The print and summary methods provide verbal descriptions of the sensitivity analysis results
obtained with the function sensemakr. The function ovb_minimal_reporting provides
latex or html code for a minimal
sensitivity analysis reporting, as suggested in Cinelli and Hazlett (2020).
an object of class sensemakr.
minimal number of significant digits.
arguments passed to other methods.
an object of class sensemakr.
if `TRUE`, the function prints the LaTeX code with cat
code format to print, either latex or html. The default html version
has some mathematical content that requires mathjax or equivalent library to parse.
If you need only html, use the option "pure_html".
The function ovb_minimal_reporting returns the LaTeX/HTML code invisibly in character form and also prints with
cat the LaTeX code. To suppress automatic printing, set verbose = FALSE.
Cinelli, C. and Hazlett, C. (2020), "Making Sense of Sensitivity: Extending Omitted Variable Bias." Journal of the Royal Statistical Society, Series B (Statistical Methodology).
# 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)
# print
sensitivity
#> Sensitivity Analysis to Unobserved Confounding
#>
#> Model Formula: peacefactor ~ directlyharmed + age + farmer_dar + herder_dar +
#> pastvoted + hhsize_darfur + female + village
#>
#> Null hypothesis: q = 1 and reduce = TRUE
#>
#> Unadjusted Estimates of ' directlyharmed ':
#> Coef. estimate: 0.09732
#> Standard Error: 0.02326
#> t-value: 4.18445
#>
#> Sensitivity Statistics:
#> Partial R2 of treatment with outcome: 0.02187
#> Robustness Value, q = 1 : 0.13878
#> Robustness Value, q = 1 alpha = 0.05 : 0.07626
#>
#> For more information, check summary.
# summary
summary(sensitivity)
#> Sensitivity Analysis to Unobserved Confounding
#>
#> Model Formula: peacefactor ~ directlyharmed + age + farmer_dar + herder_dar +
#> pastvoted + hhsize_darfur + female + village
#>
#> Null hypothesis: q = 1 and reduce = TRUE
#> -- This means we are considering biases that reduce the absolute value of the current estimate.
#> -- The null hypothesis deemed problematic is H0:tau = 0
#>
#> Unadjusted Estimates of 'directlyharmed':
#> Coef. estimate: 0.0973
#> Standard Error: 0.0233
#> t-value (H0:tau = 0): 4.1844
#>
#> Sensitivity Statistics:
#> Partial R2 of treatment with outcome: 0.0219
#> Robustness Value, q = 1: 0.1388
#> Robustness Value, q = 1, alpha = 0.05: 0.0763
#>
#> Verbal interpretation of sensitivity statistics:
#>
#> -- Partial R2 of the treatment with the outcome: an extreme confounder (orthogonal to the covariates) that explains 100% of the residual variance of the outcome, would need to explain at least 2.19% of the residual variance of the treatment to fully account for the observed estimated effect.
#>
#> -- Robustness Value, q = 1: unobserved confounders (orthogonal to the covariates) that explain more than 13.88% of the residual variance of both the treatment and the outcome are strong enough to bring the point estimate to 0 (a bias of 100% of the original estimate). Conversely, unobserved confounders that do not explain more than 13.88% of the residual variance of both the treatment and the outcome are not strong enough to bring the point estimate to 0.
#>
#> -- Robustness Value, q = 1, alpha = 0.05: unobserved confounders (orthogonal to the covariates) that explain more than 7.63% of the residual variance of both the treatment and the outcome are strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0 (a bias of 100% of the original estimate), at the significance level of alpha = 0.05. Conversely, unobserved confounders that do not explain more than 7.63% of the residual variance of both the treatment and the outcome are not strong enough to bring the estimate to a range where it is no longer 'statistically different' from 0, at the significance level of alpha = 0.05.
#>
#> Bounds on omitted variable bias:
#>
#> --The table below shows the maximum strength of unobserved confounders with association with the treatment and the outcome bounded by a multiple of the observed explanatory power of the chosen benchmark covariate(s).
#>
#> Bound Label R2dz.x R2yz.dx Treatment Adjusted Estimate Adjusted Se
#> 1x female 0.0092 0.1246 directlyharmed 0.0752 0.0219
#> 2x female 0.0183 0.2493 directlyharmed 0.0529 0.0204
#> 3x female 0.0275 0.3741 directlyharmed 0.0304 0.0187
#> Adjusted T Adjusted Lower CI Adjusted Upper CI
#> 3.4389 0.0323 0.1182
#> 2.6002 0.0130 0.0929
#> 1.6281 -0.0063 0.0670
# prints latex code for minimal sensitivity analysis reporting
ovb_minimal_reporting(sensitivity)
#> \begin{table}[!h]
#> \centering
#> \begin{tabular}{lrrrrrr}
#> \multicolumn{7}{c}{Outcome: \textit{peacefactor}} \\
#> \hline \hline
#> Treatment: & Est. & S.E. & t-value & $R^2_{Y \sim D |{\bf X}}$ & $RV_{q = 1}$ & $RV_{q = 1, \alpha = 0.05}$ \\
#> \hline
#> \textit{directlyharmed} & 0.097 & 0.023 & 4.184 & 2.2\% & 13.9\% & 7.6\% \\
#> \hline
#> df = 783 & & \multicolumn{5}{r}{ \small \textit{Bound (1x female)}: $R^2_{Y\sim Z| {\bf X}, D}$ = 12.5\%, $R^2_{D\sim Z| {\bf X} }$ = 0.9\%} \\
#> \end{tabular}
#> \end{table}