install.packages("konfound")

install.packages("devtools")
devtools::install_github("konfound-project/konfound")

library(konfound)
#> Sensitivity analysis as described in Frank, 
#> Maroulis, Duong, and Kelcey (2013) and in 
#> Frank (2000).
#> For more information visit http://konfound-it.com.

pkonfound(est_eff = 2, 
          std_err = .4, 
          n_obs = 100, 
          n_covariates = 3)
#> Robustness of Inference to Replacement (RIR):
#> RIR = 60
#> 
#> To invalidate the inference of an effect using the threshold of 0.794 for
#> statistical significance (with null hypothesis = 0 and alpha = 0.05), 60.295%
#> of the (2) estimate would have to be due to bias. This implies that to
#> invalidate the inference one would expect to have to replace 60 (60.295%)
#> observations with data points for which the effect is 0 (RIR = 60).
#> 
#> See Frank et al. (2013) for a description of the method.
#> 
#> Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
#> What would it take to change an inference?
#> Using Rubin's causal model to interpret the robustness of causal inferences.
#> Education, Evaluation and Policy Analysis, 35 437-460.
#> 
#> Accuracy of results increases with the number of decimals reported.
#> For other forms of output, run
#>           ?pkonfound and inspect the to_return argument
#> For models fit in R, consider use of konfound().
pkonfound(est_eff = 2, 
          std_err = .4, 
          n_obs = 100, 
          n_covariates = 3, 
          index = "IT")
#> Impact Threshold for a Confounding Variable (ITCV):
#> 
#> The minimum impact of an omitted variable to invalidate an inference for
#> a null hypothesis of an effect of nu (0) is based on a correlation of 0.566
#> with the outcome and 0.566 with the predictor of interest (conditioning
#> on all observed covariates in the model; signs are interchangeable). This is
#> based on a threshold effect of 0.2 for statistical significance (alpha = 0.05).
#> 
#> Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be 
#> 0.566 X 0.566 = 0.321 to invalidate an inference for a null hypothesis of an effect of nu (0).
#> 
#> For calculation of unconditional ITCV using pkonfound(), additionally include
#> the R2, sdx, and sdy as input, and request raw output.
#> 
#> See Frank (2000) for a description of the method.
#> 
#> Citation:
#> Frank, K. (2000). Impact of a confounding variable on the inference of a
#> regression coefficient. Sociological Methods and Research, 29 (2), 147-194
#> 
#> Accuracy of results increases with the number of decimals reported.
#> 
#> The ITCV analysis was originally derived for OLS standard errors. If the
#> standard errors reported in the table were not based on OLS, some caution
#> should be used to interpret the ITCV.
#> For other forms of output, run
#>           ?pkonfound and inspect the to_return argument
#> For models fit in R, consider use of konfound().

m1 <- lm(mpg ~ wt + disp, data = mtcars)
m1
#> 
#> Call:
#> lm(formula = mpg ~ wt + disp, data = mtcars)
#> 
#> Coefficients:
#> (Intercept)           wt         disp  
#>    34.96055     -3.35083     -0.01772
summary(m1)
#> 
#> Call:
#> lm(formula = mpg ~ wt + disp, data = mtcars)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -3.4087 -2.3243 -0.7683  1.7721  6.3484 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) 34.96055    2.16454  16.151 4.91e-16 ***
#> wt          -3.35082    1.16413  -2.878  0.00743 ** 
#> disp        -0.01773    0.00919  -1.929  0.06362 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 2.917 on 29 degrees of freedom
#> Multiple R-squared:  0.7809, Adjusted R-squared:  0.7658 
#> F-statistic: 51.69 on 2 and 29 DF,  p-value: 2.744e-10

konfound(m1, wt)
#> Robustness of Inference to Replacement (RIR):
#> RIR = 9
#> 
#> To invalidate the inference of an effect using the threshold of -2.381 for
#> statistical significance (with null hypothesis = 0 and alpha = 0.05), 28.946%
#> of the (-3.351) estimate would have to be due to bias. This implies that to
#> invalidate the inference one would expect to have to replace 9 (28.946%)
#> observations with data points for which the effect is 0 (RIR = 9).
#> 
#> See Frank et al. (2013) for a description of the method.
#> 
#> Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. (2013).
#> What would it take to change an inference?
#> Using Rubin's causal model to interpret the robustness of causal inferences.
#> Education, Evaluation and Policy Analysis, 35 437-460.
#> 
#> Accuracy of results increases with the number of decimals reported.
#> NULL

konfound(m1, wt, index = "IT")
#> Impact Threshold for a Confounding Variable (ITCV):
#> 
#> The minimum (in absolute value) impact of an omitted variable to invalidate
#> an inference for a null hypothesis of an effect of nu (0) is based on
#> a correlation of -0.425 with the outcome and 0.425 with the predictor of
#> interest (conditioning on all observed covariates in the model; signs are
#> interchangeable). This is based on a threshold effect of -0.355 for statistical
#> significance (alpha = 0.05).
#> 
#> Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be
#> -0.425 X 0.425 = -0.18 to invalidate an inference for a null hypothesis of an effect of nu (0).
#> 
#> See Frank (2000) for a description of the method.
#> 
#> Citation:
#> Frank, K. (2000). Impact of a confounding variable on the inference of a
#> regression coefficient. Sociological Methods and Research, 29 (2), 147-194
#> 
#> Accuracy of results increases with the number of decimals reported.
#> 
#> The ITCV analysis was originally derived for OLS standard errors. If the
#> standard errors reported in the table were not based on OLS, some caution
#> should be used to interpret the ITCV.
#> NULL

mkonfound_ex
#> # A tibble: 30 × 2
#>         t    df
#>     <dbl> <dbl>
#>  1  7.08    178
#>  2  4.13    193
#>  3  1.89     47
#>  4 -4.17    138
#>  5 -1.19     97
#>  6  3.59     87
#>  7  0.282   117
#>  8  2.55     75
#>  9 -4.44    137
#> 10 -2.05    195
#> # ℹ 20 more rows
mkonfound(mkonfound_ex, t, df)
#> # A tibble: 30 × 7
#>         t    df action        inference      pct_bias_to_change_i…¹   itcv r_con
#>     <dbl> <dbl> <chr>         <chr>                           <dbl>  <dbl> <dbl>
#>  1  7.08    178 to_invalidate reject_null                     68.8   0.378 0.614
#>  2  4.13    193 to_invalidate reject_null                     50.6   0.168 0.41 
#>  3  1.89     47 to_sustain    fail_to_rejec…                   5.47 -0.012 0.11 
#>  4 -4.17    138 to_invalidate reject_null                     50.3   0.202 0.449
#>  5 -1.19     97 to_sustain    fail_to_rejec…                  39.4  -0.065 0.255
#>  6  3.59     87 to_invalidate reject_null                     41.9   0.19  0.436
#>  7  0.282   117 to_sustain    fail_to_rejec…                  85.5  -0.131 0.361
#>  8  2.55     75 to_invalidate reject_null                     20.6   0.075 0.274
#>  9 -4.44    137 to_invalidate reject_null                     53.0   0.225 0.475
#> 10 -2.05    195 to_invalidate reject_null                      3.51  0.006 0.077
#> # ℹ 20 more rows
#> # ℹ abbreviated name: ¹​pct_bias_to_change_inference