Breakdown analysis for a dark-figure conclusion — morie_dark_figure

How much survey under-reporting would it take to overturn "the true victimisation rate is below threshold"? The conclusion holds for every admissible noise pair while the under-reporting box \(\bar\beta\) stays below \(1 - v_{obs}/t\) (Research.P1.conclusion_holds_below_breakdown); at or above that value there is an admissible noise pair with a true rate of at least threshold (Research.P1.conclusion_fails_above_breakdown). Report the breakdown value next to the interval so a reader can judge whether the required under-reporting is plausible.

Usage

morie_dark_figure_breakdown(v_obs, threshold)

Arguments

v_obs: Survey victimisation rate in (0, 1].
threshold: The rate the conclusion claims is not reached; above v_obs.

Value

A list with breakdown_beta_max (\(1 - v_{obs}/t\)), the ratio \(t/v_{obs}\) of the threshold to the survey rate, and theorems.

Examples

# survey 6 percent; does the true rate stay below 10 percent?
morie_dark_figure_breakdown(0.06, threshold = 0.10)   # only if under-reporting < 40 percent
#> $breakdown_beta_max
#> [1] 0.4
#> 
#> $ratio
#> [1] 1.666667
#> 
#> $theorems
#> [1] "Research.P1.conclusion_holds_below_breakdown"
#> [2] "Research.P1.conclusion_fails_above_breakdown"
#>