Helper function for PostPI OLS estimation (analytic correction)
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.
- 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 toInf.
Value
A list of outputs: estimate of the inference model parameters and corresponding standard error estimate.
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_analytic_ols(X_l, Y_l, f_l, X_u, f_u)
#> $est
#> [1] 0.7667848 0.9350185
#>
#> $se
#> [1] 0.09724918 0.09473152
#>