R: Likelihood ratio test

RFratiotest {RandomFields}

R Documentation

Likelihood ratio test

Description

The function performs an approximate chi2 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`	vector of x coordinates, or object of class `GridTopology` or `raster`; for more options see RFsimulateAdvanced.
`y,z`	optional vectors of y (z) coordinates, which should not be given if `x` is a matrix.
`T`	optional vector of time coordinates, `T` must always be an equidistant vector. Instead of `T=seq(from=From, by=By, len=Len)`, one may also write `T=c(From, By, Len)`.
`grid`	logical; the function finds itself the correct value in nearly all cases, so that usually `grid` need not be given. See also RFsimulateAdvanced.
`data`	matrix, data.frame or object of class `RFsp`; If a matrix is given the ordering of the colums is the following: space, time, multivariate, repetitions, i.e. the index for the space runs the fastest and that for repetitions the slowest.
`lower`	list or vector. Lower bounds for the parameters. If `lower` is a vector, `lower` has to be a vector as well and its length must equal the number of parameters to be estimated. The order of `lower` has to be maintained. A component being `NA` means that no manual lower bound for the corresponding parameter is set. If `lower` is a list, `lower` has to be of (exactly) the same structure of the model.
`upper`	list or vector. Upper bounds for the parameters. See `lower`.
`methods`	Main methods to be used for estimating. If several methods are given, estimation will be performed with each method and the results reported.
`sub.methods`	variants of the least squares fit of the variogram. variants of the maximum likelihood fit of the covariance function. See RFfit for details.
`users.guess`	User's guess of the parameters. All the parameters must be given using the same rules as for `lower` (except that no NA's should be contained).
`distances,dim`	another alternative for the argument `x` to pass the (relative) coordinates, see RFsimulateAdvanced.
`optim.control`	control list for `optim`, which uses ‘L-BFGS-B’. However `parscale` may not be given.
`transform`	obsolete for users; use `param` instead. `transform=list()` will return structural information to set up the correct function.
`...`	for advanced use: further options and control arguments for the simulation that are passed to and processed by `RFoptions`. If `params` is given, then `...` may include also the variables used in `params`.

Details

nullmodel (and the alternative) can be

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

If RFoptions ratiotest_approx is TRUE 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

Examples

[Package RandomFields version 3.3.4 Index]

Likelihood ratio test

Description

Usage

Arguments

Details

Value

Methods

Note

Note

Note

Author(s)

See Also

Examples