Computes the (extreme) robustness value for IV

Computes robustness values for iv_fit objects, adapting the robustness value definitions of sensemakr to instrumental variables as described in Cinelli and Hazlett (2025). For parm = "iv", returns robustness values for the IV estimate; for parm = "fs" or parm = "rf", dispatches to sensemakr methods on the corresponding lm models.

Usage

robustness_value(...)

extreme_robustness_value(...)

xrv(...)

rv(...)

# S3 method for class 'iv_fit'
extreme_robustness_value(
  model,
  parm = "iv",
  q = 1,
  alpha = 0.05,
  min = TRUE,
  ...
)

# S3 method for class 'iv_fit'
robustness_value(model, parm = "iv", q = 1, alpha = 0.05, min = TRUE, ...)

Arguments

...

further arguments passed to or from other methods.

model

an iv_fit model

parm

parameter for which the robustness value is computed. Default is iv, meaning that the robustness value of the IV estimate is computed. Other options are to compute the robustness value of auxiliary estimates, such as the first stage (fs) or the reduced form (rf).

q

percent change of the effect estimate that would be deemed problematic. Default is 1, which means a reduction (increase) of 100% of the current effect estimate (bring estimate to zero). It has to be greater than zero.

alpha

significance level.

min

in many cases, researchers are interested in biases as large or larger than a certain amount (for instance, the strength of confounding to bring a positive estimate to zero or below). Setting min = TRUE (default) computes the robustness value for such cases. Setting min = FALSE computes the robustness value for a bias of exactly q.

Value

A numeric value with the (extreme) robustness value.

References

Cinelli, C. and Hazlett, C. (2025), "An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables." Biometrika. doi:10.1093/biomet/asaf004

Examples

data("card")
y <- card$lwage
d <- card$educ
z <- card$nearc4
x <- model.matrix( ~ exper + expersq + black + south + smsa + reg661 + reg662 +
                     reg663 + reg664 + reg665+ reg666 + reg667 + reg668 + smsa66,
                   data = card)
card.fit <- iv_fit(y, d, z, x)

# robustness value of the IV estimate
rv(card.fit)
#>      iv 
#> 0.00667 
#> Parameters: q >= 1, alpha = 0.05 

# extreme robustness value
xrv(card.fit)
#>       iv 
#> 0.000523 
#> Parameters: q >= 1, alpha = 0.05 

# robustness values for first-stage and reduced-form
rv(card.fit, parm = "fs")
#>     fs 
#> 0.0302 
#> Parameters: q = 1, alpha = 0.05, invert = FALSE 
rv(card.fit, parm = "rf")
#>      rf 
#> 0.00667 
#> Parameters: q = 1, alpha = 0.05, invert = FALSE