The age-crime curve of a mixture of offender types

The aggregate age-crime curve is the share-weighted mean of the curves of latent types (adolescence-limited, life-course persistent, and so on), and one aggregate curve fits many mixtures: the aggregate alone cannot tell one type from several (Moffitt 1993; Gottfredson and Hirschi 1990). What does tell them apart is the covariance of an individual's offending at two ages: with one type it is 0 (given the type, ages are independent), with several it is the covariance across types of their curves at the two ages, which cov gives for every pair of ages. With a panel of individuals observed at two ages, the observed covariance and its permutation test say whether one type is enough. See proof("agemix").

Usage

agemix(
  curves = NULL,
  shares = NULL,
  ages = NULL,
  panel = NULL,
  nperm = 2000,
  seed = NULL
)

Arguments

curves: NULL, or the curves of the types: a numeric matrix or a data frame, one row per age and one column per type (at most 30).
shares: The share of each type: numbers from 0 that sum to 1.
ages: NULL (1, 2, ...) or the age of each row of curves.
panel: NULL, or the outcomes of individuals at two ages: a numeric matrix or data frame of two columns, at least three rows.
nperm: The number of permutations of the second age's outcomes for the panel test: a whole number from 0.
seed: NULL (the draws follow set.seed()) or a whole number from 0.

Value

An object of class agemix, a list: curve (age, agg the aggregate, then the types' curves; with curves), cov (the covariance across types between ages, a matrix named by age; with curves) and panel (cov, p the permutation p-value, NA without permutations, n, nperm; with panel); the parts not asked for are NULL.

References

Moffitt, T. E. (1993). Adolescence-limited and life-course-persistent antisocial behavior: a developmental taxonomy. Psychological Review, 100(4), 674-701. doi:10.1037/0033-295X.100.4.674

Examples

ages <- 12:30
al <- dnorm(ages, 17, 2)
lcp <- rep(0.08, length(ages))
r <- agemix(cbind(al = al, lcp = lcp), c(0.8, 0.2), ages)
r$cov["15", "25"]
#> [1] -0.0005241738