The identification region of a proportion under nonresponse

With reporting (or response) rate r and observed share p_obs among those who report, the population proportion lies in \([r p_{obs},\; r p_{obs} + 1 - r]\), both ends attained (Research.P1.Nonresponse.region_sharp), of width exactly \(1 - r\) (region_width). With \(r = 0.106\) the region has width 0.894.

Usage

morie_nonresponse_region(p_obs, r)

Arguments

p_obs

Observed share among reporters, in \([0, 1]\).

r

Reporting rate, in \([0, 1]\); recycled against p_obs.

Value

A data frame: p_obs, r, lower, upper, width.

References

Manski CF (2003). Partial Identification of Probability Distributions, ch. 2 eq. 2.4. Springer. Lohr SL (2019). Sampling: Design and Analysis, 2nd ed., section 8.1. CRC.

Examples

morie_nonresponse_region(p_obs = 0.4, r = c(0.106, 0.5, 0.9))
#>   p_obs     r  lower  upper width
#> 1   0.4 0.106 0.0424 0.9364 0.894
#> 2   0.4 0.500 0.2000 0.7000 0.500
#> 3   0.4 0.900 0.3600 0.4600 0.100