attrlateweight {causalweight}

Local average treatment effect estimation in multiple follow-up periods with outcome attrition based on inverse probability weighting

Description

Instrumental variable-based evaluation of local average treatment effects using weighting by the inverse of the instrument propensity score.

Usage

attrlateweight(
  y1,
  y2,
  s1,
  s2,
  d,
  z,
  x0,
  x1,
  weightmax = 0.1,
  boot = 1999,
  cluster = NULL
)

Arguments

y1

Outcome variable in the first outcome period.

y2

Outcome variable in the second outcome period.

s1

Selection indicator for first outcome period. Must be one if y1 is observed (non-missing) and zero if y1 is not observed (missing).

s2

Selection indicator for second outcome period. Must be one if y1 is observed (non-missing) and zero if y1 is not observed (missing).

d

Treatment, must be binary (either 1 or 0), must not contain missings.

z

Instrument for the endogenous treatment, must be binary (either 1 or 0), must not contain missings.

x0

Baseline (pre-instrument) confounders of the instrument and outcome, must not contain missings.

x1

Confounders in outcome period 1 (may include outcomes of period 1 y1)

weightmax

Trimming rule based on the maximum relative weight a single observation may obtain in estimation - observations with higher weights are discarded. Default is 0.1 (no observation can be assigned more than 10 percent of weights)

boot

Number of bootstrap replications for estimating standard errors. Default is 1999.

cluster

A cluster ID for block or cluster bootstrapping when units are clustered rather than iid. Must be numerical. Default is NULL (standard bootstrap without clustering).

Details

Estimation of local average treatment effects of a binary endogenous treatment on outcomes in two follow up periods that are prone to attrition. Treatment endogeneity is tackled by a binary instrument that is assumed to be conditionally valid given observed baseline confounders x0. Outcome attrition is tackled by either assuming that it is missing at random (MAR), i.e. selection w.r.t. observed variables d, z, x0, x1 (in the case of y2), and s1 (in the case of y2); or by assuming latent ignorability (LI), i.e. selection w.r.t. the treatment compliance type as well as z, x0, x1 (in the case of y2), and s1 (in the case of y2). Units are weighted by the inverse of their conditional instrument and selection propensities, which are estimated by probit regression. Standard errors are obtained by bootstrapping the effect.

Value

An attrlateweight object contains one component results:

results: a 4X4 matrix containing the effect estimates in the first row ("effects"), standard errors in the second row ("se"), p-values in the third row ("p-value"), and the number of trimmed observations due to too large weights in the fourth row ("trimmed obs"). The first column provides the local average treatment effect (LATE) on y1 among compliers under missingness at random (MAR). The second column provides the local average treatment effect (LATE) on y2 under missingness at random (MAR). The third column provides the local average treatment effect (LATE) on y1 under latent ignorability (LI). The forth column provides the local average treatment effect (LATE) on y2 under latent ignorability (LI).

References

Frölich, M., Huber, M. (2014): "Treatment Evaluation With Multiple Outcome Periods Under Endogeneity and Attrition", Journal of the American Statistical Association, 109, 1697-1711.

Examples

# A little example with simulated data (4000 observations)
## Not run: 
n=4000
e=(rmvnorm(n,rep(0,3), matrix(c(1,0.3,0.3,  0.3,1,0.3,  0.3,0.3,1),3,3) ))
x0=runif(n,0,1)
z=(0.25*x0+rnorm(n)>0)*1
d=(1.2*z-0.25*x0+e[,1]>0.5)*1
y1_star=0.5*x0+0.5*d+e[,2]
s1=(0.25*x0+0.25*d+rnorm(n)>-0.5)*1
y1=s1*y1_star
x1=(0.5*x0+0.5*rnorm(n))
y2_star=0.5*x0+x1+d+e[,3]
s2=s1*((0.25*x0+0.25*x1+0.25*d+rnorm(n)>-0.5)*1)
y2=s2*y2_star
# The true LATEs on y1 and y2 are equal to 0.5 and 1, respectively.
output=attrlateweight(y1=y1,y2=y2,s1=s1,s2=s2,d=d,z=z,x0=x0,x1=x1,boot=19)
round(output$results,3)
## End(Not run)