Robustness of an inference: percent bias to invalidate, RIR and ITCV

With the threshold estimate delta# = t_crit * se, Frank et al give the percent bias to invalidate an inference and the equivalent number of cases that would have to be replaced (RIR). Frank (2000) gives the impact threshold for a confounding variable: an omitted variable correlated sqrt(ITCV) with both the predictor and the outcome would exactly overturn the inference. Degrees of freedom follow the reference implementation of these indices, df = n - n_covariates - 3.

Usage

Konfound(est, se, n, threshold, n_covariates = 0)

Arguments

est: Unstandardised coefficient.
se: Its standard error.
n: Sample size.
threshold: Two-sided significance level alpha.
n_covariates: Number of covariates besides the focal predictor.

Value

List with estimate (percent bias), pct_bias, rir, rir_cases, delta_threshold, t, t_crit, r_xy, r_crit, itcv, r_cv, impact, df, significant, n, method.

Details

Formula: pct = 100 (1 - delta#/|est|); RIR = n (1 - delta#/|est|); ITCV = (|r_xy| - r#)/(1 - r#) with r# = t_crit/sqrt(t_crit^2 + df).

References

Frank, Maroulis, Duong and Kelcey (2013), What would it take to change an inference?, Educational Evaluation and Policy Analysis 35(4):437-460, doi:10.3102/0162373713493129 ; Frank (2000), Impact of a confounding variable on a regression coefficient, Sociological Methods and Research 29(2):147-194. doi:10.1177/0049124100029002001

Examples

Konfound(est = 5L, se = 5L, n = 5L, threshold = 0.5)
#> $estimate
#> [1] 18.35034
#> 
#> $pct_bias
#> [1] 18.35034
#> 
#> $rir
#> [1] 0.9175171
#> 
#> $rir_cases
#> [1] 0
#> 
#> $delta_threshold
#> [1] 4.082483
#> 
#> $t
#> [1] 1
#> 
#> $t_crit
#> [1] 0.8164966
#> 
#> $r_xy
#> [1] 0.5773503
#> 
#> $r_crit
#> [1] 0.5
#> 
#> $itcv
#> [1] 0.1547005
#> 
#> $r_cv
#> [1] 0.3933199
#> 
#> $impact
#> [1] 0.1547005
#> 
#> $df
#> [1] 2
#> 
#> $significant
#> [1] 1
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "Frank et al (2013) percent bias / RIR and Frank (2000) ITCV"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"