softbart_probit {SoftBart}

SoftBart Probit Regression

Description

Fits a nonparametric probit regression model with the nonparametric function modeled using a SoftBart model. Specifically, the model takes \Pr(Y = 1 \mid X = x) = \Phi\{a + r(x)\} where a is an offset and r(x) is a Soft BART ensemble.

Usage

softbart_probit(
  formula,
  data,
  test_data,
  num_tree = 20,
  k = 1,
  hypers = NULL,
  opts = NULL,
  verbose = TRUE
)

Arguments

formula

A model formula with a binary factor on the left-hand-side and predictors on the right-hand-side.

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).

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).

verbose

If TRUE, progress of the chain will be printed to the console.

Value

Returns a list with the following components:

• sigma_mu: samples of the standard deviation of the leaf node parameters

• var_counts: a matrix with a column for each predictor group containing the number of times each predictor is used in the ensemble at each iteration.

• mu_train: samples of the nonparametric function evaluated on the training set; pnorm(mu_train) gives the success probabilities.

• mu_test: samples of the nonparametric function evaluated on the test set; pnorm(mu_train) gives the success probabilities .

• p_train: samples of probabilities on training set.

• p_test: samples of probabilities on test set.

• mu_train_mean: posterior mean of mu_train.

• mu_test_mean: posterior mean of mu_test.

• p_train_mean: posterior mean of p_train.

• p_test_mean: posterior mean of p_test.

• offset: we fit model of the form (offset + BART), with the offset estimated empirically prior to running the chain.

• pnorm_offset: the pnorm of the offset, which is chosen to match the probability of the second factor level.

• formula: the formula specified by the user.

• ecdfs: empirical distribution functions, used by the predict function.

• opts: the options used when running the chain.

• forest: a forest object; see the MakeForest documentation for more details.

Examples

## 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) - 14) / 5
  X_test <- matrix(runif(n_test * P), nrow = n_test)
  mu_test <- (f_fried(X_test) - 14) / 5
  Y <- factor(rbinom(n_train, 1, pnorm(mu)), levels = c(0,1))
  Y_test <- factor(rbinom(n_test, 1, pnorm(mu_test)), levels = c(0,1))
  
  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_probit <- softbart_probit(Y ~ ., df, df_test, opts = opts)

## Plot results

plot(fitted_probit$mu_test_mean, sim_data$mu_test)
abline(a = 0, b = 1)