unweighted_gplm: Unweighted (baseline) estimator for the generalised partially linear model

Description

Estimates the parameter of interest $\theta_0$ in the generalised partially linear regression model $$g(\mathbb{E}[Y|X,Z]) = X\theta_0 + f_0(Z),$$ as in roseRF_gplm but without any weights i.e. $J=1$, $M_1(X)=X$ and $w_1\equiv 1$.

Usage

unweighted_gplm(
  y_on_xz_formula,
  y_on_xz_learner,
  y_on_xz_pars = list(),
  Gy_on_z_formula,
  Gy_on_z_learner,
  Gy_on_z_pars = list(),
  x_formula,
  x_learner,
  x_pars = list(),
  link = "identity",
  data,
  K = 5,
  S = 1
)

Value

A list containing:

theta: The estimator of $\theta_0$.
stderror: Huber robust estimate of the standard error of the $\theta_0$-estimator.
coefficients: Table of $\theta_0$ coefficient estimator, standard error, z-value and p-value.

Arguments

y_on_xz_formula: a two-sided formula object describing the regression model for $\mathbb{E}[Y|X,Z]$ (regressing $Y$ on $(X,Z)$).
y_on_xz_learner: a string specifying the regression method to fit the regression as given by y_on_xz_formula (e.g. randomforest, xgboost, neuralnet, gam).
y_on_xz_pars: a list containing hyperparameters for the y_on_xz_learner chosen. Default is an empty list, which performs hyperparameter tuning.
Gy_on_z_formula: a two-sided formula object describing the regression model for $\mathbb{E}[g(\mathbb{E}[Y|X,Z])|Z]$ (regressing $g(\hat{E}[Y|X,Z])$ on $Z$).
Gy_on_z_learner: a string specifying the regression method to fit the regression as given by Gy_on_z_formula (e.g. randomforest, xgboost, neuralnet, gam).
Gy_on_z_pars: a list containing hyperparameters for the Gy_on_z_learner chosen. Default is an empty list, which performs hyperparameter tuning.
x_formula: a two-sided formula object describing the regression model for $\mathbb{E}[X|Z]$.
x_learner: a string specifying the regression method to fit the regression of $X$ on $Z$ as given by x_formula (e.g. randomforest, xgboost, neuralnet, gam).
x_pars: a list containing hyperparameters for the x_learner chosen. Default is an empty list, which performs hyperparameter tuning.
link: link function ($g$). Options include identity, log, sqrt, logit, probit. Default is identity.
data: a data frame containing the variables for the partially linear model.
K: the number of folds used for $K$-fold cross-fitting. Default is 5.
S: the number of repeats to mitigate the randomness in the estimator on the sample splits used for $K$-fold cross-fitting. Default is 5.