spaMM (version 4.5.0)

fixedLRT: Likelihood ratio test of fixed effects.

Description

fixedLRT performs a likelihood ratio (LR) test between two models, the “full” and the “null” models, currently differing only in their fixed effects. Parametric bootstrap p-values can be computed, either using the raw bootstrap distribution of the likelihood ratio, or a bootstrap estimate of the Bartlett correction of the LR statistic. This function differs from LRT in its arguments (model fits for LRT, versus all arguments required to fit the models for fixedLRT), and in the format of its return value.

Usage

fixedLRT(null.formula, formula, data, method, HLmethod = method, 
         REMLformula = NULL, boot.repl=0, control="DEPRECATED",
         control.boot="DEPRECATED", fittingFunction, seed=NULL,
         resp_testfn = NULL, weights.form = NULL, ...)

Value

An object of class fixedLRT, actually a list with as-yet unstable format, but here with typical elements (depending on the options)

fullfit

the HLfit object for the full model;

nullfit

the HLfit object for the null model;

LRTori

A likelihood ratio chi-square statistic

LRTprof

Another likelihood ratio chi-square statistic, after a profiling step, if any.

df

the number of degrees of freedom of the test.

trace.info

Information on various steps of the computation.

and, if a bootstrap was performed, the additional elements described in LRT.

Arguments

null.formula

Either a formula (as in glm) or a predictor (see Predictor) for the null model.

formula

Either a formula or a predictor for the full model.

data

A data frame containing the variables in the model.

method

A method to fit the full and null models. See method information about such methods. The two most meaningful values of method in fixedLRT calls are: 'ML' for an LRT based on ML fits (generally recommended); and 'PQL/L' for an LRT based on PQL/L fits (recommended for spatial binary data).

Also feasible, but more tricky, and not really recommended (see Rousset and Ferdy, 2014), is 'REML'. This will perform an LRT based on two REML fits of the data, *both* of which use the same conditional (or “restricted”) likelihood of residuals for estimating dispersion parameters \(\lambda\) and \(\phi\) (see REMLformula argument). Further, REML will not be effective on a given dispersion parameter if a non-trivial init.corrHLfit value is provided for this parameter.

HLmethod

Kept for back-compatibility. Same as method, but may work only for
fittingFunction=corrHLfit.

REMLformula

a formula specifying the fixed effects which design matrix is used in the REML correction for the estimation of dispersion parameters, if these are estimated by REML. This formula is by default that for the *full* model.

weights.form

Specification of prior weights by a one-sided formula: use weights.form = ~ pw instead of prior.weights = pw. The effect will be the same except that such an argument, known to evaluate to an object of class "formula", is suitable to enforce safe programming practices (see good-practice).

boot.repl

the number of bootstrap replicates.

control

Deprecated.

control.boot

Deprecated.

fittingFunction

Character string giving the function used to fit each model: either "corrHLfit" or "fitme". Default is "corrHLfit" for small data sets (fewer than 300 observations), and "fitme" otherwise, but this may change in future versions.

seed

Passed to simulate.HLfit

resp_testfn

See argument resp_testfn of spaMM_boot

...

Further arguments passed to or from other methods; presently, additional arguments passed to fitting functions.

Details

Comparison of REML fits is a priori not suitable for performing likelihood ratio tests. Nevertheless, it is possible to contrive them for testing purposes (Welham & Thompson 1997). This function generalizes some of Wehlam & Thompson's methods to GLMMs.

See Details in LRT for details of the bootstrap procedures.

References

Rousset F., Ferdy, J.-B. (2014) Testing environmental and genetic effects in the presence of spatial autocorrelation. Ecography, 37: 781-790. tools:::Rd_expr_doi("10.1111/ecog.00566")

Welham, S. J., and Thompson, R. (1997) Likelihood ratio tests for fixed model terms using residual maximum likelihood, J. R. Stat. Soc. B 59, 701-714.

See Also

See LRT for simular tests with a different interface, and perhaps as_LMLT for access to a different testing approach for LMMs, implemented in lmerTest::contest.

Examples

if (spaMM.getOption("example_maxtime")>1.9) {
 data("blackcap")
 ## result comparable to the corrHLfit examples based on blackcap
 fixedLRT(null.formula=migStatus ~ 1 + Matern(1|longitude+latitude),
       formula=migStatus ~ means + Matern(1|longitude+latitude), 
       method='ML',data=blackcap)
}
if (spaMM.getOption("example_maxtime")>156) {
 ## longer version with bootstrap
 fixedLRT(null.formula=migStatus ~ 1 + Matern(1|longitude+latitude),
       formula=migStatus ~ means + Matern(1|longitude+latitude), 
       method='ML',data=blackcap, boot.repl=100, seed=123) 
 }