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Design-based causal effects of a 0/1 treatment

Source: R/cbatt.R
cbatt.Rd

The battery of estimators of the effect of a 0/1 treatment d on an outcome y given covariates x that do not learn the nuisances by cross-fitting: Hajek-normalised inverse probability weighting, g-computation, subclassification on the propensity, nearest-neighbour matching on the propensity with a caliper, and entropy balancing, covariate-balancing weights for the effect on the treated. dmlx() gives the cross-fitted ones (augmented inverse probability weighting, targeted maximum likelihood, the interactive model).

Usage

cbatt(
  y,
  d,
  x,
  est = "ipw",
  tgt = "ate",
  ps = NULL,
  k = 1,
  calip = NULL,
  nsub = 5,
  reps = 499,
  seed = NULL,
  level = 0.95
)

Arguments

y

The outcome: finite numbers, one per unit.

d

The treatment: 0 or 1 (or FALSE or TRUE), two units in each arm at least.

x

The covariates: a numeric matrix, a data frame or list of numeric columns, or one numeric vector, one row per unit.

est

"ipw", "gcomp", "sub", "psm" or "ebal".

tgt

"ate", "att" or "atc".

ps

NULL or the propensity of each unit, strictly between 0 and 1.

k

The controls matched to each unit: a whole number from 1.

calip

NULL or the caliper in standard deviations of the propensity.

nsub

The subclasses: a whole number from 2.

reps

The bootstrap samples: a whole number from 0 (none).

seed

The seed of the bootstrap: NULL to draw it from R's generator, or a whole number from 0.

level

The confidence level of the normal interval.

Value

An object of class cbatt, a list: res, one row (est, se, lo, hi, med, n1, n0); ps, the propensities (NA for "gcomp" and "ebal"); w, the weights ("ipw", "ebal"; else NULL); match ("psm": the rows of each focal unit and its match; else NULL); est; tgt; and level.

Details

The propensity is the logistic regression of d on an intercept and x (the learner of lgtreg()) unless ps gives it. tgt picks the average effect ("ate"), the effect on the treated ("att") or on the controls ("atc").

  • "ipw": the weighted mean of the treated less that of the controls, each normalised to sum to one (Hajek), with weights 1 / e and 1 / (1 - e) (ATE), 1 and e / (1 - e) (ATT), (1 - e) / e and 1 (ATC).

  • "gcomp": least squares of y on x in each arm; the mean difference of the two predictions over the target units.

  • "sub": nsub subclasses cut at the quantiles of the propensity among the target units; the subclasses' differences of means weighted by their target units.

  • "psm": greedy k:1 matching without replacement on the propensity, the treated (ATT) or the controls (ATC) in decreasing propensity ('MatchIt”s default order), within calip standard deviations of the propensity. The estimate is the mean over the matched units of the treated outcome less its controls' mean; med is their median, the median causal effect of the matched pairs; the standard error is that of a mean of independent matched sets.

  • "ebal": entropy balancing (Hainmueller 2012): control weights proportional to exp(l'x), the nearest to uniform in entropy whose weighted means equal the treated means exactly; the ATT is the treated mean less the weighted control mean.

Standard errors (but "psm") are the standard deviations over reps bootstrap samples of the units, with the propensity fitted again in each; intervals are normal.

A clpre list from clprep() may be given as y: its elements fill the arguments by name (the otis-*-cbatt presets).

References

Hainmueller, J. (2012). Entropy balancing for causal effects: a multivariate reweighting method to produce balanced samples in observational studies. Political Analysis, 20(1), 25-46. doi:10.1093/pan/mpr025

Imbens, G. W. and Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press. doi:10.1017/CBO9781139025751

Austin, P. C. (2011). An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate Behavioral Research, 46(3), 399-424. doi:10.1080/00273171.2011.568786

Examples

set.seed(1)
x <- matrix(rnorm(400), 200)
d <- rbinom(200, 1, plogis(x[, 1]))
y <- 2 * d + x[, 1] - x[, 2] + rnorm(200)
cbatt(y, d, x, reps = 99, seed = 1)$res
#>        est        se       lo      hi med n1  n0
#> 1 2.077253 0.1680322 1.747917 2.40659  NA 99 101
cbatt(y, d, x, est = "ebal", tgt = "att", reps = 99, seed = 1)$res
#>        est        se       lo       hi med n1  n0
#> 1 2.067763 0.1830696 1.708953 2.426573  NA 99 101
cbatt(y, d, x, est = "psm", tgt = "att", calip = 0.2)$res
#>        est        se       lo       hi      med n1  n0
#> 1 2.011912 0.2508233 1.520307 2.503517 2.228522 99 101