sensemakr (version 0.1.6)

adjusted_critical_value: 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)

Value

Numeric vector with bias-adjusted critical values.

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`.

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)