Assumption Lean inference for generalized linear model parameters

Assumption lean inference via cross-fitting (Double ML). See <doi:10.1111/rssb.12504

alean(
  response_model,
  exposure_model,
  data,
  link = "identity",
  g_model,
  nfolds = 1,
  silent = FALSE,
  mc.cores,
  ...
)

Arguments

response_model: formula or ml_model object (formula => glm)
exposure_model: model for the exposure
data: data.frame
link: Link function (g)
g_model: Model for $E[g(Y|A,W)|W]$
nfolds: Number of folds
silent: supress all messages and progressbars
mc.cores: mc.cores Optional number of cores. parallel::mcmapply used instead of future
...: additional arguments to future.apply::future_mapply

Value

alean.targeted object

Details

Let $Y$ be the response variable, $A$ the exposure and $W$ covariates. The target parameter is: $$\Psi(P) = \frac{E(Cov[A, g\{E(Y|A,W)\}\mid W])} {E\{Var(A\mid W)\}} $$

The response_model is the model for $E(Y|A,W)$, and exposure_model is the model for $E(A|W)$. link specifies $g$.

Author

Klaus Kähler Holst

Examples


sim1 <- function(n, family=gaussian(), ...) {
   m <- lvm() |>
     distribution(~ y, binomial.lvm()) |>
     regression('a', value=function(l) l) |>
     regression('y', value=function(a,l) a + l)
     if (family$family=="binomial")
        distribution(m, ~a) <- binomial.lvm()
   sim(m, n)
}

library(splines)
f <- binomial()
d <- sim1(1e4, family=f)
e <- alean(response_model=ML(y ~ a + bs(l, df=3), family=binomial),
           exposure_model=ML(a ~ bs(l, df=3), family=f),
           data=d,
           link = "logit", mc.cores=1, nfolds=1)
e
#>   Estimate Std.Err   2.5% 97.5%   P-value
#> a    1.027 0.05293 0.9237 1.131 6.133e-84

e <- alean(response_model=ML(y ~ a + l, family=binomial),
           exposure_model=ML(a ~ l),
           data=d,
           link = "logit", mc.cores=1, nfolds=1)
e
#>   Estimate Std.Err   2.5% 97.5% P-value
#> a    1.027 0.05315 0.9226 1.131 3.8e-83