medweight {causalweight}

Causal mediation analysis based on inverse probability weighting with optional sample selection correction.

Description

Causal mediation analysis (evaluation of natural direct and indirect effects) based on weighting by the inverse of treatment propensity scores as suggested in Huber (2014) and Huber and Solovyeva (2018).

Usage

medweight(
  y,
  d,
  m,
  x,
  w = NULL,
  s = NULL,
  z = NULL,
  selpop = FALSE,
  ATET = FALSE,
  trim = 0.05,
  logit = FALSE,
  boot = 1999,
  cluster = NULL
)

Arguments

y

Dependent variable, must not contain missings.

d

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

m

Mediator(s), may be a scalar or a vector, must not contain missings.

x

Pre-treatment confounders of the treatment, mediator, and/or outcome, must not contain missings.

w

Post-treatment confounders of the mediator and the outcome. Default is NULL. Must not contain missings.

s

Optional selection indicator. Must be one if y is observed (non-missing) and zero if y is not observed (missing). Default is NULL, implying that y does not contain any missings. Is ignored if w is not NULL.

z

Optional instrumental variable(s) for selection s. If NULL, outcome selection based on observables (x,d,m) - known as "missing at random" - is assumed.

selpop

Only to be used if both s and z are defined. If TRUE, the effects are estimated for the selected subpopulation with s=1 only. If FALSE, the effects are estimated for the total population.

ATET

If FALSE, the average treatment effect (ATE) and the corresponding direct and indirect effects are estimated. If TRUE, the average treatment effect on the treated (ATET) and the corresponding direct and indirect effects are estimated. Default is FALSE.

trim

Trimming rule for discarding observations with extreme propensity scores. In the absence of post-treatment confounders (w=NULL), observations with Pr(D=1|M,X)<trim or Pr(D=1|M,X)>(1-trim) are dropped. In the presence of post-treatment confounders (w is defined), observations with Pr(D=1|M,W,X)<trim or Pr(D=1|M,W,X)>(1-trim) are dropped. Default is 0.05. If s is defined (only considered if w is NULL!) and z is NULL, observations with low selection propensity scores, Pr(S=1|D,M,X)<trim, are discarded, too. If s and z are defined, the treatment propensity scores to be trimmed change to Pr(D=1|M,X,Pr(S=1|D,X,Z)).

logit

If FALSE, probit regression is used for propensity score estimation. If TRUE, logit regression is used. Default is FALSE.

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 causal mechanisms (natural direct and indirect effects) of a binary treatment under a selection on observables assumption assuming that all confounders of the treatment and the mediator, the treatment and the outcome, or the mediator and the outcome are observed. Units are weighted by the inverse of their conditional treatment propensities given the mediator and/or observed confounders, which are estimated by probit or logit regression. The form of weighting depends on whether the observed confounders are exclusively pre-treatment (x), or also contain post-treatment confounders of the mediator and the outcome (w). In the latter case, only partial indirect effects (from d to m to y) can be estimated that exclude any causal paths from d to w to m to y, see the discussion in Huber (2014). Standard errors are obtained by bootstrapping the effects. In the absence of post-treatment confounders (such that w is NULL), defining s allows correcting for sample selection due to missing outcomes based on the inverse of the conditional selection probability. The latter might either be related to observables, which implies a missing at random assumption, or in addition also to unobservables, if an instrument for sample selection is available. Effects are then estimated for the total population, see Huber and Solovyeva (2018) for further details.

Value

A medweight object contains two components, results and ntrimmed:

results: a 3X5 matrix containing the effect estimates in the first row ("effects"), standard errors in the second row ("se"), and p-values in the third row ("p-value"). The first column provides the total effect, namely the average treatment effect (ATE) if ATET=FALSE or the average treatment effect on the treated (ATET) if ATET=TRUE. The second and third columns provide the direct effects under treatment and control, respectively ("dir.treat", "dir.control"). See equation (6) if w=NULL (no post-treatment confounders) and equation (13) if w is defined, respectively, in Huber (2014). If w=NULL, the fourth and fifth columns provide the indirect effects under treatment and control, respectively ("indir.treat", "indir.control"), see equation (7) in Huber (2014). If w is defined, the fourth and fifth columns provide the partial indirect effects under treatment and control, respectively ("par.in.treat", "par.in.control"), see equation (14) in Huber (2014).

ntrimmed: number of discarded (trimmed) observations due to extreme propensity score values.

References

Huber, M. (2014): "Identifying causal mechanisms (primarily) based on inverse probability weighting", Journal of Applied Econometrics, 29, 920-943.

Huber, M. and Solovyeva, A. (2018): "Direct and indirect effects under sample selection and outcome attrition ", SES working paper 496, University of Fribourg.

Examples

# A little example with simulated data (10000 observations)
## Not run: 
n=10000
x=rnorm(n)
d=(0.25*x+rnorm(n)>0)*1
w=0.2*d+0.25*x+rnorm(n)
m=0.5*w+0.5*d+0.25*x+rnorm(n)
y=0.5*d+m+w+0.25*x+rnorm(n)
# The true direct and partial indirect effects are all equal to 0.5
output=medweight(y=y,d=d,m=m,x=x,w=w,trim=0.05,ATET=FALSE,logit=TRUE,boot=19)
round(output$results,3)
output$ntrimmed
## End(Not run)