RFratiotest: Likelihood ratio test
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value Methods Note Note Note See Also Examples

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.

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, ...)

`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`	\argX
`y,z`	\argYz
`T`	\argT
`grid`	\argGrid
`data`	\argData
`lower`	\argLower
`upper`	\argUpper
`methods`	\argFitmethods
`sub.methods`	\argFitsubmethods See RFfit for details.
`users.guess`	\argUsersguess
`distances,dim`	\argDistances
`optim.control`	\argOptimcontrol
`transform`	\argTransform
`...`	\argDots

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.

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".

print: prints the summary
summary: gives a summary

An important RFoptions is ratiotest_approx.

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

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.

RFfit, RMmodel, RandomFields, weather.