Performes approximate t tests of regression coefficients based on jackknife variance estimates.
jack.test(object, ncomp = object$ncomp, use.mean = TRUE)# S3 method for jacktest
print(x, P.values = TRUE, ...)
jack.test returns an object of class "jacktest", with
components
The estimated regression coefficients
The square root of the jackknife variance estimates
The \(t\) statistics
The `degrees of freedom' used for calculating \(p\) values
The calculated \(p\) values
print.jacktest returns the "jacktest" object (invisibly).
an mvr object. A cross-validated model fitted with
jackknife = TRUE.
the number of components to use for estimating the variances
logical. If TRUE (default), the mean coefficients
are used when estimating the (co)variances; otherwise the coefficients from
a model fitted to the entire data set. See var.jack for
details.
an jacktest object, the result of jack.test.
logical. Whether to print \(p\) values (default).
Further arguments sent to the underlying print function
printCoefmat.
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
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.
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.
var.jack, mvrCv
data(oliveoil)
mod <- pcr(sensory ~ chemical, data = oliveoil, validation = "LOO", jackknife = TRUE)
jack.test(mod, ncomp = 2)
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