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#' Partial Dependence Function for SoftBART Probit Regression
#'
#' Computes the partial dependence function for a given covariate at a given set of covariate values for the probit model.
#'
#' @param fit A fitted model of type \code{softbart_probit}.
#' @param test_data A data set used to form the baseline distribution of covariates for the partial dependence function.
#' @param var_str A string giving the variable name of the predictor to compute the partial dependence function for.
#' @param grid The values of the predictor to compute the partial dependence function at.
#'
#' @return Returns a list with the following components:
#' \itemize{
#' \item \code{pred_df}: a data frame containing columns for a MCMC iteration ID (\code{sample}), the value on the grid, and the partial dependence function value.
#' \item \code{p}: a matrix containing the same information as \code{pred_df}, with the rows corresponding to iterations and columns corresponding to grid values.
#' \item \code{grid}: the grid used as input.
#' }
#' @export
partial_dependence_probit <- function(fit, test_data, var_str, grid) {
out <- list()
out_mu <- list()
for(i in 1:length(grid)) {
newdata <- test_data
newdata[[var_str]] <- grid[[i]]
preds <- predict.softbart_probit(object = fit, newdata = newdata)
out[[i]] <- data.frame(sample = nrow(preds$p),
p = rowMeans(preds$p))
out[[i]][[var_str]] <- grid[[i]]
out_mu[[i]] <- rowMeans(preds$p)
}
out_list <- list(pred_df = do.call(rbind, out), p = do.call(cbind, out_mu),
grid = grid)
return(out_list)
}
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