sensemakr for Python (PySensemakr) implements a suite of sensitivity analysis tools that
extends the traditional omitted variable bias framework and makes it
easier to understand the impact of omitted variables in regression
models, as discussed in Cinelli, C. and Hazlett, C. (2020) “Making
Sense of Sensitivity: Extending Omitted Variable Bias.” Journal of the
Royal Statistical Society, Series B (Statistical
Methodology).
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The R version of the package can be downloaded here: https://github.com/carloscinelli/sensemakr/.
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The Stata version of the package can be downloaded here: https://github.com/resonance1/sensemakr-stata.
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The Shiny App is available at: https://carloscinelli.shinyapps.io/robustness_value/.
For theoretical details, please see the JRSS-B paper.
For practical details of the package, see the the package documentation.
Make sure you have Python 3.8, or higher, installed.
To install the latest development version on GitHub, run:
pip3 install git+https://github.com/nlapier2/PySensemakr
A user version on PyPI can be installed via:
pip3 install PySensemakr
# Imports
import sensemakr as smkr
import statsmodels.formula.api as smf# loads data
darfur = smkr.load_darfur()# runs regression model
reg_model = smf.ols(formula='peacefactor ~ directlyharmed + age + farmer_dar + herder_dar + '\
'pastvoted + hhsize_darfur + female + village', data=darfur)
darfur_model = reg_model.fit()# Create a sensemakr object and print summary of results
darfur_sense = smkr.Sensemakr(model = darfur_model,
treatment = "directlyharmed",
benchmark_covariates = ["female"],
kd = [1,2,3])
darfur_sense.summary()Sensitivity Analysis to Unobserved Confounding
Model Formula: peacefactor ~ directlyharmed + age + farmer_dar + herder_dar + pastvoted + hhsize_darfur + female + village
Null hypothesis: q = 1.0 and reduce = True
-- This means we are considering biases that reduce the absolute value of the current estimate.
-- The null hypothesis deemed problematic is H0:tau = 0.0
Unadjusted Estimates of ' directlyharmed ':
Coef. estimate: 0.097
Standard Error: 0.023
t-value: 4.184
Sensitivity Statistics:
Partial R2 of treatment with outcome: 0.022
Robustness Value, q = 1.0 : 0.139
Robustness Value, q = 1.0 alpha = 0.05 : 0.076
Verbal interpretation of sensitivity statistics:
-- Partial R2 of the treatment with the outcome: an extreme confounder (orthogonal to the covariates) that explains 100% of the residual variance of the outcome, would need to explain at least 2.187 % of the residual variance of the treatment to fully account for the observed estimated effect.
-- Robustness Value, q = 1.0 : unobserved confounders (orthogonal to the covariates) that explain more than 13.878 % of the residual variance of both the treatment and the outcome are strong enough to bring the point estimate to 0.0 (a bias of 100.0 % of the original estimate). Conversely, unobserved confounders that do not explain more than 13.878 % of the residual variance of both the treatment and the outcome are not strong enough to bring the point estimate to 0.0 .
-- Robustness Value, q = 1.0 , alpha = 0.05 : unobserved confounders (orthogonal to the covariates) that explain more than 7.626 % of the residual variance of both the treatment and the outcome are strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0.0 (a bias of 100.0 % of the original estimate), at the significance level of alpha = 0.05 . Conversely, unobserved confounders that do not explain more than 7.626 % of the residual variance of both the treatment and the outcome are not strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0.0 , at the significance level of alpha = 0.05 .
Bounds on omitted variable bias:
--The table below shows the maximum strength of unobserved confounders with association with the treatment and the outcome bounded by a multiple of the observed explanatory power of the chosen benchmark covariate(s).
bound_label r2dz_x r2yz_dx treatment adjusted_estimate \
0 1x female 0.009164 0.124641 directlyharmed 0.075220
1 2x female 0.018329 0.249324 directlyharmed 0.052915
2 3x female 0.027493 0.374050 directlyharmed 0.030396
adjusted_se adjusted_t adjusted_lower_CI adjusted_upper_CI
0 0.021873 3.438904 0.032283 0.118158
1 0.020350 2.600246 0.012968 0.092862
2 0.018670 1.628062 -0.006253 0.067045
# contour plot for the estimate
darfur_sense.plot()
# contour plot for the t-value
darfur_sense.plot(sensitivity_of = 't-value')
# extreme scenarios plot
darfur_sense.plot(plot_type = 'extreme')
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