Jackknife approximate t tests of regression coefficients
Performes approximate t tests of regression coefficients based on jackknife variance estimates.
jack.test(object, ncomp = object$ncomp, use.mean = TRUE) ## S3 method for class 'jacktest' print(x, P.values = TRUE, ...)
object |
an |
ncomp |
the number of components to use for estimating the variances |
use.mean |
logical. If |
x |
an |
P.values |
logical. Whether to print p values (default). |
... |
Further arguments sent to the underlying print function
|
jack.test uses the variance estimates from var.jack to
perform t tests of the regression coefficients. The resulting object
has a print method, print.jacktest, which uses
printCoefmat for the actual printing.
jack.test returns an object of class "jacktest", with components
coefficients |
The estimated regression coefficients |
sd |
The square root of the jackknife variance estimates |
tvalues |
The t statistics |
df |
The ‘degrees of freedom’ used for calculating p values |
pvalues |
The calculated p values |
print.jacktest returns the "jacktest" object (invisibly).
The jackknife variance estimates are known to be biased (see
var.jack).
Also, the distribution of the regression coefficient estimates and the
jackknife variance estimates are unknown (at least in PLSR/PCR).
Consequently, the distribution (and in particular, the degrees of
freedom) of the resulting t statistics is unknown. The present code
simply assumes a t distribution with m - 1 degrees of
freedom, where m is the number of cross-validation segments.
Therefore, the resulting p values should not be used uncritically, and should perhaps be regarded as mere indicator of (non-)significance.
Finally, also keep in mind that as the number of predictor variables increase, the problem of multiple tests increases correspondingly.
Bjørn-Helge Mevik
Martens H. and Martens M. (2000) Modified Jack-knife Estimation of Parameter Uncertainty in Bilinear Modelling by Partial Least Squares Regression (PLSR). Food Quality and Preference, 11, 5–16.
data(oliveoil) mod <- pcr(sensory ~ chemical, data = oliveoil, validation = "LOO", jackknife = TRUE) jack.test(mod, ncomp = 2)
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