adjusted_critical_value: Bias-adjusted critical values

In chadhazlett/sensemakr: Sensitivity Analysis Tools for Regression Models

Bias-adjusted critical values

Description

These functions compute bias adjusted critical values for a given postulated strength of omitted variable with the dependent and independent variables of an OLS regression.

Researchers can thus easily perform sensitivity analysis by simply substituting traditional thresholds with bias-adjusted thresholds, when testing a particular null hypothesis, or when constructing confidence intervals.

Usage

adjusted_critical_value(r2dz.x, r2yz.dx, dof, alpha = 0.05, max = T)

Arguments

r2dz.x	hypothetical partial R2 of unobserved confounder Z with treatment D, given covariates X.
r2yz.dx	hypothetical partial R2 of unobserved confounder Z with outcome Y, given covariates X and treatment D.
dof	residual degrees of freedom of the regression.
alpha	significance level. Default is '0.05'.
max	if 'TRUE' (default) it computes the worst possible adjusted critical threshold for an omitted variable with strength limited by 'r2dz.x' and 'r2yz.dx'.

Value

Numeric vector with bias-adjusted critical values.

References

Cinelli, C. and Hazlett, C. (2020), "Making Sense of Sensitivity: Extending Omitted Variable Bias." Journal of the Royal Statistical Society, Series B (Statistical Methodology).

Cinelli, C. and Hazlett, C. (2023), "An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables."

Examples

# traditional critical threshold (no confounding) is 1.96 (dof = 1e4)
adjusted_critical_value(r2dz.x = 0, r2yz.dx = 0, dof = 1e4, alpha = 0.05)

# adjusted critical threshold, r2 = 1% is 2.96 (dof = 1e4)
adjusted_critical_value(r2dz.x = 0.01, r2yz.dx = 0.01, dof = 1e4, alpha = 0.05)

chadhazlett/sensemakr documentation built on Dec. 12, 2023, 11:20 a.m.