带 Pearson 残差的马赛克图
色块面积与单元格频数成正比，并按相对于独立性的 Pearson 残差着色。
马赛克图将二维列联表画成一个被切分成若干色块的正方形。列的宽度是第一个变量的边际比例，色块的高度是第二个变量的条件比例，因此每个色块的面积与其频数成正比。与 vcd::mosaic(shade = TRUE) 一样，颜色表示 Pearson 残差（观测值 − 期望值）/ √期望值：蓝色色块的人数多于独立假设的预测，红色色块则较少；残差超过 ±2 或 ±4 的单元格正是驱动 χ² 的关键所在。
数据为 statsmodels 自带的 1974 年 Redbook 对 6,366 名已婚女性的调查（sm.datasets.fair）：自评婚姻质量与婚外情所花时间。色块用 ax.bar 手工绘制；期望频数由 scipy.stats.chi2_contingency 计算。
代码及图中文字均为英文。
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import statsmodels.api as sm
from matplotlib.colors import TwoSlopeNorm
from scipy import stats
# Data: marriage rating (1-5, 1-2 pooled) × time spent in affairs (none / ≤ 1 / > 1)
df = sm.datasets.fair.load_pandas().data
rating = pd.cut(df.rate_marriage, [0, 2, 3, 4, 5], labels=["Poor", "Fair", "Good", "Very good"])
affairs = pd.cut(df.affairs, [-1, 0, 1, np.inf], labels=["None", "Occasional", "Frequent"])
table = pd.crosstab(rating, affairs)
obs = table.to_numpy()
# Chi-squared test and Pearson residuals
chi2, p, dof, expected = stats.chi2_contingency(obs, correction=False)
resid = (obs - expected) / np.sqrt(expected)
fig, ax = plt.subplots(figsize=(8.5, 5.6))
cmap = plt.get_cmap("RdBu") # red = fewer than expected, blue = more
norm = TwoSlopeNorm(0, vmin=-12, vmax=12)
gap = 0.012
widths = obs.sum(axis=1) / obs.sum()
x0 = 0
for i, w in enumerate(widths):
heights = obs[i] / obs[i].sum()
y0 = 0
for j, h in enumerate(heights):
ax.bar(x0, h - gap, width=w - gap, bottom=y0, align="edge",
color=cmap(norm(resid[i, j])), edgecolor="none")
sep = " " if h < 0.12 else "\n" # thin tiles get a one-line label
ax.text(x0 + (w - gap) / 2, y0 + (h - gap) / 2, f"{obs[i, j]}{sep}{resid[i, j].round(1) + 0:+.1f}", ha="center", va="center",
fontsize=9, linespacing=1.3, color="white" if abs(resid[i, j]) > 7 else "#1D1D1F")
y0 += h
ax.text(x0 + (w - gap) / 2, -0.03, f"{table.index[i]}\n(n = {obs[i].sum()})", ha="center", va="top",
fontsize=10, color="#3A3A3C")
x0 += w
# Row labels on the left, placed at the heights of the first column
y0 = 0
for j, h in enumerate(obs[0] / obs[0].sum()):
ax.text(-0.015, y0 + (h - gap) / 2, table.columns[j], ha="right", va="center", fontsize=10, color="#3A3A3C")
y0 += h
sm_ = plt.cm.ScalarMappable(norm=norm, cmap=cmap)
cb = fig.colorbar(sm_, ax=ax, shrink=0.8, pad=0.02, ticks=[-12, -8, -4, 0, 4, 8, 12])
cb.set_label("Pearson residual", color="#3A3A3C")
cb.outline.set_visible(False)
ax.set_xlim(0, 1 - gap); ax.set_ylim(0, 1 - gap)
ax.axis("off")
ax.text(0.5, -0.15, "Self-rated marriage quality", transform=ax.transAxes, ha="center", fontsize=11)
ax.text(-0.19, 0.5, "Time spent in affairs", transform=ax.transAxes, rotation=90, va="center", fontsize=11)
ax.set_title("Unhappy marriages carry far more affairs than chance predicts", pad=26)
ax.text(0, 1.02, f"Pearson χ²({dof}) = {chi2:.0f}, p < .001 · n = {obs.sum():,} · "
"tile labels: count and residual", transform=ax.transAxes, fontsize=9.5, color="#6E6E73")
plt.show()
图表使用了可选的 PyStatlas 样式：添加 plt.style.use("pystatlas.mplstyle") 即可完全还原其外观。
数据来源
- Redbook survey of married women, 1974 (Fair's affairs data). Fair, R. C. (1978). A theory of extramarital affairs. Journal of Political Economy, 86(1), 45–61. https://doi.org/10.1086/260646
Data from the 1974 Redbook magazine survey; distributed with statsmodels (sm.datasets.fair) with the author's permission.
这些示例用于说明统计方法。图表标题描述的是该图在这些特定数据中呈现的内容——这些数据往往样本较小、年代较早或并不完整——而不是作者对实质问题的立场。关于解释、背景和数据质量，请以此处引用的原始来源为准。
如何引用
PyStatlas 由 Thierry Warin 创建并维护。如果它对你的工作有所帮助，敬请引用。
Warin, T. (2026). Mosaic plot with Pearson residuals. In PyStatlas: A Python Gallery of Statistical Graphics for the Social Sciences. https://warint.github.io/pystatlas/proportions-surveys/mosaic-plot/
@misc{warin2026statlas,
author = {Warin, Thierry},
title = {PyStatlas: A Python Gallery of Statistical Graphics for the Social Sciences},
year = {2026},
howpublished = {\url{https://warint.github.io/pystatlas/}},
note = {Source code: https://github.com/warint/pystatlas}
}
