Skip to contents

Test of Linearity

Source: R/bart_package_f_tests.R
linearity_test.Rd

Test to investigate \(H_0:\) the functional relationship between the response and the regressors is linear. We fit a linear model and then test if the residuals are a function of the regressors using the

Usage

linearity_test(
  lin_mod = NULL,
  X = NULL,
  y = NULL,
  num_permutation_samples = 100,
  plot = TRUE,
  verbose = TRUE,
  ...
)

Arguments

lin_mod

A linear model you can pass in if you do not want to use the default which is lm(y ~ X). Default is NULL which should be used if you pass in X and y.

X

Data frame of predictors. Factors are automatically converted to dummies internally. Default is NULL which should be used if you pass in lin_mode.

y

Vector of response variable. If y is numeric or integer, a BART model for regression is built. If y is a factor with two levels, a BART model for classification is built. Default is NULL which should be used if you pass in lin_mode.

num_permutation_samples

This function relies on cov_importance_test (see documentation there for details).

plot

This function relies on cov_importance_test (see documentation there for details).

verbose

If TRUE, prints progress and summary messages.

...

Additional parameters to be passed to bartMachine, the model constructed on the residuals of the linear model.

Value

permutation_samples_of_error

This function relies on cov_importance_test (see documentation there for details).

observed_error_estimate

This function relies on cov_importance_test (see documentation there for details).

pval

The approximate p-value for this test. See the documentation at cov_importance_test.

See also

cov_importance_test

Author

Adam Kapelner

Examples

if (FALSE) { # \dontrun{
##regression example

##generate Friedman data i.e. a nonlinear response model
set.seed(11)
n  = 200
p = 5
X = data.frame(matrix(runif(n * p), ncol = p))
y = 10 * sin(pi* X[ ,1] * X[,2]) +20 * (X[,3] -.5)^2 + 10 * X[ ,4] + 5 * X[,5] + rnorm(n)

##now test if there is a nonlinear relationship between X1, ..., X5 and y.
linearity_test(X = X, y = y)
## note the plot and the printed p-value.. should be approx 0

#generate a linear response model
y = 1 * X[ ,1] + 3 * X[,2] + 5 * X[,3] + 7 * X[ ,4] + 9 * X[,5] + rnorm(n)
linearity_test(X = X, y = y)
## note the plot and the printed p-value.. should be > 0.05

} # }