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maps: human haze on all ipsative maps (synthetic resample for big5/16pf/humor)

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Split the PCA-fit basis from the scattered cloud in plot_ipsative_pca: add a
'haze' arg so instruments with only society-level mean+sd get a backdrop
(marginal Normal resample per country) without that resample dictating the
axes. mfq2 keeps its real Atari respondents (fit + haze). Previously only mfq2
had any human scatter; big5/16pf/humor showed bare society dots.

Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>
This commit is contained in:
wassname
2026-06-25 07:30:37 +08:00
co-authored by Claudypoo
parent 5be5451e13
commit 0e92e66415
2 changed files with 47 additions and 17 deletions
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scripts/plot_steer_showcase.py
+32 -4
View File
@@ -54,6 +54,28 @@ def human_matrix(instr) -> tuple[list[str], np.ndarray]:
return countries, _frac(raw, instr.human_scale_max)
def human_haze(instr, n_per_country: int = 200, seed: int = 0) -> np.ndarray:
"""Synthetic individual-respondent cloud (n x K, 0-1 fraction) for instruments that ship only
society-level stats (big5/16pf/humor: no raw per-person data like mfq2's Atari file). For each
(country, factor) we resample n Normal(mean, sd) draws from the published country mean+sd, so the
cloud carries BOTH between-country (different means) and within-country (sd) human spread. Caveat:
factors are drawn independently, so this marginal resample loses the cross-factor correlation a
real respondent matrix has -- it is a backdrop envelope, not a covariance estimate, and is NOT
used as the PCA basis (that stays the society means M)."""
dims = instr.dimensions
rng = np.random.default_rng(seed)
stats: dict[tuple[str, str], tuple[float, float]] = {}
with open(instr.human_csv, newline="") as fh:
for r in csv.DictReader(fh):
stats[(r["country"], r["foundation"])] = (float(r["mean"]), float(r["sd"]))
countries = sorted({c for (c, _f) in stats})
blocks = []
for c in countries:
cols = [rng.normal(stats[(c, f)][0], stats[(c, f)][1], n_per_country) for f in dims]
blocks.append(np.clip(np.stack(cols, axis=1), 1.0, instr.human_scale_max))
return _frac(np.concatenate(blocks, axis=0), instr.human_scale_max)
def human_strip(instr) -> dict[str, list[tuple[str, float]]]:
"""{factor: [(country, mean_on_model_scale)]}. Human 1-H rescaled to model 1-M for the range."""
h = read_human_csv(instr.human_csv)
@@ -87,12 +109,18 @@ def plot_ordinal(run_dir: Path, out: Path, name: str, vec_label: str, C: float)
countries, Mfrac = human_matrix(instr)
labels = (f"base (c=0)", f"+C={C:+.2f}", f"-C={-C:+.2f}")
# mfq2 has per-respondent Atari data -> scatter the individual cloud behind the societies and
# fit the ipsative PCA on PEOPLE (better-conditioned, the real envelope). Other instruments: None.
respondents = T.maps.respondent_profiles(dims, instr.scale_max) if name == "mfq2" else None
# mfq2 has per-respondent Atari data -> scatter the REAL individual cloud behind the societies AND
# fit the ipsative PCA on it (better-conditioned, the true envelope). Other instruments have no raw
# per-person data, so scatter a marginal resample from each country's published mean+sd as the haze
# while keeping the PCA basis on the society means M.
if name == "mfq2":
respondents, haze = T.maps.respondent_profiles(dims, instr.scale_max), None
else:
respondents, haze = None, human_haze(instr)
figm = T.maps.plot_ipsative_pca(instr, dims, countries, Mfrac,
_frac(base, instr.scale_max), _frac(pos, instr.scale_max),
_frac(neg, instr.scale_max), respondents=respondents, labels=labels)
_frac(neg, instr.scale_max), respondents=respondents, haze=haze,
labels=labels)
paths = [T.maps.save_both(figm, out / name, "map_pca_ipsative")]
plt.close(figm)
src/tinymfv/maps.py
+15 -13
View File
@@ -141,19 +141,20 @@ def _axis_gloss(load1: np.ndarray, dims: list[str], n: int = 2) -> str:
def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str], M: np.ndarray,
base: np.ndarray, pos: np.ndarray | None, neg: np.ndarray | None,
*, respondents: np.ndarray | None = None, boots: dict | None = None,
pad=(0.18, 0.16),
*, respondents: np.ndarray | None = None, haze: np.ndarray | None = None,
boots: dict | None = None, pad=(0.18, 0.16),
labels: tuple[str, str, str] = ("baseline (c=0)", "honest (c=+2)", "dishonest (c=-2)")):
"""Ipsative culture map. M is societies x K (0-1 fraction); base / pos / neg are the length-K
fraction vectors for the base model and its two steer poles (or None). `labels` is the legend
text (base, +pole, -pole) -- override it for a non-honesty steer or a different coefficient.
`respondents` (n_resp x K, SAME 0-1 fraction scale as M) scatters individual respondents as a
grey haze and, crucially, becomes the PCA BASIS: fitting on people (thousands of points, real
covariance) beats fitting on a handful of noisy society means, and the cloud IS the honest
cross-cultural envelope the model is placed against. The crop then frames that cloud's core
(2-98 pct) unioned with the anchors. None -> old behaviour (fit on M, pad-based crop, no haze).
`boots` optionally maps the role keys 'base'/'honest'/'dis' -> (n x K) bootstrap fraction
matrices for the uncertainty cross. Returns the Figure."""
`respondents` (n_resp x K, SAME 0-1 fraction scale as M) is the PCA BASIS when given: fitting on
people (thousands of points, real covariance) beats fitting on a handful of noisy society means.
`haze` (n x K, same fraction scale) is the human cloud SCATTERED behind the societies and used
for the crop -- separate from the fit so instruments with only society-level mean+sd (big5/16pf/
humor: a marginal resample) get a backdrop without that resample dictating the axes. mfq2 passes
real `respondents` (also used as the haze when `haze` is None). With neither, fit on M, pad-crop,
no backdrop. `boots` optionally maps 'base'/'honest'/'dis' -> (n x K) bootstrap matrices. Returns
the Figure."""
try:
import textalloc as ta
except ImportError:
@@ -161,6 +162,7 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
fit_on = respondents if respondents is not None else M
_, Vt, var, mu, Pc = ipsative_pca(fit_on) # signs already stabilized inside the helper
P = (M @ Pc - mu) @ Vt[:2].T
cloud = haze if haze is not None else respondents # what we scatter + crop to (fit is separate)
def proj(v):
return ((v @ Pc) - mu) @ Vt[:2].T if v is not None else None
@@ -169,8 +171,8 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
fig, ax = plt.subplots(figsize=(8.5, 7.5))
ax.set_facecolor("#faf8f2")
ax.grid(True, color="#eceadf", lw=0.3, zorder=0)
if respondents is not None: # grey haze = individual respondents (rasterized; SVG-safe)
Pi = (respondents @ Pc - mu) @ Vt[:2].T
if cloud is not None: # grey haze = human respondents (rasterized; SVG-safe)
Pi = (cloud @ Pc - mu) @ Vt[:2].T
ax.scatter(Pi[:, 0], Pi[:, 1], s=4, c="#8f8a7e", alpha=0.14, edgecolors="none",
zorder=1, rasterized=True)
ax.scatter(P[:, 0], P[:, 1], s=26, c=C_HUM, alpha=0.7, edgecolors="white", linewidths=0.5, zorder=3)
@@ -202,8 +204,8 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
ax.annotate(lab, pt, xytext=dxy, textcoords="offset points", fontsize=9, color=col,
fontweight="bold", ha=ha, va="center", zorder=8)
compass(ax, Vt[:2].T, dims, title=f"{instr.display} compass")
if respondents is not None:
# crop to the respondent-cloud core (2-98 pct) unioned with every anchor, so societies +
if cloud is not None:
# crop to the human-cloud core (2-98 pct) unioned with every anchor, so societies +
# poles fill the frame instead of being buried in one corner of the full cloud.
anc = np.vstack([P] + [p for p in (pb, ph, pf) if p is not None])
cx, cy = np.percentile(Pi[:, 0], [2, 98]), np.percentile(Pi[:, 1], [2, 98])