linearity_test: Test of Linearity

In bartMachine: Bayesian Additive Regression Trees

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.

Author(s)

Adam Kapelner

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)

bartMachine documentation built on July 9, 2023, 5:59 p.m.