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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.
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
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.
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).pairs = "all" skip-level edges, prune() for
redundant/artifactual factors, and boot_edges() bootstrap
edge CIs.cor = "polychoric"
(WLSMV for ESEM), check_items() pre-analysis screening, and
near-singularity diagnostics.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.autoplot() hierarchy diagrams
and
tidy()/glance()/summary().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.
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.