significance.test {CovRegRF} | R Documentation |
Significance test
Description
This function runs a permutation test to evaluate the effect of a subset of covariates on the covariance matrix estimates. Returns an estimated p-value.
Usage
significance.test(
formula,
data,
params.rfsrc = list(ntree = 1000, mtry = ceiling(px/3), nsplit = max(round(n/50),
10)),
nodesize.set = round(0.5^(1:100) * round(0.632 * n))[round(0.5^(1:100) * round(0.632
* n)) > py],
nperm = 500,
test.vars = NULL
)
Arguments
formula |
Object of class |
data |
The multivariate data set which has |
params.rfsrc |
List of parameters that should be passed to
|
nodesize.set |
The set of |
nperm |
Number of permutations. |
test.vars |
Subset of covariates whose effect on the covariance matrix
estimates will be evaluated. A character vector defining the names of the
covariates. The default is |
Value
An object of class (covregrf, significancetest)
which is a list
with the following components:
pvalue |
Estimated *p*-value, see below for details. |
best.nodesize |
Best |
best.nodesize.control |
Best |
test.vars |
Covariates whose effect on the covariance matrix estimates is evaluated. |
control.vars |
Controlling set of covariates. |
predicted.oob |
OOB predicted covariance matrices for training
observations using all covariates including the |
predicted.perm |
Predicted covariance matrices for the permutations
using all covariates including the |
predicted.oob.control |
OOB predicted covariance matrices for training
observations using only the set of controlling covariates. If
|
predicted.perm.control |
Predicted covariance matrices for the
permutations using only the set of controlling covariates. If
|
Details
We perform a hypothesis test to evaluate the effect of a subset of covariates
on the covariance matrix estimates, while controlling for the rest of the
covariates. Define the conditional covariance matrix of Y
given all
X
variables as \Sigma_{X}
, and the conditional covariance
matrix of Y
given only the set of controlling X
variables as
\Sigma_{X}^{c}
. If a subset of covariates has an effect on the
covariance matrix estimates obtained with the proposed method, then
\Sigma_{X}
should be significantly different from \Sigma_{X}^{c}
.
We conduct a permutation test for the null hypothesis
H_0 : \Sigma_{X} = \Sigma_{X}^{c}
We estimate a
p
-value with the permutation test. If the p
-value is less than the
pre-specified significance level \alpha
, we reject the null
hypothesis.
Testing the global effect of the covariates on the conditional covariance
estimates is a particular case of the proposed significance test. Define
the unconditional covariance matrix estimate of Y
as
\Sigma_{root}
which is computed as the sample covariance matrix of
Y
, and the conditional covariance matrix of Y
given X
as
\Sigma_{X}
which is obtained with covregrf()
. If there is a
global effect of X
on the covariance matrix estimates, the
\Sigma_{X}
should be significantly different from \Sigma_{root}
.
The null hypothesis for this particular case is
H_0 : \Sigma_{X} = \Sigma_{root}
See Also
covregrf
predict.covregrf
print.covregrf