R: Likelihood ratio test

RFratiotest {RandomFields} | R Documentation

## Likelihood ratio test

### Description

The function performs an approximate $chi^2 test or a Monte Carlo likelihood ratio test based on `fitgauss`. Currently it only works for Gaussian random fields.

### Usage

    RFratiotest(nullmodel, alternative, x, y = NULL, z = NULL, T = NULL,
    grid=NULL, data,
    alpha, n = 5 / alpha, seed = 0,
    lower = NULL, upper = NULL, methods,
    sub.methods, optim.control = NULL, users.guess = NULL,
    distances = NULL, dim, transform = NULL, ...)

### Arguments

`nullmodel, alternative` | See Details. The set of parameters to be estimated for `nullmodel` should be a subset of the parameters to be estimated for `alternative` if `alternative` is given.
`alpha` | value in [0,1] or missing. Significance level.
`n` | integer. The test is based on `n-1` simulations.
`seed` | integer. If not `NULL` and not `NA`, the .Random.seed is set to `seed`. Otherwise, `set.seed` is set to the value of `RFoptions{}$basic$seed` if the latter is not `NA`.
`x, y, z, T, grid, data, lower, upper, methods, sub.methods, optim.control, users.guess, distances, dim, transform, ...` | see `RFfit`

### Details

`nullmodel` (and the `alternative`) can be

- a covariance model, see `RMmodel` or type `RFgetModelNames(type="variogram")` to get all options.

  Depending weather the `RFoptions` `ratiotest_approx` is TRUE the the chisq approximation is performed. Otherwise a Monte Carlo ratio test is performed.

- `RFfit` or `RMmodelFit`

  Here, a chisq approximative test is always performed on the already fitted models.

`RFratiotest` tries to detect whether `nullmodel` is a submodel of `alternative`. If it fails,

- a message is printed that says that an automatic detection has not been possible;

- it is not guaranteed anymore that the `alternative` model returns a (log) likelihood that is at least as large as that of the `nullmodel`, even if `nullmodel` is a submodel of `alternative`. This is due to numerical optimisation which is never perfect.

Otherwise it is guaranteed that the `alternative` model has a (log) likelihood that is at least as large as that of the `nullmodel`.

### Value

The test returns a message whether the null hypothesis, i.e. the smaller model is accepted. Invisibly, a list that also contains

- `p`, the p-value

- `n`

- `data.ratio` the log ratio for the data

- `simu.ratio` the log ratio for the simulations

- `data.fit` the models fitted to the data

- `msg` the message that is also directly returned

It has S3 class `"RFratiotest"`.

### Methods

print

  prints the summary

summary

  gives a summary

### Note

An important `RFoptions` is `ratiotest_approx`.

### Note

Note that the likelihood ratio test may take a huge amount of time.

### Note

This function does not depend on the value of `RFoptions``()$PracticalRange`. The function `RFratiotest` always uses the standard specification of the covariance model as given in `RMmodel`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### See Also

`RFfit` `RMmodel`, `RandomFields`, `weather`.

### Examples

[Package RandomFields version 3.1.50 Index]