IV/LATE/CACE Power Analysis

sample size for LATE.R

#  ------------------------------------------------------------------
#  |PROGRAM NAME: sample size for LATE.R
#  |DATE: 1/30/19
#  |CREATED BY: MATT BOGARD 
#  |PROJECT FILE: M:\Matt B\MB Coders Corner  
#  |----------------------------------------------------------------
#  | PURPOSE: sample size and power calculations for LATE in instrumental variables analysis
#  |----------------------------------------------------------------
# based on: Kirk Bansak. "A Generalized Framework for the Estimation of Causal Moderation Effects with
# Randomized Treatments and Non-Randomized Moderators." (Under Review) https://arxiv.org/pdf/1610.08580.pdf


# conservative N LATE Power Analysis (p.21 in Bansak 2017 using formulas on p. 19)

M <- qnorm(1-.05/2) + qnorm(.8) # multiplier
pi <- .63 # compliance rate 
p <- .67  # treatment assignment probability
k <- .10 # effect size

# Nlow <- (M^2*(1+.25*k^2 -k))/(p*(1-p)*k^2*pi^2)
Nhigh <- (M^2*(1+.25*k^2 + k))/(p*(1-p)*k^2*pi^2)
print(Nhigh)


Nstar  <-(M^2*(1+.25*k^2))/(p*(1-p)*k^2*pi^2)
print(Nstar)