pidoutcomes: Partial Identification of Conditional Expectations with...

In gabrielfgm/rbounds: rbounds: Bounds Estimators for Partially Identified Parameters

Description

pidoutcomes computes the upper and lower bounds on the conditional expectation function when there are missing outcomes. It only works for a dependent variable scaled such that y \in (0,1). It is based on the work of Manski (2007). Assume we want to estimate

P(y|x) = P(y|x,z=1)P(z=1|x) + P(y|x,z=0)P(z=0|x),

where z is a binary variable indicating missingness and y is a binary outcome. All of the quantities are identifiable from the data apart from P(y|x,z=0) which is by definition unobservable. However, this missing quantity cannot be less than zero or greater than one so the absolute bounds on the conditional probability are

P(y|x,z=1)P(z=1|x) ≤ P(y|x) ≤ P(y|x,z=1)P(z=1|x) + P(z=0|x).

pidoutcomes() computes these upper and lower bounds.

Usage

pidoutcomes(outformula, z, data, alpha = 0.95, ...)

Arguments

outformula	A formula
z	A column from your data that indicates missing outcomes, must be 0 or 1
data	Your data
alpha	The alpha significance level for the CI. Default is alpha=.95
...	Other arguments accepted by npreg

Details

We also compute confidence intervals based on Manski and Imbens (2004). We focus on intervals that are guaranteed to cover the parameter at the specified level, rather than intervals that are guaranteed to cover the bounds at the specified level.

Value

The function returns a list of 4 values: lower_ci, lower, upper and upper_ci, each a vector of length nrow(data). These are the lower and upper confidence intervals on the location of the parameter (as described in Manski and Imbens (2004)), and the estimated lower and upper bounds of the partially identified conditional mean

Examples

#' N <- 1000
x <- rnorm(N)
e <- rnorm(N)
y <- as.numeric(2*x + e > 0)
z <- rbinom(N, 1, .75)
y_obs <- z*y
df <- data.frame(y_obs, x, z)
m1 <- pidoutcomes(y_obs ~ x, z, df)
m1

gabrielfgm/rbounds documentation built on May 8, 2019, 8:09 a.m.