Estimate Bias

Returns the bias based on the different parameters in the bias decomposition

Usage

estimate_bias(rho, R2, weights, sigma2)

Arguments

rho

Correlation between the error in the weights and outcome

R2

R2 measure for how much variation in the true weights is explained by the error term, must be bound on the range [0,1)

weights

Vector of estimated weights

sigma2

Estimated variance of the outcome (i.e., stats::var(Y) for obervational setting; stats::var(tau) for generalization setting)

Value

Estimated bias from omitting a confounder from weights

Examples

set.seed(331)
Y = rnorm(1000)
weights = rlogis(1000)
weights = weights/mean(weights)
estimate_bias(rho = 0.5, R2 = 0.5, weights = weights, sigma2 = var(Y))
#> [1] 40.30893