DoWhy因果API演示

我们展示了一个简单的例子，向任何数据框添加因果扩展。

import dowhy.datasets
import dowhy.api
from dowhy.graph import build_graph_from_str

import numpy as np
import pandas as pd

from statsmodels.api import OLS

data = dowhy.datasets.linear_dataset(beta=5,
        num_common_causes=1,
        num_instruments = 0,
        num_samples=1000,
        treatment_is_binary=True)
df = data['df']
df['y'] = df['y'] + np.random.normal(size=len(df)) # Adding noise to data. Without noise, the variance in Y|X, Z is zero, and mcmc fails.
nx_graph = build_graph_from_str(data["dot_graph"])

treatment= data["treatment_name"][0]
outcome = data["outcome_name"][0]
common_cause = data["common_causes_names"][0]
df

	W0	v0	y
0	0.037488	假	-0.174667
1	-0.523050	假	-1.292853
2	2.070420	True	9.443895
3	0.068183	假	1.113386
4	0.104074	True	5.843495
...	...	...	...
995	-0.265148	True	4.197523
996	-0.973204	假	-0.142424
997	-1.241690	假	-2.795862
998	-1.825721	假	-3.752621
999	-0.607617	真	2.775188

1000 行 × 3 列

# data['df'] is just a regular pandas.DataFrame
df.causal.do(x=treatment,
             variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
             outcome=outcome,
             common_causes=[common_cause],
            ).groupby(treatment).mean().plot(y=outcome, kind='bar')

<Axes: xlabel='v0'>

df.causal.do(x={treatment: 1},
              variable_types={treatment:'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              method='weighting',
              common_causes=[common_cause]
              ).groupby(treatment).mean().plot(y=outcome, kind='bar')

<Axes: xlabel='v0'>

cdf_1 = df.causal.do(x={treatment: 1},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              graph=nx_graph
              )

cdf_0 = df.causal.do(x={treatment: 0},
              variable_types={treatment: 'b', outcome: 'c', common_cause: 'c'},
              outcome=outcome,
              graph=nx_graph
              )

cdf_0

	W0	v0	y	倾向得分	权重
0	-0.713942	假	-0.832839	0.774908	1.290476
1	0.378506	False	1.757012	0.329282	3.036907
2	-0.416285	假	-1.897409	0.669419	1.493834
3	-1.022786	假	-3.304443	0.856541	1.167486
4	0.541459	False	1.429673	0.268558	3.723594
...	...	...	...	...	...
995	-0.873678	False	0.280653	0.820688	1.218489
996	0.933586	False	2.296218	0.154328	6.479718
997	-0.961088	假	-1.653206	0.842488	1.186961
998	-0.057126	假	0.769879	0.516302	1.936850
999	-0.328091	假	0.223023	0.633746	1.577919

1000 行 × 5 列

cdf_1

	W0	v0	y	倾向得分	权重
0	-0.752117	True	3.312724	0.213443	4.685087
1	-0.568538	True	4.378100	0.273487	3.656476
2	1.378671	True	7.617855	0.923760	1.082532
3	0.917073	True	6.610054	0.841791	1.187943
4	-0.871327	True	2.153620	0.179929	5.557742
...	...	...	...	...	...
995	0.260021	True	5.172035	0.622504	1.606415
996	3.495361	True	14.133175	0.998108	1.001895
997	-1.526145	True	1.050194	0.063908	15.647445
998	-0.324753	True	4.160558	0.367636	2.720078
999	1.709055	True	6.392574	0.956211	1.045794

1000 行 × 5 列

将估计值与线性回归进行比较

首先，使用因果数据框架估计效果，以及95%的置信区间。

(cdf_1['y'] - cdf_0['y']).mean()

$\displaystyle 5.40925954703069$

1.96*(cdf_1['y'] - cdf_0['y']).std() / np.sqrt(len(df))

$\displaystyle 0.191657653401046$

与OLS的估计进行比较。

model = OLS(np.asarray(df[outcome]), np.asarray(df[[common_cause, treatment]], dtype=np.float64))
result = model.fit()
result.summary()

OLS Regression Results

因变量:	y	R平方（未中心化）:	0.957
模型:	OLS	调整后的R平方（未居中）:	0.957
方法:	最小二乘法	F统计量:	1.102e+04
日期:	2024年11月24日 星期日	概率 (F统计量):	0.00
时间:	18:03:52	对数似然:	-1410.0
观测数量：	1000	AIC:	2824.
残差自由度:	998	BIC:	2834.
自由度模型:	2
协方差类型：	非稳健

	系数	标准误差	t值	P>|t|	[0.025	0.975]
x1	2.1425	0.034	63.535	0.000	2.076	2.209
x2	4.9804	0.048	103.470	0.000	4.886	5.075

综合统计量:	0.734	德宾-沃森统计量:	1.928
概率(Omnibus):	0.693	Jarque-Bera (JB):	0.658
偏度:	0.060	JB概率:	0.720
峰度:	3.038	条件编号	1.67

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.