var.jack(object, ncomp = object$ncomp, covariance = FALSE, use.mean = TRUE)
covariance
is FALSE
, an $p\times q \times c$
array of variance estimates, where $p$ is the number of
predictors, $q$ is the number of responses, and $c$ is the
number of components. If covariance
id TRUE
, an $pq\times pq \times c$
array of variance-covariance estimates.
Thus, the results of var.jack
should be used with caution.
This is the definition var.jack
uses by default.
However, Martens and Martens (2000) defined the estimator as
$(g-1)/g \sum_{i=1}^g(\tilde\beta_{-i} - \hat\beta)^2$, where
$\hat\beta$ is the coefficient estimate using the entire data set.
I.e., they use the original fitted coefficients instead of the
mean of the jackknife replicates. Most (all?) other jackknife
implementations for PLSR use this estimator. var.jack
can be
made to use this definition with use.mean = FALSE
. In
practice, the difference should be small if the number of
observations is sufficiently large. Note, however, that all
theoretical results about the jackknife refer to the `proper'
definition. (Also note that this option might disappear in a future
version.)
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.
Hinkley D.V. (1977), Jackknifing in Unbalanced Situations. Technometrics, 19(3), 285--292.
Wu C.F.J. (1986) Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis. Te Annals of Statistics, 14(4), 1261--1295.
mvrCv
, jack.test
data(oliveoil)
mod <- pcr(sensory ~ chemical, data = oliveoil, validation = "LOO",
jackknife = TRUE)
var.jack(mod, ncomp = 2)
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