adjusted_estimate function

Bias-adjusted estimates, standard-errors, t-values and confidence intervals

These functions compute bias adjusted estimates (adjusted_estimate), standard-errors (adjusted_se) and t-values (adjusted_t), given a hypothetical strength of the confounder in the partial R2 parameterization.

The functions work either with an lm object, or directly passing in numerical inputs, such as the current coefficient estimate, standard error and degrees of freedom.

adjusted_estimate(...)

## S3 method for class 'lm'
adjusted_estimate(model, treatment, r2dz.x, r2yz.dx, reduce = TRUE, ...)

## S3 method for class 'fixest'
adjusted_estimate(model, treatment, r2dz.x, r2yz.dx, reduce = TRUE, ...)

## S3 method for class 'numeric'
adjusted_estimate(estimate, se, dof, r2dz.x, r2yz.dx, reduce = TRUE, ...)

adjusted_se(...)

## S3 method for class 'numeric'
adjusted_se(se, dof, r2dz.x, r2yz.dx, ...)

## S3 method for class 'lm'
adjusted_se(model, treatment, r2dz.x, r2yz.dx, ...)

## S3 method for class 'fixest'
adjusted_se(model, treatment, r2dz.x, r2yz.dx, message = TRUE, ...)

adjusted_ci(...)

## S3 method for class 'lm'
adjusted_ci(
  model,
  treatment,
  r2dz.x,
  r2yz.dx,
  which = c("both", "lwr", "upr"),
  reduce = TRUE,
  alpha = 0.05,
  ...
)

## S3 method for class 'fixest'
adjusted_ci(
  model,
  treatment,
  r2dz.x,
  r2yz.dx,
  which = c("both", "lwr", "upr"),
  reduce = TRUE,
  alpha = 0.05,
  message = T,
  ...
)

## S3 method for class 'numeric'
adjusted_ci(
  estimate,
  se,
  dof,
  r2dz.x,
  r2yz.dx,
  which = c("both", "lwr", "upr"),
  reduce = TRUE,
  alpha = 0.05,
  ...
)

adjusted_t(...)

## S3 method for class 'lm'
adjusted_t(model, treatment, r2dz.x, r2yz.dx, reduce = TRUE, h0 = 0, ...)

## S3 method for class 'fixest'
adjusted_t(
  model,
  treatment,
  r2dz.x,
  r2yz.dx,
  reduce = TRUE,
  h0 = 0,
  message = T,
  ...
)

## S3 method for class 'numeric'
adjusted_t(estimate, se, dof, r2dz.x, r2yz.dx, reduce = TRUE, h0 = 0, ...)

adjusted_partial_r2(...)

## S3 method for class 'numeric'
adjusted_partial_r2(
  estimate,
  se,
  dof,
  r2dz.x,
  r2yz.dx,
  reduce = TRUE,
  h0 = 0,
  ...
)

## S3 method for class 'lm'
adjusted_partial_r2(
  model,
  treatment,
  r2dz.x,
  r2yz.dx,
  reduce = TRUE,
  h0 = 0,
  ...
)

## S3 method for class 'fixest'
adjusted_partial_r2(
  model,
  treatment,
  r2dz.x,
  r2yz.dx,
  reduce = TRUE,
  h0 = 0,
  ...
)

bias(...)

## S3 method for class 'numeric'
bias(se, dof, r2dz.x, r2yz.dx, ...)

## S3 method for class 'lm'
bias(model, treatment, r2dz.x, r2yz.dx, ...)

## S3 method for class 'fixest'
bias(model, treatment, r2dz.x, r2yz.dx, ...)

relative_bias(...)

## S3 method for class 'lm'
relative_bias(model, treatment, r2dz.x, r2yz.dx, ...)

## S3 method for class 'fixest'
relative_bias(model, treatment, r2dz.x, r2yz.dx, ...)

## S3 method for class 'numeric'
relative_bias(estimate, se, dof, r2dz.x, r2yz.dx, ...)

rel_bias(r.est, est)

Arguments

• ...: arguments passed to other methods.
• model: An lm or fixest object with the outcome regression.
• treatment: A character vector with the name of the treatment variable of the model.
• 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.
• reduce: should the bias adjustment reduce or increase the absolute value of the estimated coefficient? Default is TRUE.
• estimate: Coefficient estimate.
• se: standard error of the coefficient estimate.
• dof: residual degrees of freedom of the regression.
• message: should messages be printed? Default = TRUE.
• which: which limit of the confidence interval to show? Options are "both", lower limit ("lwr") or upper limit ("upr").
• alpha: significance level.
• h0: Null hypothesis for computation of the t-value. Default is zero.
• r.est: restricted estimate. A numerical vector.
• est: unrestricted estimate. A numerical vector.

Returns

Numeric vector with bias, adjusted estimate, standard error, or t-value.

Examples

# loads data
data("darfur")

# fits model
model <- lm(peacefactor ~ directlyharmed + age +
                          farmer_dar + herder_dar +
                           pastvoted + hhsize_darfur +
                           female + village, data = darfur)

# computes adjusted estimate for confounder with  r2dz.x = 0.05, r2yz.dx = 0.05
adjusted_estimate(model, treatment = "directlyharmed", r2dz.x = 0.05, r2yz.dx = 0.05)

# computes adjusted SE for confounder with  r2dz.x = 0.05, r2yz.dx = 0.05
adjusted_se(model, treatment = "directlyharmed", r2dz.x = 0.05, r2yz.dx = 0.05)

# computes adjusted t-value for confounder with  r2dz.x = 0.05, r2yz.dx = 0.05
adjusted_t(model, treatment = "directlyharmed", r2dz.x = 0.05, r2yz.dx = 0.05)

# Alternatively, pass in numerical values directly.
adjusted_estimate(estimate = 0.09731582, se = 0.02325654,
                  dof = 783, r2dz.x = 0.05, r2yz.dx = 0.05)

adjusted_se(estimate = 0.09731582, se = 0.02325654,
            dof = 783, r2dz.x = 0.05, r2yz.dx = 0.05)

adjusted_t(estimate = 0.09731582, se = 0.02325654,
           dof = 783, r2dz.x = 0.05, r2yz.dx = 0.05)

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).