ARsensitivity.ci: ARsensitivity.ci

Description

Calculates the confidence interval for the effect of a treatment (endogenous) variable using an instrumental variable, which is based on an extension of Anderson-Rubin test and allows IV be possibly invalid within a certain range.

Usage

ARsensitivity.ci(ivmodel, Delta=NULL, conflevel=.95)

Arguments

ivmodel

Instrumental variable (IV) model fit using ivreg. Make sure to use the option x=TRUE when fitting the ivreg model.

Delta

The allowance of sensitivity parameter for possibly invalid IV. If Delta=NULL, the ARsensitivity.ci function will calculate the confidence interval for a standard Anderson-Rubin test with valid IV.

conflevel

Confidence level for confidence interval.

Value

confidence.interval: Confidence interval for effect of treatment. If it's a 2*2 matrix, the confidence interval is consisted of two disjoint intervals, each row of the matrix is one interval.
printinfo: Report the confidence interval in one printing sentence.
ci.type: If ci.type=1, the confidence interval is finite. If ci.type=2, the confidence interval is infinite. If ci.type=3, the confidence interval is an empty set.

References

Anderson, T.W. and Rubin, H. (1949), Estimation of the parameters of a single equation in a complete system of stochastic equations, Annals of Mathematical Statistics, 20, 46-63. Jiang, Y., Zhang, N. and Small, D. (2013), Sensitivity analysis and power for instrumental variable studies, Working paper.

Examples

Run this code

### a simulated data set
z = rnorm(100)
d = z+rnorm(100)
y = d+0.1*z+rnorm(100)
ivmodel = ivreg(y~d|z, x=TRUE)

### calculate confidence interval, given the allowance of sensitivity is (-0.1, 0.1)
ARsensitivity.ci(ivmodel, Delta=c(-0.1, 0.1))

### calculate confidence interval, assuming that IV is valid
ARsensitivity.ci(ivmodel)