Recorded counts from true counts through a recording matrix

A police service turns true offence counts c (one per category) into recorded counts M %*% c, where M[i, j] is the share of true category-j offences recorded as category i. If every column of M sums to one (pure re-classification, e.g. robbery recorded as theft) the recorded total equals the true total (Research.P9.total_invariant_of_colStochastic): downgrading is invisible in totals and visible only in category ratios. If columns sum to less than one (offences "cuffed" out of the notifiable set) the total falls by exactly the dropped mass (Research.P9.total_le_of_colSubstochastic).

Usage

morie_recording_map(M, counts)

Arguments

M: Square non-negative matrix with column sums at most one.
counts: True counts per category (length ncol(M)).

Value

A list with recorded, true_total, recorded_total, dropped (per category and total), regime ("reclassification" when every column sums to one, "cuffing" otherwise), ratio_true and ratio_recorded (each category over the first) and theorems.

Examples

M <- rbind(c(0.7, 0), c(0.3, 1))          # 30 percent of robberies recorded as theft
rownames(M) <- colnames(M) <- c("robbery", "theft")
morie_recording_map(M, c(robbery = 100, theft = 400))
#> $recorded
#> robbery   theft 
#>      70     430 
#> 
#> $true_total
#> [1] 500
#> 
#> $recorded_total
#> [1] 500
#> 
#> $dropped
#> $dropped$by_category
#> robbery   theft 
#>       0       0 
#> 
#> $dropped$total
#> [1] 0
#> 
#> 
#> $regime
#> [1] "reclassification"
#> 
#> $ratio_true
#> robbery   theft 
#>       1       4 
#> 
#> $ratio_recorded
#>  robbery    theft 
#> 1.000000 6.142857 
#> 
#> $theorems
#> [1] "Research.P9.total_invariant_of_colStochastic"
#> [2] "Research.P9.total_le_of_colSubstochastic"    
#>