# jack.test: Jackknife approximate t tests of regression coefficients In pls: Partial Least Squares and Principal Component Regression

 jack.test R Documentation

## Jackknife approximate t tests of regression coefficients

### Description

Performes approximate t tests of regression coefficients based on jackknife variance estimates.

### Usage

``````jack.test(object, ncomp = object\$ncomp, use.mean = TRUE)

## S3 method for class 'jacktest'
print(x, P.values = TRUE, ...)
``````

### Arguments

 `object` an `mvr` object. A cross-validated model fitted with `jackknife = TRUE`. `ncomp` the number of components to use for estimating the variances `use.mean` 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. `x` an `jacktest` object, the result of `jack.test`. `P.values` logical. Whether to print `p` values (default). `...` Further arguments sent to the underlying print function `printCoefmat`.

### Details

`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.

### Value

`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).

### Warning

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.

### Author(s)

Bjørn-Helge Mevik

### References

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`

### Examples

``````
data(oliveoil)
mod <- pcr(sensory ~ chemical, data = oliveoil, validation = "LOO", jackknife = TRUE)
jack.test(mod, ncomp = 2)

``````

pls documentation built on Nov. 18, 2023, 1:11 a.m.