PostPI OLS (Bootstrap Correction)

Helper function for PostPI OLS estimation (bootstrap correction)

Usage

postpi_boot_ols(
  X_l,
  Y_l,
  f_l,
  X_u,
  f_u,
  nboot = 100,
  se_type = "par",
  rel_func = "lm",
  scale_se = TRUE,
  n_t = Inf,
  seed = NULL
)

Arguments

X_l

(matrix): n x p matrix of covariates in the labeled data.

Y_l

(vector): n-vector of labeled outcomes.

f_l

(vector): n-vector of predictions in the labeled data.

X_u

(matrix): N x p matrix of covariates in the unlabeled data.

f_u

(vector): N-vector of predictions in the unlabeled data.

nboot

(integer): Number of bootstrap samples. Defaults to 100.

se_type

(string): Which method to calculate the standard errors. Options include "par" (parametric) or "npar" (nonparametric). Defaults to "par".

rel_func

(string): Method for fitting the relationship model. Options include "lm" (linear model), "rf" (random forest), and "gam" (generalized additive model). Defaults to "lm".

scale_se

(boolean): Logical argument to scale relationship model error variance. Defaults to TRUE; FALSE option is retained for posterity.

n_t

(integer, optional) Size of the dataset used to train the prediction function (necessary if n_t < nrow(X_l). Defaults to Inf.

seed

(optional) An integer seed for random number generation.

Value

A list of outputs: estimate of inference model parameters and corresponding standard error based on both parametric and non-parametric bootstrap methods.

Details

Methods for correcting inference based on outcomes predicted by machine learning (Wang et al., 2020) https://www.pnas.org/doi/abs/10.1073/pnas.2001238117

Examples

dat <- simdat(model = "ols")

form <- Y - f ~ X1

X_l <- model.matrix(form, data = dat[dat$set == "labeled",])

Y_l <- dat[dat$set == "labeled", all.vars(form)[1]] |> matrix(ncol = 1)

f_l <- dat[dat$set == "labeled", all.vars(form)[2]] |> matrix(ncol = 1)

X_u <- model.matrix(form, data = dat[dat$set == "unlabeled",])

f_u <- dat[dat$set == "unlabeled", all.vars(form)[2]] |> matrix(ncol = 1)

postpi_boot_ols(X_l, Y_l, f_l, X_u, f_u, nboot = 200)
#> $est
#> [1] 0.8830688 1.1519981
#> 
#> $se
#> [1] 0.1087724 0.1081908
#>