expbnd
Rates and disparities when exposure is measured by a proxy
expbnd(y, m, gamma, ref = 1)crimlab.expbnd(y, m, gamma, ref=None)crimlab expbnd --y VALUE --m VALUE --gamma VALUE [--ref VALUE]Recorded counts (stops, searches, uses of force) are rates per unit of
exposure to police, and exposure is seldom observed. If each group’s true
exposure lies within a factor gamma of an observed proxy (residents,
drivers on the road, calls for service), each group’s true rate lies
within a factor gamma of its proxy rate, and the ratio of two groups’
true rates within a factor gamma^2 of the proxy ratio. The direction of
a disparity is settled only when the proxy ratio lies outside that band.
See proof("expbnd").
Parameters
Section titled “Parameters”yRecorded counts by group: positive numbers, as a numeric vector, a 1-d table, a list of single numbers or a one-row data frame.
mThe exposure proxy by group: positive numbers, in the forms of
y; named inputs are matched toyby name, unnamed ones by position (only names protect against a mismatch).gammaThe factor within which true exposure lies around the proxy: one number, at least 1.
refThe reference group, by name (matched exactly, case included; a factor by its label) or by position in
yas given.
Returns
Section titled “Returns”A data frame with one row per group, in the order of y:
group, ref (TRUE for the reference group), rate (y / m),
lo and hi (the bounds on the true rate), ratio (the proxy rate
against the reference group), rlo and rhi (the bounds on the true
ratio; every end is reached by some admissible exposure), and sign: 1
when the true ratio exceeds 1 for every admissible exposure, -1 when it
is below 1 for every one, 0 when the data leave it open.
References
Section titled “References”Knox, D., Lowe, W. and Mummolo, J. (2020). Administrative records mask racially biased policing. American Political Science Review, 114(3), 619-637. doi:10.1017/S0003055420000039
Examples
Section titled “Examples”expbnd(y = c(white = 100, black = 300), m = c(1000, 1000), gamma = 1.5)Generated from the R help page: expbnd in the R reference.