I'm trying to analyze the total active minutes per user before and after an experiment. Here I've included the associated user data before and after the experiment - variant_number = 0 indicates control group while 1 means treatment group. Specifically, I'm interested in the mean (average total active minutes per user).
First, I calculated the before-after difference in treatment outcome and the before-after difference in control outcome (-183.7 and 19.4 respectively). The difference in differences = 203.1 in this case.
I'm wondering how I can use Python to construct a 95% confidence interval of the difference in differences? (I can provide more code/context if needed)
You can use a linear model and measure the interaction effect (group[T.1]:period[T.pre] below). The average difference in differences for these simulated data is -223.1779, the p-value for the interaction is p < 5e-4 so highly significant and the 95% confidence interval is [-276.360, -169.995].
import statsmodels.api as sm
import statsmodels.formula.api as smf
import pandas as pd
import numpy as np
np.random.seed(14)
minutes_0_pre = np.random.normal(loc=478, scale=1821, size=39776)
minutes_1_pre = np.random.normal(loc=275, scale=1078, size=9921)
minutes_0_post = np.random.normal(loc=458, scale=1653, size=37425)
minutes_1_post = np.random.normal(loc=458, scale=1681, size=9208)
df = pd.DataFrame({'minutes': np.concatenate((minutes_0_pre, minutes_1_pre, minutes_0_post, minutes_1_post)),
'group': np.concatenate((np.repeat(a='0', repeats=minutes_0_pre.size),
np.repeat(a='1', repeats=minutes_1_pre.size),
np.repeat(a='0', repeats=minutes_0_post.size),
np.repeat(a='1', repeats=minutes_1_post.size))),
'period': np.concatenate((np.repeat(a='pre', repeats=minutes_0_pre.size + minutes_1_pre.size),
np.repeat(a='post', repeats=minutes_0_post.size + minutes_1_post.size)))
})
model = smf.glm('minutes ~ group * period', df, family=sm.families.Gaussian()).fit()
print(model.summary())
Output:
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: minutes No. Observations: 96330
Model: GLM Df Residuals: 96326
Model Family: Gaussian Df Model: 3
Link Function: identity Scale: 2.8182e+06
Method: IRLS Log-Likelihood: -8.5201e+05
Date: Mon, 18 Jan 2021 Deviance: 2.7147e+11
Time: 23:05:53 Pearson chi2: 2.71e+11
No. Iterations: 3
Covariance Type: nonrobust
============================================================================================
coef std err z P>|z| [0.025 0.975]
--------------------------------------------------------------------------------------------
Intercept 456.2792 8.678 52.581 0.000 439.271 473.287
group[T.1] 14.9314 19.529 0.765 0.445 -23.344 53.207
period[T.pre] 21.7417 12.089 1.798 0.072 -1.953 45.437
group[T.1]:period[T.pre] -223.1779 27.134 -8.225 0.000 -276.360 -169.995
============================================================================================
Since your summary statistics show that your distribution is heavily skewed, bootstrapping is actually a more reliable method to estimate confidence intervals:
r = 1000
bootstrap = np.zeros(r)
for i in range(0, r):
sample_index = np.random.choice(a=range(0, df.shape[0]), size=df.shape[0], replace=True)
df_sample = df.iloc[sample_index]
model = smf.glm('minutes ~ group * period', df_sample, family=sm.families.Gaussian()).fit()
bootstrap[i] = model.params.iloc[3] # interaction
bootstrap = pd.DataFrame(bootstrap, columns=['interaction'])
print(bootstrap.quantile([0.025, 0.975]).T)
Output:
0.025 0.975
interaction -273.524899 -175.373177