From b2532acd90bd59478c46d422587b08d9f9059fa0 Mon Sep 17 00:00:00 2001 From: wassname <1103714+wassname@users.noreply.github.com> Date: Sat, 4 Jul 2026 20:22:23 +0800 Subject: [PATCH] Switch zone blobs to country-mean covariance ellipses, fit PCA on means Per feedback the individual-respondent contours filled the frame (within >> between variance). Now each IW zone is a ~1.6-sigma covariance ellipse over its member country-mean dots, with an eigenvalue floor so 1-2 country zones get a visible blob instead of a dot/line (fixes big5 SG/PK orphans). PCA now fits on the country means M so the axes are between-country and zones separate. mfq2/big5/mfv read cleanly; humor still overlaps (real negative result: humor country profiles don't cluster the IW way). Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com> --- docs/RESEARCH_JOURNAL.md | 13 +++++ scripts/plot_steer_showcase.py | 44 ++++++++-------- src/tinymfv/maps.py | 91 +++++++++++----------------------- 3 files changed, 62 insertions(+), 86 deletions(-) diff --git a/docs/RESEARCH_JOURNAL.md b/docs/RESEARCH_JOURNAL.md index 06762f2..9aad702 100644 --- a/docs/RESEARCH_JOURNAL.md +++ b/docs/RESEARCH_JOURNAL.md @@ -749,3 +749,16 @@ over people; a person-level contour honestly shows the overlap the country-mean view hides. Secondary caveat: several mfq2 zones are single-country in the Atari 19 (Confucian=Japan, Orthodox=Russia, Protestant=Switzerland), so those ellipses are one country's spread wearing a zone label. + +Follow-up (same day, after eyeballing): the individual-respondent contour was the +wrong call for the map -- it fills the frame and every zone overlaps, exactly +because within >> between variance. Switched the zone blob to a ~1.6-sigma +covariance ellipse over each zone's COUNTRY-MEAN dots (between-country spread) with +an eigenvalue floor so a 1- or 2-country zone still gets a circle/ellipse instead +of a dot/line. Also fit the ipsative PCA on the country means M (not the respondent +cloud) so the axes are between-country. Result: mfq2/big5/mfv separate cleanly and +Economist-like, every country is grouped (big5 SG/PK no longer orphaned). humor +STILL overlaps heavily even on country means -- humor-style country profiles do not +cluster the IW way on the top 2 ipsative PCs, a real negative result, not a plot +bug. (Whether any linear axis separates humor zones is the LDA question, tested +separately.) diff --git a/scripts/plot_steer_showcase.py b/scripts/plot_steer_showcase.py index 03bfc42..38b1924 100644 --- a/scripts/plot_steer_showcase.py +++ b/scripts/plot_steer_showcase.py @@ -153,14 +153,15 @@ 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).""" +def human_haze(instr, n_per_country: int = 200, seed: int = 0) -> tuple[np.ndarray, list[str]]: + """Synthetic individual-respondent cloud (n x K, 0-1 fraction) + the country of each row, 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). The returned country-per-row list lets the map contour it by IW zone.""" dims = instr.dimensions rng = np.random.default_rng(seed) stats: dict[tuple[str, str], tuple[float, float]] = {} @@ -168,11 +169,12 @@ def human_haze(instr, n_per_country: int = 200, seed: int = 0) -> np.ndarray: 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 = [] + blocks, row_country = [], [] 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) + row_country.extend([c] * n_per_country) + return _frac(np.concatenate(blocks, axis=0), instr.human_scale_max), row_country def human_strip(instr) -> dict[str, list[tuple[str, float]]]: @@ -276,23 +278,19 @@ def plot_ordinal(run_dir: Path, out: Path, name: str, vec_label: str, C: float, # 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. - # mfq2 has real per-respondent data -> draw a p90 respondent ELLIPSE per zone (grounded in - # people) and drop the country-mean hull. Other instruments have only society means -> the - # country-mean convex HULL is the best-available zone blob. - _, emph = zones_for(countries) + # Each IW zone is a covariance ellipse over its member COUNTRY-MEAN dots (drawn in maps). mfq2 + # scatters its real Atari respondents behind; the others scatter a per-country resample. + zones, emph = zones_for(countries) if name == "mfq2": - resp_countries, respondents = T.maps.respondent_profiles(dims, instr.scale_max) - haze, zones = None, None - respondent_zones = [_zone_of(c) for c in resp_countries] + _, respondents = T.maps.respondent_profiles(dims, instr.scale_max) + haze = None else: - respondents, haze = None, human_haze(instr) - zones, respondent_zones = zones_for(countries)[0], None + respondents, (haze, _) = None, human_haze(instr) traj = {c: _frac(prof_c[c], instr.scale_max) for c in coh_cs} 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, haze=haze, - traj=traj, zones=zones, emphasize=emph, - respondent_zones=respondent_zones, labels=labels) + traj=traj, emphasize=emph, zones=zones, labels=labels) figm.axes[0].set_title(f"{instr.display}: humans vs LLMs steered for {vec_label}", fontsize=10) paths = [T.maps.save_both(figm, out / name, "map_pca_ipsative")] plt.close(figm) @@ -366,9 +364,9 @@ def plot_mfv_map(run_dir: Path, out: Path, vec_label: str, C: float, coh_cs: lis neg_c = min(c for c in coh_cs if c < 0.0) labels = ("base (c=0)", f"c={pos_c:+g}", f"c={neg_c:+g}") traj = {c: prof[c] for c in coh_cs} - zones, emph = zones_for(countries) + zones, emph = zones_for(countries) # MFV: 5 country dots, no cloud fig = T.maps.plot_ipsative_pca(_MFV_INSTR, founds, countries, M, prof[0.0], prof[pos_c], prof[neg_c], - traj=traj, zones=zones, emphasize=emph, labels=labels) + traj=traj, emphasize=emph, zones=zones, labels=labels) fig.axes[0].set_title(f"MFV vignettes: humans vs LLMs steered for {vec_label}", fontsize=10) path = T.maps.save_both(fig, out / "mfv", "map_pca_ipsative") plt.close(fig) diff --git a/src/tinymfv/maps.py b/src/tinymfv/maps.py index 0478593..b95e776 100644 --- a/src/tinymfv/maps.py +++ b/src/tinymfv/maps.py @@ -93,24 +93,6 @@ ZONE_COLORS = { } -def convex_hull(pts: np.ndarray) -> np.ndarray: - """2D convex-hull vertices (CCW) via Andrew's monotone chain. Inline instead of scipy so the - `maps` install extra stays matplotlib-only (scipy is dev-only). pts (n,2) -> polygon (m,2).""" - P = sorted(map(tuple, pts.tolist())) - if len(P) <= 2: - return np.array(P, dtype=float) - cross = lambda o, a, b: (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]) - lower: list = [] - for p in P: - while len(lower) >= 2 and cross(lower[-2], lower[-1], p) <= 0: - lower.pop() - lower.append(p) - upper: list = [] - for p in reversed(P): - while len(upper) >= 2 and cross(upper[-2], upper[-1], p) <= 0: - upper.pop() - upper.append(p) - return np.array(lower[:-1] + upper[:-1], dtype=float) def save_both(fig, fig_dir: Path, stem: str, dpi: int = 200) -> Path: @@ -218,8 +200,8 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str], *, respondents: np.ndarray | None = None, haze: np.ndarray | None = None, traj: dict[float, np.ndarray] | None = None, traj_incoherent: set | None = None, boots: dict | None = None, - zones: dict[str, list[str]] | None = None, emphasize: set[str] | None = None, - respondent_zones: list[str] | None = None, + emphasize: set[str] | None = None, + zones: dict[str, list[str]] | None = None, 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 @@ -237,18 +219,19 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str], drawn hollow. `boots` optionally maps 'base'/'honest'/'dis' -> (n x K) bootstrap matrices. `zones` maps an Inglehart-Welzel zone name to the subset of `countries` (verbatim strings) in it; each zone with >=3 members gets a shaded convex hull (echoes the Economist WVS map's zone blobs), - testing whether moral-foundation space recovers the WVS clusters. `emphasize` is a subset of + `emphasize` is a subset of `countries` labelled bold-first so named outliers (China, US, Sweden...) always survive the - label-collision drop. `respondent_zones` (length = rows of the projected cloud, i.e. - `respondents` when `haze` is None) is each respondent's IW zone; each zone with enough respondents - gets a p90 Gaussian ellipse of its cloud (the real-respondent analogue of a zone hull, mfq2 only). - Returns the Figure.""" + label-collision drop. `zones` maps an IW zone name to its member `countries`; each becomes a + covariance ellipse over that zone's COUNTRY-MEAN points (between-country spread, so zones stay + separate -- contouring individual respondents instead gives huge overlap since within-culture + variance dominates). An eigenvalue floor gives a 1- or 2-country zone a visible blob. The PCA is + fit on the country means M; `respondents`/`haze` only scatter + set the crop. Returns the + Figure.""" try: import textalloc as ta except ImportError: ta = None - fit_on = respondents if respondents is not None else M - _, Vt, var, mu, Pc = ipsative_pca(fit_on) # signs already stabilized inside the helper + _, Vt, var, mu, Pc = ipsative_pca(M) # fit on country means: between-country axes P = (M @ Pc - mu) @ Vt[:2].T cloud = haze if haze is not None else respondents # what we scatter + crop to (fit is separate) @@ -259,50 +242,32 @@ 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 cloud is not None: # grey haze = human respondents (rasterized; SVG-safe) + if cloud is not None: # grey haze/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) - # Per-zone p90 respondent ellipse (mfq2 only): the real-respondent analogue of a zone hull. - # A 90%-mass contour of the bivariate-Gaussian fit to each zone's projected cloud; the radius - # is the chi-square(2 dof) 0.90 quantile, sqrt(4.605)=2.1459 (hardcoded to avoid a scipy dep). - if respondent_zones is not None: - assert len(respondent_zones) == Pi.shape[0], "respondent_zones must align with the cloud rows" - zr = np.asarray(respondent_zones) - for zname in dict.fromkeys(respondent_zones): # stable order, unique - zp = Pi[zr == zname] - if len(zp) < 30: # too few respondents -> unreliable contour - continue - cen = zp.mean(0) - evals, evecs = np.linalg.eigh(np.cov(zp.T)) - ang = np.degrees(np.arctan2(evecs[1, -1], evecs[0, -1])) - w, h = 2 * 2.1459 * np.sqrt(np.maximum(evals[::-1], 0)) - zcol = ZONE_COLORS.get(zname, "#888888") - ax.add_patch(Ellipse(cen, w, h, angle=ang, facecolor="none", - edgecolor=zcol, alpha=0.75, lw=1.4, ls="--", zorder=1.6)) - ax.text(cen[0], cen[1], zname, fontsize=8.5, color=zcol, ha="center", - va="center", style="italic", fontweight="bold", zorder=2, alpha=0.9) - # Inglehart-Welzel zone hulls: a shaded convex blob per zone with >=3 member societies, drawn - # UNDER the society dots (zorder<3). The zone name sits at the hull centroid in grey, echoing the - # Economist WVS map. A 2-member zone has no polygon, so it's shown as its connecting segment. + # Per-zone blob: a ~1.6-sigma covariance ellipse over that zone's COUNTRY-MEAN points. Between- + # country spread keeps the zones separate; an eigenvalue floor (a fraction of the overall P + # spread) gives a 1-country zone a small circle and a 2-country zone real width instead of a line. if zones: cidx = {c: i for i, c in enumerate(countries)} + floor = (0.07 * float(np.hypot(*(P.max(0) - P.min(0))))) ** 2 for zname, members in zones.items(): - mi = [cidx[c] for c in members if c in cidx] - if len(mi) < 2: + zp = P[[cidx[c] for c in members if c in cidx]] + if len(zp) == 0: continue - zpts = P[mi] + cen = zp.mean(0) + cov = np.cov(zp.T) if len(zp) > 1 else np.zeros((2, 2)) + evals, evecs = np.linalg.eigh(cov) + ang = np.degrees(np.arctan2(evecs[1, -1], evecs[0, -1])) + w, h = 2 * 1.6 * np.sqrt(np.maximum(evals[::-1], floor)) zcol = ZONE_COLORS.get(zname, "#888888") - if len(mi) >= 3: - hull = convex_hull(zpts) - ax.add_patch(plt.Polygon(hull, closed=True, facecolor=zcol, edgecolor=zcol, - alpha=0.13, lw=1.0, zorder=1.6)) - ax.plot(*np.vstack([hull, hull[:1]]).T, color=zcol, lw=1.0, alpha=0.45, zorder=1.7) - else: - ax.plot(zpts[:, 0], zpts[:, 1], color=zcol, lw=1.2, alpha=0.5, zorder=1.7) - cx, cy = zpts.mean(0) - ax.text(cx, cy, zname, fontsize=8.5, color="#6b6b6b", ha="center", va="center", - style="italic", zorder=2, alpha=0.85) + ax.add_patch(Ellipse(cen, w, h, angle=ang, facecolor=zcol, edgecolor=zcol, + alpha=0.12, lw=1.0, zorder=1.5)) + ax.add_patch(Ellipse(cen, w, h, angle=ang, facecolor="none", edgecolor=zcol, + alpha=0.7, lw=1.2, zorder=1.7)) + ax.text(cen[0], cen[1], zname, fontsize=8.5, color=zcol, ha="center", + va="center", style="italic", fontweight="bold", zorder=2, alpha=0.9) ax.scatter(P[:, 0], P[:, 1], s=26, c=C_HUM, alpha=0.7, edgecolors="white", linewidths=0.5, zorder=3) # Society labels: each name/ISO code is pinned RIGHT NEXT to its dot (small fixed offset, no # leader line). A label is dropped if its box would collide with an already-placed one -- better an