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Doubly robust estimation of the LATE and LATT

Source: R/drlate.R
drlate.Rd

Estimates the local average treatment effect (LATE) or the local average treatment effect on the treated (LATT) with a binary instrument, following Słoczyński, Uysal, and Wooldridge (2022). A faithful R port of the Stata package drlate (SSC S459708): point estimates come from sequential weighted regressions, and standard errors are computed jointly for the instrument propensity score, the outcome regression, the treatment regression, and the causal estimand by stacking all moment conditions into a single M-estimation system.

Usage

drlate(
  outcome,
  treatment,
  instrument,
  data,
  omodel = c("linear", "logit", "probit", "poisson", "flogit", "fprobit"),
  tmodel = c("logit", "probit", "linear", "poisson"),
  ivmodel = c("logit", "cbps", "ipt", "probit"),
  method = c("ipwra", "ipw", "aipw", "ra", "kappa", "kappa0", "kappa10"),
  estimand = c("late", "latt"),
  normalized = TRUE,
  weights = NULL,
  cluster = NULL,
  pstolerance = 1e-05,
  osample = FALSE,
  subset = NULL,
  keep_data = TRUE,
  vcov = c("analytic", "bootstrap"),
  boot_reps = 999L,
  boot_seed = NULL,
  cores = 1L
)

Arguments

outcome

A formula y ~ covariates for the outcome model. Use y ~ 1 for no covariates (required when method = "ipw").

treatment

A formula d ~ covariates for the treatment model.

instrument

A formula z ~ covariates for the instrument propensity score model; z must be binary 0/1. Use z ~ 1 when method = "ra".

data

A data frame containing all variables.

omodel

Outcome model family: "linear" (default; continuous), "logit" or "probit" (outcome must be 0/1), "poisson" (outcome must be non-negative), or "flogit" / "fprobit" (fractional outcome in [0, 1], e.g. a proportion). The f-prefixed families share all estimation with "logit" / "probit" and only relax the response to the unit interval, matching the Stata lateffects omodel options.

tmodel

Treatment model family: "logit" (default; treatment must be 0/1), "probit", "linear", or "poisson".

ivmodel

Instrument propensity score model: "logit" (maximum likelihood; default), "cbps" (covariate balancing, Imai and Ratkovic 2014; not available with estimand = "latt"), "ipt" (inverse probability tilting, Graham, Pinto, and Egel 2012), or "probit" (maximum likelihood; mirrors kappalate's zmodel(probit) and is available only for the weighting estimators that command covers — "ipw", "kappa", "kappa0", "kappa10" — with estimand = "late").

method

Estimator: "ipwra" (inverse-probability-weighted regression adjustment; default), "ipw", "aipw", "ra", or one of the kappa-weighting estimators of Słoczyński, Uysal, and Wooldridge (2025): "kappa" (unnormalized Abadie kappa; kappalate's tau_a), "kappa0" (untreated-arm kappa; tau_a,0), or "kappa10" (normalized kappa; tau_a,10). The kappa estimators require intercept-only outcome and treatment formulas, a binary treatment, and estimand = "late"; ivmodel = "cbps" is available for "kappa" only, and "ipt" for none of them. drlate's normalized and unnormalized "ipw" coincide with kappalate's tau_u and tau_a,1.

estimand

"late" (default) or "latt".

normalized

Logical; use normalized moment conditions (default TRUE). Only relevant for method = "ipw" and method = "aipw".

weights

Optional sampling weights (a numeric vector, or a column name in data given as a string).

cluster

Optional cluster identifier for clustered standard errors (a vector, or a column name in data given as a string).

pstolerance

Overlap tolerance: estimation stops with an error if any estimated instrument propensity score is below pstolerance or above 1 - pstolerance. Default 1e-5.

osample

Logical; if TRUE, overlap violations do not stop estimation with an error. Instead drlate() returns (invisibly) a logical vector marking the violating observations.

subset

Optional logical or integer vector selecting rows of data.

keep_data

Logical; retain the internal estimation context (model matrices, fitted propensity scores, weights) on the returned object (default TRUE). Required by plot.drlate(), balance(), and the bootstrap; set to FALSE for a leaner object.

vcov

"analytic" (default) for the joint M-estimation sandwich replicating the Stata package, or "bootstrap" for nonparametric bootstrap standard errors and percentile confidence intervals (whole clusters are resampled when cluster is supplied). The analytic variance is always computed and stored either way. Draws that fail (degenerate resamples, non-convergence, overlap violations) are dropped and counted; because such failures concentrate where identification is weak, a non-trivial failure rate is itself a sign that percentile intervals are unreliable and the Fieller set (confint(., method = "fieller")) should be preferred.

boot_reps

Number of bootstrap replications (default 999).

boot_seed

Optional seed for reproducible bootstrap draws. Results are reproducible for a fixed number of cores; serial and parallel runs use different (both valid) random streams.

cores

Number of CPU cores for the bootstrap (default 1). Values above 1 use a PSOCK cluster and require the package to be installed (not merely loaded with devtools::load_all()).

Value

An object of class "drlate", a list with components including coefficients (the causal estimate, the numerator effect of Z on Y, and the denominator effect of Z on D), vcov3 (their variance matrix, diagonal by construction, as in the Stata package), vcov_full (the joint variance matrix of all stacked parameters), theta (all stacked parameter estimates), N, dmeanz1, dmeanz0, and the call. For method = "kappa10" only the causal estimate is reported (the estimator is a difference of two ratios, so no single numerator/denominator pair exists). For "kappa" and "kappa0" the third coefficient is the mean of the corresponding kappa weight: under the LATE assumptions it estimates the same complier share as the IPW first-stage contrast (the population ATE of Z on D), but it is a different sample statistic and the two can diverge under propensity score misspecification.

References

Słoczyński, T., S. D. Uysal, and J. M. Wooldridge (2022). "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment." doi:10.48550/arXiv.2208.01300

Słoczyński, T., S. D. Uysal, and J. M. Wooldridge (2025). "Abadie's Kappa and Weighting Estimators of the Local Average Treatment Effect." Journal of Business & Economic Statistics 43(1), 164–177. doi:10.1080/07350015.2024.2332763

Examples

data(drlate_sim)
fit <- drlate(lwage ~ age + educ, nvstat ~ age + educ,
              rsncode ~ age + educ, data = drlate_sim)
summary(fit)
#> 
#> Local average treatment effect
#> Number of obs    : 2,000
#> Estimator        : IPWRA
#> Outcome model    : linear
#> Treatment model  : logit
#> Instrument model : logit (MLE)
#> 
#>              Estimate Std. Error z value   Pr(>|z|) [95% conf. interval]
#> LATE: D on Y   0.4705    0.07915   5.944  2.786e-09     0.3153    0.6256
#> ATE: Z on Y    0.2845    0.05043   5.642  1.679e-08     0.1857    0.3834
#> ATE: Z on D    0.6048    0.01837  32.929 8.326e-238     0.5688    0.6408
#> 
#> First stage (Z on D): z = 32.93 (z^2 ~ first-stage F = 1084)