Two recording regimes from one recorded series

A recorded vector alone cannot say whether it came from pure re-classification or from cuffing: the same series is produced by the identity map on true counts equal to the series and by the map \((1-\epsilon) I\) on true counts \(r/(1-\epsilon)\), whose true total is larger (Research.P9.regimes_not_identified). A second source that fixes the true total separates the two: re-classification reproduces the total exactly, cuffing a positive share records strictly less (Research.P9.second_source_separates).

Usage

morie_recording_regimes(recorded, cuffed_share = 0.1, true_total = NULL)

Arguments

recorded

Non-negative recorded counts per category.

cuffed_share

The share \(\epsilon\) in (0, 1) used for the cuffing construction.

true_total

Optional true total from a second source (a victimisation survey, an audit). When given, the regime the pair of numbers allows is reported.

Value

A list with recorded_total, two constructions (reclassification and cuffing, each with M, counts and true_total), identified_from_series (always FALSE), second_source (NULL, or the regime, the dropped mass and whether the pair is consistent) and theorems.

Examples

r <- c(robbery = 70, theft = 430)
two <- morie_recording_regimes(r, cuffed_share = 0.2)
two$reclassification$true_total; two$cuffing$true_total
#> [1] 500
#> [1] 625
morie_recording_regimes(r, true_total = 550)$second_source
#> $true_total
#> [1] 550
#> 
#> $dropped_mass
#> [1] 50
#> 
#> $regime
#> [1] "cuffing"
#> 
#> $consistent
#> [1] TRUE
#>