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).
# S3 method for sensemakr print(x, digits = max(3L, getOption("digits") - 2L), ...) # S3 method for sensemakr summary(object, digits = max(3L, getOption("digits") - 3L), ...) ovb_minimal_reporting( x, digits = 3, verbose = TRUE, format = c("latex", "html", "pure_html"), ... )
| x | an object of class |
|---|---|
| digits | minimal number of significant digits. |
| ... | arguments passed to other methods. |
| object | an object of class |
| verbose | if `TRUE`, the function prints the LaTeX code with |
| format | code format to print, either |
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.#> 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}