incap
Incapacitation: crime rate, share prevented and the marginal year
incap(lam, q, s, share = NULL)crimlab.incap(lam, q, s, share=None)crimlab incap --lam VALUE --q VALUE --s VALUE [--share VALUE]An offender commits crimes at rate lam a year while free, and each crime
leads to a custodial sentence of s years with probability q. Over a
career the crime rate is lam / (1 + lam q s): the share of offending
prevented, lam q s / (1 + lam q s), never reaches 1, longer or surer
sentences lower the rate, and one more year of sentence prevents
lam^2 q / ((1 + lam q s) (1 + lam q (s + 1))) crimes a year, less for
each year added. A sentence uniform across offenders prevents a larger
share of the offending of those with the higher rate. The model holds
the rate fixed over the career and replaces nobody; see incapr() for
both. See proof("incap").
Parameters
Section titled “Parameters”lamOffending rates while free (crimes a year): positive numbers, one per group, as a numeric vector, a 1-d table, a list of single numbers or a one-row data frame.
qThe chance a crime leads to a custodial sentence: numbers in the interval from 0 (excluded) to 1, recycled to the length of
lam; one per group, in the forms oflamand matched to it by name when both are named (unnamed, by position: only names protect against a mismatch).sSentence lengths in years: non-negative numbers, recycled; one per group, in the forms of
lam, matched by name.shareNULL, or one non-negative population share per group, summing to 1, in the forms oflam, matched by name.
Returns
Section titled “Returns”A data frame with one row per group: group, lam, q, s,
rate (the long-run crime rate), prev (the share prevented) and
marg (the crimes a year one more year of sentence prevents). With
share, a last row all holds the weighted free rate in lam, the
weighted rate in rate and the share of all offending prevented in
prev.
References
Section titled “References”Avi-Itzhak, B. and Shinnar, R. (1973). Quantitative models in crime control. Journal of Criminal Justice, 1(3), 185-217. doi:10.1016/0047-2352(73)90061-5
Examples
Section titled “Examples”incap(lam = c(low = 2, high = 10), q = 0.1, s = 1, share = c(0.8, 0.2))Generated from the R help page: incap in the R reference.