corrHLfit: Fits a mixed model, typically a spatial GLMM.

Description

This was the first function for fitting all spatial models in spaMM, and is still fully functional, but it is recommended to use fitme which has different defaults and generally selects more efficient fitting methods, and will handle all classes of models that spaMM can fit, including non-spatial ones. corrHLfit performs the joint estimation of correlation parameters, fixed effect and dispersion parameters.

Usage

corrHLfit(formula, data, init.corrHLfit = list(), 
          init.HLfit = list(), ranFix = list(), lower = list(), 
          upper = list(), 
          objective = NULL, resid.model = ~1, 
          control.dist = list(), control.corrHLfit = list(),
          processed = NULL, family = gaussian(), method="REML",
          nb_cores = NULL, ...)

Arguments

formula

Either a linear model formula (as handled by various fitting functions) or a predictor, i.e. a formula with attributes (see Predictor and examples below). See Details in spaMM for allowed terms in the formula.

data

A data frame containing the variables in the response and the model formula.

init.corrHLfit

An optional list of initial values for correlation and/or dispersion parameters, e.g. list(rho=1,nu=1,lambda=1,phi=1) where rho and nu are parameters of the Mat<U+00E9>rn family (see Matern), and lambda and phi are dispersion parameters (see Details in spaMM for the meaning of these parameters). All are optional, but giving values for a dispersion parameter changes the ways it is estimated (see Details). rho may be a vector (see make_scaled_dist) and, in that case, it is possible that some or all of its elements are NA, for which corrHLfit substitutes automatically determined values.

init.HLfit

See identically named HLfit argument.

ranFix

A list similar to init.corrHLfit, but specifying fixed values of the parameters not estimated. See ranFix for further information.

lower

An optional (sub)list of values of the parameters specified through init.corrHLfit, in the same format as init.corrHLfit, used as lower values in calls to optim. See Details for default values.

upper

Same as lower, but for upper values.

objective

For development purpose, not documented (this had a distinct use in the first version of spaMM, but has been deprecated as such).

resid.model

See identically named HLfit argument.

control.dist

See control.dist in HLCor

control.corrHLfit

This may be used control the optimizer. See spaMM.options

processed

For programming purposes, not documented.

family

Either a family or a multi value.

method

Character: the fitting method to be used, such as "ML", "REML" or "PQL/L". "REML" is the default. Other possible values of HLfit's method argument are handled.

nb_cores

Not yet operative, only for development purposes. Number of cores to use for parallel computations.

…

Optional arguments passed to HLCor, HLfit or mat_sqrt, for example the distMatrix argument of HLCor. Arguments that do not fit within these functions are detected and a warning is issued.

Value

The return value of an HLCor call, with additional attributes. The HLCor call is evaluated at the estimated correlation parameter values. These values are included in the return object as its $corrPars member. The attributes added by corrHLfit include the original call of the function (which can be retrived by getCall(<fitted object>), and information about the optimization call within corrHLfit.

Details

For approximations of likelihood, see method. For the possible structures of random effects, see random-effects,

By default corrHLfit will estimate correlation parameters by maximizing the objective value returned by HLCor calls wherein the dispersion parameters are estimated jointly with fixed effects for given correlation parameters. If dispersion parameters are specified in init.corrHLfit, they will also be estimated by maximizing the objective value, and HLCor calls will not estimate them jointly with fixed effects. This means that in general the fixed effect estimates may vary depending on init.corrHLfit when any form of REML correction is applied.

Correctly using corrHLfit for likelihood ratio tests of fixed effects may then be tricky. It is safe to perform full ML fits of all parameters (using method="ML") for such tests (see Examples). The higher level function fixedLRT is a safe interface for likelihood ratio tests using some form of REML estimation in corrHLfit.

attr(<fitted object>,"optimInfo")$lower and ...$upper gives the lower and upper bounds for optimization of correlation parameters. These are the default values if the user did not provide explicit values. For the adjacency model, the default values are the inverse of the maximum and minimum eigenvalues of the adjMatrix. For the Mat<U+00E9>rn model, the default values are not so easily summarized: they are intended to cover the range of values for which there is statistical information to distinguish among them.

Examples

Run this code

# NOT RUN {
# Example with an adjacency matrix (autoregressive model):
if (spaMM.getOption("example_maxtime")>0.7) {          
  corrHLfit(cases~I(prop.ag/10) +adjacency(1|gridcode)+offset(log(expec)),
          adjMatrix=Nmatrix,family=poisson(),data=scotlip,method="ML") 
}

#### Examples with Matern correlations
## A likelihood ratio test based on the ML fits of a full and of a null model.
if (spaMM.getOption("example_maxtime")>1.4) {
 data("blackcap")
 (fullfit <- corrHLfit(migStatus ~ means+ Matern(1|latitude+longitude),data=blackcap,
                    method="ML") )
 (nullfit <- corrHLfit(migStatus ~ 1 + Matern(1|latitude+longitude),data=blackcap,
                    method="ML",init.corrHLfit=list(phi=1e-6))) 
 ## p-value:
 1-pchisq(2*(logLik(fullfit)-logLik(nullfit)),df=1)
}
# }