Assessing Mental Health symptom correlation matrix (Forbes 2023 applied example)
Source:R/data.R
forbes2023.RdThe 155 x 155 Spearman correlation matrix among 155 mental-health symptom
variables that forms the applied example in Forbes (2023). It is a real,
deep hierarchy: ackwards(forbes2023, k_max = 10) unfolds a general factor of
psychopathology at the top down to 10 fine-grained components, the worked
example that motivates the Forbes extension (pairs = "all", prune()).
Format
A 155 x 155 numeric matrix of Spearman correlations: symmetric, unit
diagonal, correlations in roughly 0.01–0.94. Row and column names are
the 155 symptom-variable labels (e.g. Impulsivity, Blurting).
Source
Forbes's OSF project for the 2023 paper (file corSpearman_AMH.csv),
https://osf.io/pcwm8/, redistributed here under its Creative Commons
Attribution 4.0 International (CC-BY 4.0) license (see the package's
LICENSE.note). The underlying data are from the Assessing Mental Health
study (Forbes et al., 2021).
Details
Where sim16 and bfi25 are teaching foils, forbes2023 is a
fidelity/reproduction dataset: a large, messy, published case bundled so the
package can reproduce the exact applied example analyzed in Forbes's paper.
The correlations come from the Assessing Mental Health (AMH) study – the
Australian general-population sample (N = 3,175) of Forbes et al. (2021) –
spanning symptoms of 18 DSM disorders. Being a correlation matrix, it carries
no per-variable sample size; supply n_obs = 3175 to ackwards() if you want
EFA/ESEM fit statistics scaled to the original sample.
This matrix reproduces Forbes's published results exactly: the package
regression test test-forbes-fidelity.R runs ackwards() on this exported
forbes2023 and matches her reference implementation's between-level
correlations to 1.3e-14 across all 45 level-pairs at k_max = 10.
To regenerate this dataset, run source("data-raw/forbes2023.R") from the
package root (downloads the source CSV from OSF).
References
Forbes, M. K. (2023). Improving hierarchical models of individual differences: An extension of Goldberg's bass-ackward method. Psychological Methods. doi:10.1037/met0000546
Forbes, M. K., Sunderland, M., Rapee, R. M., Batterham, P. J., Calear, A. L., Carragher, N., Ruggero, C., Zimmerman, M., Baillie, A. J., Lynch, S. J., Mewton, L., Slade, T., & Krueger, R. F. (2021). A detailed hierarchical model of psychopathology: From individual symptoms up to the general factor of psychopathology. Clinical Psychological Science, 9(2), 139–168. doi:10.1177/2167702620954799
See also
vignette("ackwards-forbes2023") for a full reproduction of the
Forbes (2023) applied example on this dataset, and
vignette("ackwards-forbes") for the method extension itself.
Examples
dim(forbes2023)
#> [1] 155 155
forbes2023[1:3, 1:3]
#> Impulsivity Reckless_behaviour__i_ Blurting
#> Impulsivity 1.0000000 0.5415115 0.6172762
#> Reckless_behaviour__i_ 0.5415115 1.0000000 0.4783731
#> Blurting 0.6172762 0.4783731 1.0000000
# \donttest{
# The Forbes (2023) applied example: a 10-level hierarchy from 155 symptoms.
x <- ackwards(forbes2023, k_max = 10, pairs = "all")
#> ℹ `n_obs` not supplied; stored as `NA`.
#> ℹ PCA level fit is eigenvalue-based and does not use N; supplying `n_obs = <N>`
#> records it in the result metadata and enables the N-based sampling-adequacy
#> checks.
x
#>
#> ── Bass-Ackwards Analysis (ackwards) ───────────────────────────────────────────
#> Engine: pca
#> Rotation: varimax
#> Basis: (user-supplied matrix)
#> n: NA
#> k (max): 10
#>
#> ── Levels ──
#>
#> ✔ k = 1: 1 factor, 31.4% variance
#> ✔ k = 2: 2 factors, 36.8% variance
#> ✔ k = 3: 3 factors, 41.1% variance
#> ✔ k = 4: 4 factors, 44.9% variance
#> ✔ k = 5: 5 factors, 48.2% variance
#> ✔ k = 6: 6 factors, 50.8% variance
#> ✔ k = 7: 7 factors, 52.9% variance
#> ✔ k = 8: 8 factors, 54.6% variance
#> ✔ k = 9: 9 factors, 56.2% variance
#> ✔ k = 10: 10 factors, 57.6% variance
#>
#> ── Edges ──
#>
#> 312 of 1320 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.
# }