Skip to content
CRIMLAB

sntbnd

Bounds on a sentence’s effect without assumptions

sntbnd(y, z, treat = NULL, w = NULL)

Each person receives one of two sentences and shows the outcome (say, reconviction) under that one only. With no assumption about who receives which, the chance of the outcome under a sentence is known only up to an interval whose width is the share who received the other sentence, and the effect of one sentence against the other lies in an interval of width exactly 1 that always contains 0: observational data alone cannot even sign it. See proof("sntbnd").

Parameters

Section titled “Parameters”
y

Outcomes: 0 or 1 for each person.

z

Sentences: a vector with exactly two distinct values, same length: character, numbers, logical or a factor (its labels; level order and whether it is ordered are ignored), not dates nor a labelled vector of codes. When y, z (and w) are all named with unique names, they are matched by name.

treat

The value of z taken as the treatment, matched exactly. NULL is allowed only where the treatment is explicit in z: TRUE for a logical z, 1 for a z of 0 and 1; otherwise it must be given, since a treatment chosen by sorting the values would be arbitrary.

w

NULL for equal weights, or one non-negative weight per person with a positive total.

Returns

Section titled “Returns”

A data frame with three rows, the comparison sentence, the treatment and effect (treatment minus comparison): term, share (the weighted share sentenced; NA for the effect), lower, upper and observed (the observed rate under each sentence and their difference).

References

Section titled “References”

Manski, C. F. and Nagin, D. S. (1998). Bounding disagreements about treatment effects: a case study of sentencing and recidivism. Sociological Methodology, 28(1), 99-137. doi:10.1111/0081-1750.00043

Examples

Section titled “Examples”
set.seed(1)
z <- sample(c("community", "custody"), 500, TRUE, c(0.6, 0.4))
y <- rbinom(500, 1, ifelse(z == "custody", 0.55, 0.35))
sntbnd(y, z, treat = "custody")

Generated from the R help page: sntbnd in the R reference.