plausible depth range from five retention criteria (parallel analysis, MAP, VSS, Comparison Data).
  • comparability() — gate hierarchy depth on split-half replicability (Everett 1983; Goldberg 1990).
  • factorability() — screen a dataset (or correlation matrix) before you fit: Kaiser-Meyer-Olkin sampling adequacy (overall and per item), Bartlett’s test of sphericity, the N:p ratio, and the Ledermann bound on identifiable factors, reported as numbers-and-bands rather than pass/fail. ackwards() runs a light version internally and warns only at the consequential extreme (k_max above the Ledermann bound for EFA/ESEM, or poor sampling adequacy).
  • Forbes (2023) extension — pairs = "all" skip-level edges, prune() for redundant/artifactual factors, and boot_edges() bootstrap edge CIs.
  • Ordinal data — cor = "polychoric" (WLSMV for ESEM), check_items() pre-analysis screening, and near-singularity diagnostics.
  • Interpretation & scoring — top_items() for reading factors; label_template()/set_factor_labels()/factor_labels() to attach persistent substantive names shown across print(), summary(), autoplot(), tidy(), and top_items(); augment()/predict() for factor scores, in and out of sample.
  • Output — autoplot() hierarchy diagrams and tidy()/glance()/summary().
  • Bundled data — bfi25 (ordinal Big Five) and sim16 (continuous), plus eight vignettes.

Beyond base R, psych is the only hard dependency; lavaan, ggplot2, and others are optional.