sensemakr {sensemakr}

Sensitivity analysis to unobserved confounders

Description

This function performs sensitivity analysis to omitted variables as discussed in Cinelli and Hazlett (2020). It returns an object of class sensemakr with several pre-computed sensitivity statistics for reporting. After running sensemakr you may directly use the plot, print and summary methods in the returned object.

Usage

sensemakr(...)

## S3 method for class 'lm'
sensemakr(
  model,
  treatment,
  benchmark_covariates = NULL,
  kd = 1,
  ky = kd,
  q = 1,
  alpha = 0.05,
  r2dz.x = NULL,
  r2yz.dx = r2dz.x,
  bound_label = "Manual Bound",
  reduce = TRUE,
  ...
)

## S3 method for class 'fixest'
sensemakr(
  model,
  treatment,
  benchmark_covariates = NULL,
  kd = 1,
  ky = kd,
  q = 1,
  alpha = 0.05,
  r2dz.x = NULL,
  r2yz.dx = r2dz.x,
  bound_label = "Manual Bound",
  reduce = TRUE,
  ...
)

## S3 method for class 'formula'
sensemakr(
  formula,
  method = c("lm", "feols"),
  vcov = "iid",
  data,
  treatment,
  benchmark_covariates = NULL,
  kd = 1,
  ky = kd,
  q = 1,
  alpha = 0.05,
  r2dz.x = NULL,
  r2yz.dx = r2dz.x,
  bound_label = "",
  reduce = TRUE,
  ...
)

## S3 method for class 'numeric'
sensemakr(
  estimate,
  se,
  dof,
  treatment = "D",
  q = 1,
  alpha = 0.05,
  r2dz.x = NULL,
  r2yz.dx = r2dz.x,
  bound_label = "manual_bound",
  r2dxj.x = NULL,
  r2yxj.dx = r2dxj.x,
  benchmark_covariates = "manual_benchmark",
  kd = 1,
  ky = kd,
  reduce = TRUE,
  ...
)

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.

benchmark_covariates

The user has two options: (i) character vector of the names of covariates that will be used to bound the plausible strength of the unobserved confounders. Each variable will be considered separately; (ii) a named list with character vector names of covariates that will be used, as a group, to bound the plausible strength of the unobserved confounders. The names of the list will be used for the benchmark labels. Note: for factor variables with more than two levels, you need to provide the name of each level as encoded in the fixest model (the columns of model.matrix).

kd

numeric vector. Parameterizes how many times stronger the confounder is related to the treatment in comparison to the observed benchmark covariate. Default value is 1 (confounder is as strong as benchmark covariate).

ky

numeric vector. Parameterizes how many times stronger the confounder is related to the outcome in comparison to the observed benchmark covariate. Default value is the same as kd.

q

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

alpha

significance level.

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.

bound_label

label to bounds provided manually in r2dz.x and r2yz.dx.

reduce

should the bias adjustment reduce or increase the absolute value of the estimated coefficient? Default is TRUE.

formula

an object of the class formula: a symbolic description of the model to be fitted.

method

the default is lm. This argument can be changed to estimate the model using feols. In this case the formula needs to be written so it can be estimated with feols and the package needs to be installed.

vcov

the variance/covariance used in the estimation when using feols. See vcov.fixest for more details. Defaults to "iid".

data

data needed only when you pass a formula as first parameter. An object of the class data.frame containing the variables used in the analysis.

estimate

Coefficient estimate.

se

standard error of the coefficient estimate.

dof

residual degrees of freedom of the regression.

r2dxj.x

partial R2 of covariate Xj with the treatment D (after partialling out the effect of the remaining covariates X, excluding Xj).

r2yxj.dx

partial R2 of covariate Xj with the outcome Y (after partialling out the effect of the remaining covariates X, excluding Xj).

Value

An object of class sensemakr, containing:

info

A data.frame with the general information of the analysis, including the formula used, the name of the treatment variable, parameter values such as q, alpha, and whether the bias is assumed to reduce the current estimate.

sensitivity_stats

A data.frame with the sensitivity statistics for the treatment variable, as computed by the function sensitivity_stats.

bounds

A data.frame with bounds on the strength of confounding according to some benchmark covariates, as computed by the function ovb_bounds.

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).

See Also

The function sensemakr is a convenience function. You may use the other sensitivity functions of the package directly, such as the functions for sensitivity plots (ovb_contour_plot, ovb_extreme_plot) the functions for computing bias-adjusted estimates and t-values (adjusted_estimate, adjusted_t), the functions for computing the robustness value and partial R2 (robustness_value, partial_r2), or the functions for bounding the strength of unobserved confounders (ovb_bounds), among others.

Examples

# loads dataset
data("darfur")

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

# runs sensemakr for sensitivity analysis
sensitivity <- sensemakr(model, treatment = "directlyharmed",
                               benchmark_covariates = "female",
                               kd = 1:3)
# short description of results
sensitivity

# long description of results
summary(sensitivity)

# plot bias contour of point estimate
plot(sensitivity)

# plot bias contour of t-value
plot(sensitivity, sensitivity.of = "t-value")

# plot bias contour of lower limit of CI
plot(sensitivity, sensitivity.of = "lwr")

# plot bias contour of upper limit of CI
plot(sensitivity, sensitivity.of = "upr")

# plot extreme scenario
plot(sensitivity, type = "extreme")

# latex code for sensitivity table
ovb_minimal_reporting(sensitivity)