bartMachine (version 1.2.3)

linearity_test: Test of Linearity

Description

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, ...)

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).

...

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

Examples

## Not run: 
# ##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
# 
# ## End(Not run)