generateBounds: Compute bounds and summary statistics according to Jiang et...

In eiPartialID: Ecological Regression with Partial Identification

Description

generateBounds() calculates district-level bounds. The returned object can be passed to evaluateBounds() to generate bounds across varying coverage probabilities and to apply the heuristics presented in Jiang et al. 2019.

Usage

generateBounds(x, t, n, trueBetaB = NULL, useXRangeOffset = TRUE,
  returnAdditionalStats = FALSE, printSummary = TRUE)

Arguments

x	Numeric (double-precision) vector. Contains the proportion of variable X in each precinct (or analagous geographic unit)
t	Numeric (double-precision) vector. Contains the proportion of variable T in each precinct (or analagous geographic unit)
n	Numeric (double-precision) vector. Contains the number of elements (people/households/etc.) in each precinct (or analagous geographic unit)
trueBetaB	Numeric (double-precision) vector. Contains the true conditional values (beta_i) in each precinct (or analagous geographic unit). Optional. Default NULL.
useXRangeOffset	boolean If True, an offset of 0.00001 is applied to l and u to avoid division by 0 in subsequent calculations. Default TRUE
returnAdditionalStats	boolean If True, additional summary statistics are generated. Default FALSE.
printSummary	boolean If True, the DD bounds, l and u, CI_0, CI_1, width-ratio, and (optionally) true district B are output to standard out. Default TRUE.

Value

List object with the bounds and summary statistics:

nx1 Total elements (people/households/etc.) of variable X across all geographic units

hbdl0 CI_0 lower bound

hbdu0 CI_0 upper bound

cil CI_1 lower bound

cir CI_1 upper bound

bdl Duncan-Davis lower bound

bdu Duncan-Davis upper bound

Optional: bd True district Beta

Examples

library("MASS")
library("eco")
data("census")
inputDataSet <- census
x <- inputDataSet$X
t <- inputDataSet$Y
n <- inputDataSet$N
trueBetaB <- inputDataSet$W1
outputList <- generateBounds(x, t, n, trueBetaB=trueBetaB, useXRangeOffset=TRUE,
    returnAdditionalStats=FALSE, printSummary=TRUE)

# True B: 0.674809
# Duncan-Davis bounds: [0.535618, 0.974010]
# [l,u]=[min(X_i),max(X_i)]: [0.050810, 0.939290]
# CI_0=[Bl_hat, Bu_hat]: [0.606101, 0.810082]
# CI_1: [0.572566, 0.842403]
# Width-ratio: |CI_0|/|DD|: 0.465295

eiPartialID documentation built on May 2, 2019, 4:18 a.m.