# SoftBart Varying Coefficient Regression Fits a semiparametric varying coefficient regression model with the nonparametric slope and intercept [REMOVE_ME]$$ Y = \alpha(X) + Z \beta(X) +\epsilonY = alpha + Z * beta(X) + epsilon [REMOVE_ME_2]$$ using a soft BART model. ```r vc_softbart_regression( formula, linear_var_name, data, test_data, num_tree = 20, k = 2, hypers_intercept = NULL, hypers_slope = NULL, opts = NULL, 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_var_name`: A string containing the variable in the data that is to be treated linearly. - `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 in the ensemble to use. - `k`: Determines the standard deviation of the leaf node parameters, which is given by `3 / k / sqrt(num_tree)` (intercept) and defaults to `1/k/sqrt(num_tree)` (slope). This can be modified for the slope by specifying your own hyperparameter. - `hypers_intercept`: A list of hyperparameters constructed from the `Hypers()` function (`num_tree`, `k`, and `sigma_mu` are overridden by this function). - `hypers_slope`: A list of hyperparameters constructed from the `Hypers()` function (`num_tree` is 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). - `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 term to be included in the formula for the nonlinear part. ## Returns Returns a list with the following components * `sigma_mu_alpha`: samples of the standard deviation of the leaf node parameters for the intercept. * `sigma_mu_beta`: samples of the standard deviation of the leaf node parameters for the slope. * `sigma`: samples of the error standard deviation. * `var_counts_alpha`: a matrix with a column for each predictor group containing the number of times each predictor is used in the ensemble at each iteration for the intercept. * `var_counts_beta`: a matrix with a column for each predictor group containing the number of times each predictor is used in the ensemble at each iteration for the slope. * `alpha_train`: samples of the nonparametric intercept evaluated on the training set. * `alpha_test`: samples of the nonparametric intercept evaluated on the test set. * `beta_train`: samples of the nonparametric slope evaluated on the training set. * `beta_test`: samples of the nonparametric slope evaluated on the test set. * `mu_train`: samples of the predictions evaluated on the training set. * `mu_test`: samples of the predictions evaluated on the test set. * `formula`: the formula specified by the user. * `ecdfs`: empirical distribution functions, used by the `predict` function. * `opts`: the options used when running the chain. * `mu_Y, sd_Y`: used with the `predict` function to transform predictions. * `alpha_forest`: a forest object for the intercept; see the `MakeForest` documentation for more details. * `beta_forest`: a forest object for the slope; see the `MakeForest` documentation for more details. ## Description Fits a semiparametric varying coefficient regression model with the nonparametric slope and intercept $$ Y = \alpha(X) + Z \beta(X) +\epsilonY = alpha + Z * beta(X) + epsilon $$ using a soft BART model. ## 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) Z <- rnorm(n_train) r <- f_fried(X) mu <- Z * r X_test <- matrix(runif(n_test * P), nrow = n_test) Z_test <- rnorm(n_test) r_test <- f_fried(X_test) mu_test <- Z_test * r_test Y <- mu + sigma * rnorm(n_train) Y_test <- mu + sigma * rnorm(n_test) return(list(X = X, Y = Y, Z = Z, r = r, mu = mu, X_test = X_test, Y_test = Y_test, Z_test = Z_test, r_test = r_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, Z = sim_data$Z) df_test <- data.frame(X = sim_data$X_test, Y = sim_data$Y_test, Z = sim_data$Z_test) ## Fit the model opts <- Opts(num_burn = num_burn, num_save = num_save) fitted_vc <- vc_softbart_regression(Y ~ . -Z, "Z", df, df_test, opts = opts) ## Plot results plot(colMeans(fitted_vc$mu_test), sim_data$mu_test) abline(a = 0, b = 1) ```

vc_softbart_regression function