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Rates and disparities when exposure is measured by a proxy

Source: R/pol.R
expbnd.Rd

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").

Usage

expbnd(y, m, gamma, ref = 1)

Arguments

y

Recorded counts by group: positive numbers, as a numeric vector, a 1-d table, a list of single numbers or a one-row data frame.

m

The exposure proxy by group: positive numbers, in the forms of y; named inputs are matched to y by name, unnamed ones by position (only names protect against a mismatch).

gamma

The factor within which true exposure lies around the proxy: one number, at least 1.

ref

The reference group, by name (matched exactly, case included; a factor by its label) or by position in y as given.

Value

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

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

expbnd(y = c(white = 100, black = 300), m = c(1000, 1000), gamma = 1.5)
#>   group   ref rate         lo   hi ratio       rlo  rhi sign
#> 1 white  TRUE  0.1 0.06666667 0.15     1 0.4444444 2.25    0
#> 2 black FALSE  0.3 0.20000000 0.45     3 1.3333333 6.75    1