Treatment of weights in DoubleMLIRM

[roffsin]

I am unsure as to how the weights options works in DoubleMLIRM. Are these indeed sampling weights? If so, I did a simple DGP and estimated a weighted and an unweighted model. The estimates of both are close to each other, with both being quite different from the true parameter.

Any comments would be helpful.
Thanks,
R

[SvenKlaassen]

Hi @roffsin,

the weights can be used to construct e.g. subgroup effects as e.g. the ATT (see Weighted Average Treatment Effects).
The weights are part of the score function (see e.g. IRM Score), but do not completely function as sampling weights.

It would be helpful if you would post a minimal reproducable example for your problem.

Best,
Sven

[roffsin]

Hi Sven,
Please find the code block below.

import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression, LinearRegression
from doubleml import DoubleMLData, DoubleMLIRM
from sklearn.model_selection import train_test_split
import warnings
warnings.filterwarnings("ignore")

np.random.seed(42)

# ---- Step 1: Generate data ----
n = 2000
p = 3

X = np.random.normal(0, 1, size=(n, p))
beta = np.array([1, -1, 0.5])
gamma = np.array([0.5, -0.5, 0.2])

# Propensity score and treatment assignment
def logistic(x):
    return 1 / (1 + np.exp(-x))

pscore = logistic(X @ gamma)
D = np.random.binomial(1, pscore)

# Outcome with true ATE = 2.0
theta = 2.0
epsilon = np.random.normal(0, 1, size=n)
Y = theta * D + X @ beta + epsilon

# Sampling weights
sampling_weights = np.exp(0.5 * X[:, 0])
sampling_weights = np.round(sampling_weights).astype(int)
sampling_weights[sampling_weights < 1] = 1  # enforce min weight = 1
print(np.round(pd.Series(sampling_weights).describe(), 4))

#sampling_weights = np.ones(n)
#print(np.round(pd.Series(sampling_weights).describe(), 4))

# True ATE under sampling weights
def weighted_mean(x, w):
    return np.sum(w * x) / np.sum(w)

# ---- Step 2: DoubleML with native weights ----
df = pd.DataFrame(X, columns=[f'X{i+1}' for i in range(p)])
df['Y'] = Y
df['D'] = D

ml_g = LinearRegression()
ml_m = LogisticRegression(max_iter=1000)

dml_data = DoubleMLData(df, y_col='Y', d_cols='D', x_cols=[f'X{i+1}' for i in range(p)])

dml_irm = DoubleMLIRM(dml_data, ml_g, ml_m, n_folds=5, n_rep=3, score='ATE', weights=sampling_weights)
print(dml_irm.fit().summary)

# ---- Step 3: DoubleML with row replication ----
df['rep_count'] = np.round(sampling_weights * 2).astype(int)  # multiplier helps ensure variance
df_rep = df.loc[df.index.repeat(df['rep_count'])].reset_index(drop=True)

dml_data_rep = DoubleMLData(df_rep, y_col='Y', d_cols='D', x_cols=[f'X{i+1}' for i in range(p)])
dml_irm_rep = DoubleMLIRM(dml_data_rep, ml_g, ml_m, n_folds=5, n_rep=3, score='ATE')
print(dml_irm_rep.fit().summary)

[SvenKlaassen]

Thank you.

I can see the issue.
In your example the effect on each unit is 2 and the average over your weights is roughly 1.245.

The difference is that the weights in doubleml estimates the weighted effect

$$ \mathbb{E}[(g(1,X) - g(0,X)) \omega(X)] = \mathbb{E}[2 \omega(X)] = 2\mathbb{E}[\omega(X)] \approx 2.49 $$

The Weighted Average Treatment Effect actually weights the corresponding effect, where as the row replications is not affecting the average (if all units have the same effect).

[roffsin]

Thanks!

Okay, that's making it clear. Does it mean that the weights in the doubleml need to be adjusted so that they sum to 1? Otherwise the estimate effect won't represent an average effect?

[SvenKlaassen]

In many settings the weights do not sum to $1$ but are $1$ on average, e.g.

• ATE sets all weights to $1$
• GATE for group $G$ sets all weights to $1/P(X\in G)$ for $X\in G$ or $0$ otherwise

such that the output can be interpreted as a weighted average of effects.
Overall it really depends on the specific quantity you are interested in.

[roffsin]

Thanks a lot Sven for taking time out to explain this. Much appreciated.