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Propensity score model functions

Source: R/method_ps.R
method_ps.Rd

Function to specify the propensity score (PS) model for the inverse probability weighting estimator. This function provides basic functions logistic regression with a given link function (currently we support logit, probit and cloglog) with additional information about the analytic variance estimator of the mean.

This is a function returns a list of functions that refer to specific estimation methods and variance estimators when whether the IPW alone or the DR estimator is applied. The export of this function is mainly because the functions are used in the variable selection algorithms.

Functions starting with make_log_like, make_gradient and make_hessian refer to the maximum likelihood estimation as described in the Chen et al. (2020) paper. These functions take into account different link functions defined through the link argument.

Functions make_link, make_link_inv, make_link_der, make_link_inv_der, make_link_inv_rev, and make_link_inv_rev_der refer to specific link functions and are used in the estimation process.

Functions variance_covariance1 and variance_covariance2 refer to the variance estimator of the IPW estimator as defined by Chen et al. (2020).

Functions b_vec_ipw, b_vec_dr and t_vec are specific functions defined in the Chen et al. (2020) that are used in the variance estimator of the IPW or the DR.

Finally, var_nonprob is the non-probability component of the DR estimator as defined by Chen et al. (2020).

Usage

method_ps(link = c("logit", "probit", "cloglog"), ...)

Arguments

link for the PS model

...

Additional, optional arguments.

Value

A list of functions and elements for a specific link function with the following entries:

make_log_like

log-likelihood function for a specific link function

make_gradient

gradient of the loglik

make_hessian

hessian of the loglik

make_link

link function

make_link_inv

inverse link function

make_link_der

first derivative of the link function

make_link_inv_der

first derivative of the the inverse link function

make_link_inv_rev

defines 1/inv_link

make_link_inv_rev_der

first derivative of 1/inv_link

variance_covariance1

for the IPW estimator: variance component for the non-probability sample

variance_covariance2

for the IPW estimator: variance component for the probability sample

b_vec_ipw

for the IPW estimator: the \(b\) function as defined in the Chen et al. (2020, sec. 3.2, eq. (9)-(10); sec 4.1)

b_vec_dr

for the DR estimator: the \(b\) function as defined in the Chen et al. (2020, sec. 3.3., eq. (14); sec 4.1)

t_vec

for the DR estimator: the \(b\) function as defined in the Chen et al. (2020, sec. 3.3., eq. (14); sec 4.1)

var_nonprob

for the DR estimator: non-probability component of the variance for DR estimator

link

name of the selected link function for the PS model (character)

model

model type (character)

Author

Łukasz Chrostowski, Maciej Beręsewicz

Examples

# Printing information on the model selected

method_ps()
#> Propensity score model with logit link

# extracting specific field

method_ps("cloglog")$make_gradient
#> function (X_nons, X_rand, weights, weights_rand, ...) 
#> {
#>     function(theta) {
#>         eta1 <- as.matrix(X_nons) %*% theta
#>         eta2 <- as.matrix(X_rand) %*% theta
#>         invLink1 <- inv_link(eta1)
#>         invLink2 <- inv_link(eta2)
#>         t(t(X_nons) %*% (weights * exp(eta1)/invLink1) - t(X_rand) %*% 
#>             (weights_rand * exp(eta2)))
#>     }
#> }
#> <bytecode: 0x55ff71e55f48>
#> <environment: 0x55ff7bb8bee8>