R: Jackknife approximate t tests of regression coefficients

jack.test {pls} | 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.

### See Also

`var.jack`, `mvrCv`

### Examples

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

[Package pls version 2.7-0 Index]