Helper function for Chen & Chen OLS estimation
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.
- intercept
(Logical): Do the design matrices include intercept columns? Default is
TRUE.
Value
(list): A list containing the following:
- est
(vector): vector of Chen & Chen OLS regression coefficient estimates.
- se
(vector): vector of standard errors of the coefficients.
Details
Another look at inference after prediction (Gronsbell et al., 2025) https://arxiv.org/pdf/2411.19908
Examples
dat <- simdat(model = "ols")
form <- Y - f ~ X1
X_l <- model.matrix(form, data = dat[dat$set_label == "labeled", ])
Y_l <- dat[dat$set_label == "labeled", all.vars(form)[1]] |>
matrix(ncol = 1)
f_l <- dat[dat$set_label == "labeled", all.vars(form)[2]] |>
matrix(ncol = 1)
X_u <- model.matrix(form, data = dat[dat$set_label == "unlabeled", ])
f_u <- dat[dat$set_label == "unlabeled", all.vars(form)[2]] |>
matrix(ncol = 1)
chen_ols(X_l, Y_l, f_l, X_u, f_u, intercept = TRUE)
#> $est
#> [,1]
#> (Intercept) 0.6776193
#> X1 1.0552229
#>
#> $se
#> (Intercept) X1
#> 0.09224289 0.09029692
#>