# General SoftBart Regression Fits the general (Soft) BART (GBART) model, which combines the BART model with a linear predictor. That is, it fits the semiparametric Gaussian regression model [REMOVE_ME]$$ Y = r(X) + Z^\top \beta + \epsilon [REMOVE_ME_2]$$ where the function $r(x)$ is modeled using a BART ensemble. ```r gsoftbart_regression( formula, linear_formula, data, test_data, num_tree = 20, k = 2, hypers = NULL, opts = NULL, remove_intercept = TRUE, verbose = TRUE, warn = TRUE ) ``` ## Arguments - `formula`: A model formula with a numeric variable on the left-hand-side and non-linear predictors on the right-hand-side. - `linear_formula`: A model formula with the linear variables on the right-hand-side (left-hand-side is not used). - `data`: A data frame consisting of the training data. - `test_data`: A data frame consisting of the testing data. - `num_tree`: The number of trees used in the ensemble. - `k`: Determines the standard deviation of the leaf node parameters, which is given by `3 / k / sqrt(num_tree)`. - `hypers`: A list of hyperparameters constructed from the `Hypers()` function (`num_tree`, `k`, and `sigma_mu` are overridden by this function). - `opts`: A list of options for running the chain constructed from the `Opts()` function (`update_sigma` is overridden by this function). - `remove_intercept`: If `TRUE` then any intercept term in the linear formula will be removed, with the overall location of the outcome captured by the nonparametric function. - `verbose`: If `TRUE`, progress of the chain will be printed to the console. - `warn`: If `TRUE`, remind the user that they probably don't want the linear predictors to be included in the formula for the nonlinear part. ## Returns Returns a list with the following components * `r_train`: samples of the nonparametric function evaluated on the training set. * `r_test`: samples of the nonparametric function evaluated on the test set. * `eta_train`: samples of the linear predictor on the training set. * `eta_test`: samples of the linear predictor on the test set. * `mu_train`: samples of the prediction on the training set. * `mu_test`: samples of the prediction on the test set. * `beta`: samples of the regression coefficients. * `sigma`: samples of the error standard deviation. * `sigma_mu`: samples of the standard deviation of the leaf node parameters. * `var_counts`: a matrix with a column for each nonparametric predictor containing the number of times that predictor is used in the ensemble at each iteration. * `opts`: the options used when running the chain. * `formula`: the formula specified by the user. * `ecdfs`: empirical distribution functions, used by the predict function. * `mu_Y, sd_Y`: used with the predict function to transform predictions. * `forest`: a forest object for the nonlinear part; see the `MakeForest()` documentation for more details. ## Description Fits the general (Soft) BART (GBART) model, which combines the BART model with a linear predictor. That is, it fits the semiparametric Gaussian regression model $$ Y = r(X) + Z^\top \beta + \epsilon $$ where the function $r(x)$ is modeled using a BART ensemble. ## Examples ```r ## NOTE: SET NUMBER OF BURN IN AND SAMPLE ITERATIONS HIGHER IN PRACTICE num_burn <- 10 ## Should be ~ 5000 num_save <- 10 ## Should be ~ 5000 set.seed(1234) f_fried <- function(x) 10 * sin(pi * x[,1] * x[,2]) + 20 * (x[,3] - 0.5)^2 + 10 * x[,4] + 5 * x[,5] gen_data <- function(n_train, n_test, P, sigma) { X <- matrix(runif(n_train * P), nrow = n_train) mu <- f_fried(X) X_test <- matrix(runif(n_test * P), nrow = n_test) mu_test <- f_fried(X_test) Y <- mu + sigma * rnorm(n_train) Y_test <- mu + sigma * rnorm(n_test) return(list(X = X, Y = Y, mu = mu, X_test = X_test, Y_test = Y_test, mu_test = mu_test)) } ## Simiulate dataset sim_data <- gen_data(250, 250, 100, 1) df <- data.frame(X = sim_data$X, Y = sim_data$Y) df_test <- data.frame(X = sim_data$X_test, Y = sim_data$Y_test) ## Fit the model opts <- Opts(num_burn = num_burn, num_save = num_save) fitted_reg <- gsoftbart_regression(Y ~ . - X.4 - X.5, ~ X.4 + X.5, df, df_test, opts = opts) ## Plot results plot(colMeans(fitted_reg$mu_test), sim_data$mu_test) abline(a = 0, b = 1) plot(fitted_reg$beta[,1]) plot(fitted_reg$beta[,2]) ```

gsoftbart_regression function