Asymmetric Smoothed-Association Matrices via GAM Fits

Render a pairwise, asymmetric smoothed-association matrix of continuous variables. Each cell shows the fitted spline from an 'mgcv' generalised additive model, with the upper triangle displaying 'gam(x_j ~ s(x_i))' and the lower triangle 'gam(x_i ~ s(x_j))'. Unlike Pearson's correlation matrix, the visualisation is intentionally asymmetric, revealing heteroscedasticity, leverage, and directional non-linearity that a single scalar correlation hides. An asymmetry index and a 24-category shape taxonomy quantify the directional difference and qualitative form of each fitted smooth.

janusplot

Asymmetric, GAM-based smoothed-association matrices for continuous variables. Each off-diagonal cell shows a directional mgcv::gam(y ~ s(x)) fit, so the upper and lower triangles tell different stories whenever the relationship is genuinely asymmetric — precisely where a scalar Pearson correlation loses information.

Two novelties, paired with the asymmetry story:

1. Asymmetry index A = |EDF_yx − EDF_xy| / (EDF_yx + EDF_xy) ∈ [0, 1] — a single-number summary of the directional disparity per pair.
2. 24-category shape taxonomy — each fitted smooth is classified into one of 24 named shapes (linear_up, skewed_peak, bimodal, bi_wave, rippled_monotone, …) via a (T, I) dispatch on turning-point and inflection counts, with monotonicity/convexity indices for disambiguation. The taxonomy rolls up through three broader tiers: archetype (7), monotonic (3), linear (2) — grounded in shape-constrained regression (Pya & Wood 2015), dose-response pharmacology (Calabrese 2008), and Morse critical- point classification (Milnor 1963).

Install

# development version from GitHub (fast; no vignettes)
pak::pak("max578/janusplot")

# or, with vignettes built locally (recommended — enables
# browseVignettes("janusplot") and vignette("janusplot")):
# install.packages("remotes")
remotes::install_github(
  "max578/janusplot",
  build_vignettes = TRUE,
  dependencies    = TRUE
)

Note: neither pak::pak() nor devtools::install_github() / remotes::install_github() build vignettes by default when installing from a source repository. The build_vignettes = TRUE flag above is required for browseVignettes() to find them. The CRAN release ships prebuilt vignettes and needs no extra flag.

Quick start

library(janusplot)

# Palmer penguins — four continuous traits
d <- na.omit(palmerpenguins::penguins[,
       c("bill_length_mm", "bill_depth_mm",
         "flipper_length_mm", "body_mass_g")])
janusplot(d)

Default encoding:

• Cell colour — Pearson correlation on a diverging RdBu palette symmetric around zero (override via colour_by = "spearman" / "kendall" / "edf" / "deviance_gap" / "none").
• Bottom-left — A = ... (asymmetry index) stacked over EDF = ....
• Top-right — significance glyph for the smooth’s F-test (· * ** ***).
• Below the matrix — a standing reference legend illustrating all 24 shape categories as canonical thumbnail splines, labelled <name> (<code>).

Opt into a per-cell shape marker via annotations:

# Two-letter shape code, top-left (ASCII — safe on any font / PDF):
janusplot(d, annotations = c("edf", "A", "code"))

# Unicode shape glyph, bottom-right:
janusplot(d, annotations = c("edf", "A", "shape"),
          glyph_style = "unicode")

Shape taxonomy — what gets classified

Full table (with 2-letter codes + monotonic / linear rollups + glyph + gloss) via janusplot_shape_hierarchy().

Sensitivity study — built-in

The classifier’s recovery behaviour is characterised across a full factorial of sample sizes × noise levels × ground-truth shapes:

# Precomputed 2160-fit demo sweep — zero wait
data("shape_sensitivity_demo")
janusplot_shape_sensitivity_plot(shape_sensitivity_demo, "recovery_curves")
janusplot_shape_sensitivity_plot(shape_sensitivity_demo, "confusion_archetype")

# Run your own — full grid in parallel
future::plan(future::multisession, workers = 4L)
res <- janusplot_shape_sensitivity(parallel = TRUE)

Four diagnostic plots ("confusion_fine" / "confusion_archetype" / "accuracy_grid" / "recovery_curves") + summary aggregations at fine and archetype levels. Design, pre-registered hypotheses, and full walk-through in the shape-recognition-sensitivity vignette.

Key features

• Real GAM fits via mgcv — EDF, F-test p-values, confidence envelopes, random effects via s(g, bs = "re").
• Asymmetric matrix — upper / lower triangles carry the two directional regressions.
• Three correlation flavours computed per pair — Pearson (default), Spearman, Kendall — surfaced in janusplot_data() output.
• adjust = formula — propagate covariates and random effects into every cell’s smooth.
• janusplot_data() — per-pair raw fits, correlations, EDFs, p-values, shape metrics + hierarchy columns, without the plot.
• janusplot(..., with_data = TRUE) — plot + tidy data frame in one call.
• Parallel dispatch via future.apply for large matrices and sensitivity sweeps.
• Deterministic — seed 2026L pins the shipped demo + vignette figures; user sweeps accept seed =.

Why asymmetric?

A Pearson correlation discards both the shape of an association and the direction information that a non-linear data-generating process leaves in its residuals. Under the additive-noise causal discovery setting (Hoyer et al. 2009; Peters et al. 2014) the forward regression y ~ s(x) and its inverse x ~ s(y) are generically asymmetric when the underlying DGP is non-linear, and that asymmetry identifies the causal direction under mild conditions. janusplot surfaces this asymmetry as a visual pre-discovery diagnostic — not a causal inference procedure. See the vignette and the accompanying paper for scope and explicit non-claims.

Documentation

• Reference + articles (pkgdown site)
• vignette("janusplot") — quickstart + feature tour
• vignette("shape-recognition-sensitivity") — design, hypotheses, every diagnostic plot

Status

R CMD check --as-cran clean (0 errors, 0 warnings; 2 local-environmental NOTEs only). Comprehensive testthat suite including vdiffr visual-regression snapshots; coverage tracked via the Codecov badge above.

Citation

citation("janusplot")

License

GPL (>= 3). See https://www.gnu.org/licenses/gpl-3.0.html for the full text.