print-snapshot.md
In ackwards: Bass-Ackwards Hierarchical Structural Analysis

print/summary snapshot: PCA, converged, no prune

Code
  snap_print(x)
Message

  -- Bass-Ackwards Analysis (ackwards) -------------------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 4

  -- Levels --

  v k = 1: 1 factor, 28.2% variance
  v k = 2: 2 factors, 46.5% variance
  v k = 3: 3 factors, 57.5% variance
  v k = 4: 4 factors, 67.7% variance

  -- Edges --

  9 of 20 edges have |r| >= 0.3
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

Code
  snap_print(summary(x))
Message

  -- Summary: Bass-Ackwards Analysis (ackwards) ----------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 4

  -- Levels --

  k = 1: 1 factor (28.2% cumulative variance)
  m1f1 28.2% eigenvalue 4.51

  k = 2: 2 factors (46.5% cumulative variance)
  m2f1 23.3% eigenvalue 4.51
  m2f2 23.2% eigenvalue 2.93

  k = 3: 3 factors (57.5% cumulative variance)
  m3f1 23.0% eigenvalue 4.51
  m3f2 17.5% eigenvalue 2.93
  m3f3 16.9% eigenvalue 1.76

  k = 4: 4 factors (67.7% cumulative variance)
  m4f1 17.2% eigenvalue 4.51
  m4f2 16.9% eigenvalue 2.93
  m4f3 16.8% eigenvalue 1.76
  m4f4 16.8% eigenvalue 1.63

  -- Lineage (primary parents) --

  m1f1 > m2f1, m2f2
  m2f1 > m3f2, m3f3
  m2f2 > m3f1
  m3f1 > m4f3, m4f4
  m3f2 > m4f1
  m3f3 > m4f2
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

print/summary snapshot: EFA fit-index glyph line

Code
  snap_print(summary(x))
Message

  -- Summary: Bass-Ackwards Analysis (ackwards) ----------------------------------
  Engine: efa
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 3

  -- Levels --

  k = 1: 1 factor (25.0% cumulative variance)
  m1f1 25.0%

  k = 2: 2 factors (37.8% cumulative variance)
  m2f1 19.1%
  m2f2 18.7%
  chi = 136.4 dof = 26 RMSEA = 0.065 x TLI = 0.912 x

  k = 3: 3 factors (41.9% cumulative variance)
  m3f1 19.2%
  m3f2 18.8%
  m3f3 3.9%
  chi = 58.5 dof = 18 RMSEA = 0.047 v TLI = 0.953 v

  -- Lineage (primary parents) --

  m1f1 > m2f1, m2f2
  m2f1 > m3f1
  m2f2 > m3f2, m3f3
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

print/summary snapshot: pruning digest (redundant + artifact)

Code
  snap_print(x)
Message

  -- Bass-Ackwards Analysis (ackwards) -------------------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 4

  -- Levels --

  v k = 1: 1 factor, 32.3% variance
  v k = 2: 2 factors, 49.6% variance
  v k = 3: 3 factors, 58.6% variance
  v k = 4: 4 factors, 66.2% variance

  -- Edges --

  9 of 20 edges have |r| >= 0.3

  -- Pruning --

  Redundancy (direct, |r| >= 0.9): 4 nodes flagged
  Artifact: Tucker's phi computed for 35 cross-level factor pairs
  Structural signals: 3 factors flagged (inspect `x$prune$structural`)
  --------------------------------------------------------------------------------
  Note: Pruning is interpretive relabeling, not re-estimation. Flagged nodes
  remain in the object; all edges are preserved. Inspect with `x$prune$nodes` and
  `tidy(x, what = "nodes")`.
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

Code
  snap_print(summary(x))
Message

  -- Summary: Bass-Ackwards Analysis (ackwards) ----------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 4

  -- Levels --

  k = 1: 1 factor (32.3% cumulative variance)
  m1f1 32.3% eigenvalue 3.23

  k = 2: 2 factors (49.6% cumulative variance)
  m2f1 24.9% eigenvalue 3.23
  m2f2 24.6% eigenvalue 1.73

  k = 3: 3 factors (58.6% cumulative variance)
  m3f1 24.3% eigenvalue 3.23
  m3f2 22.6% eigenvalue 1.73
  m3f3 11.6% eigenvalue 0.90

  k = 4: 4 factors (66.2% cumulative variance)
  m4f1 22.4% eigenvalue 3.23
  m4f2 17.1% eigenvalue 1.73
  m4f3 15.6% eigenvalue 0.90
  m4f4 11.2% eigenvalue 0.77

  -- Lineage (primary parents) --

  m1f1 > m2f1, m2f2
  m2f1 > m3f1
  m2f2 > m3f2, m3f3
  m3f1 > m4f2, m4f3
  m3f2 > m4f1
  m3f3 > m4f4

  -- Pruning --

  Redundant (direct, |r| >= 0.9): 4 nodes flagged
  Flagged: m2f2, m3f1, m3f2, m3f3
  Artifact: Tucker's phi computed for 35 cross-level pairs
  Structural signals: 3 factors flagged (inspect `x$prune$structural`)
  --------------------------------------------------------------------------------
  Note: Pruning is interpretive relabeling, not re-estimation. Flagged nodes
  remain in the object with all edges preserved.
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

print snapshot: a non-converged level shows the red cross

Code
  snap_print(x)
Message

  -- Bass-Ackwards Analysis (ackwards) -------------------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 3

  -- Levels --

  v k = 1: 1 factor, 28.2% variance
  x k = 2: 2 factors, 46.5% variance
  v k = 3: 3 factors, 57.5% variance

  -- Edges --

  5 of 8 edges have |r| >= 0.3
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

print/summary snapshot: near-singular caution

Code
  snap_print(x)
Message

  -- Bass-Ackwards Analysis (ackwards) -------------------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 3

  -- Levels --

  v k = 1: 1 factor, 28.2% variance
  v k = 2: 2 factors, 46.5% variance
  v k = 3: 3 factors, 57.5% variance

  -- Edges --

  5 of 8 edges have |r| >= 0.3
  ! Near-singular correlation matrix (min eigenvalue 0.0012): fit indices and
  factor scores may be unreliable. See `?ackwards` ("When to trust the result").
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output

Code
  snap_print(summary(x))
Message

  -- Summary: Bass-Ackwards Analysis (ackwards) ----------------------------------
  Engine: pca
  Rotation: varimax
  Basis: pearson
  n: 1,000
  k (max): 3

  -- Levels --

  k = 1: 1 factor (28.2% cumulative variance)
  m1f1 28.2% eigenvalue 4.51

  k = 2: 2 factors (46.5% cumulative variance)
  m2f1 23.3% eigenvalue 4.51
  m2f2 23.2% eigenvalue 2.93

  k = 3: 3 factors (57.5% cumulative variance)
  m3f1 23.0% eigenvalue 4.51
  m3f2 17.5% eigenvalue 2.93
  m3f3 16.9% eigenvalue 1.76

  -- Lineage (primary parents) --

  m1f1 > m2f1, m2f2
  m2f1 > m3f2, m3f3
  m2f2 > m3f1

  ! Near-singular correlation matrix (min eigenvalue 0.0012): per-level fit
  indices and factor scores may be unreliable -- the solution rests on a
  rank-deficient matrix. See `?ackwards` ("When to trust the result").
  --------------------------------------------------------------------------------
  Note: This is a series of linked solutions, not a fitted hierarchical model.
  Cross-level edges are descriptive score correlations. Per-level fit indices
  (EFA/ESEM) describe how well a k-factor model fits the items at that level --
  they do not validate the edges or the hierarchy itself.
Output