spaMM (version 1.9.16)

HLCor: Fits a (spatially) correlated mixed model, for given correlation parameters

Description

A convenient interface for HLfit, constructing the correlation matrix of random effects from the arguments, then estimating fixed effects and dispersion parameters using HLfit.

Usage

HLCor(formula, data, family = gaussian(), ranPars = NULL, distMatrix, uniqueGeo = NULL, adjMatrix, corrMatrix, verbose = c(warn=TRUE,trace=FALSE,summary=FALSE), control.dist = list(), ...)

Arguments

formula

A predictor, i.e. a formula with attributes (see Predictor), or possibly simply a simple formula if an offset is not required.

ranPars

A list of values for correlation parameters (some of which are mandatory), and possibly also dispersion parameters (optional, but passed to HLfit if present). For the Matérn model, the correlation parameters are rho (scale parameter(s)), nu (smoothness parameter), and (optional) Nugget. The rho parameter can itself be a vector with different values for different geographic coordinates. For the "adjacency" model, the only correlation parameter is a scalar rho. The dispersion parameters are the random effect variance, lambda, and the residual variance, phi.

data

The data frame to be analyzed.

family

A family object describing the distribution of the response variable. See HLfit for further information.

distMatrix

A distance matrix between geographic locations, forwarded to MaternCorr

uniqueGeo

A matrix of non-redundant geographic locations. This is useful if the rho parameter is a vector with different values for different geographic coordinates, in which case a scaled distance matrix has to be reconstructed from uniqueGeo and rho.

adjMatrix

An adjacency matrix, used if a random effect of the form y ~ adjacency(1|) is present. Its rows and columns must be ordered as increasing values of the levels of the geographic location index specifying the spatial random effect. For example, if the model formula is y ~ adjacency(1|geo.loc) and $geo.loc is 2,4,3,1,... the first row/column of the matrix refers to the fourth row of the data.

corrMatrix

A arbitrary (valid) correlation matrix, used if a random effect term of the form corrMatrix(1|) is present. Each row corresponds to levels of a variable . This allows to analyze non-spatial model by giving for example a matrix of genetic correlations. See corrMatrix for details.

verbose

A vector of booleans. trace controls various diagnostic (possibly messy) messages about the iterations. summary controls whether a summary of the fit is called by HLfit. warn is for programming purposes and best ignored.

control.dist

A list of arguments that control the computation of the distance argument of the correlation functions. Possible elements are

...

Further parameters passed to HLfit or to designL.from.Corr.

Value

The return value of an HLfit call, with the following additional attributes:

Details

The correlation matrix for random effects can be specified by various combination of formula terms and other arguments (see Examples):

References

Wall M.M. (2004) A close look at the spatial structure implied by the CAR and SAR models: Journal of Statistical Planning and Inference 121: 311-324.

Martellosio, F. (2012) The correlation structure of spatial autoregressions, Econometric Theory 28, 1373-1391.

See Also

MaternCorr, HLfit, corrHLfit

Examples

# Example with an adjacency matrix (autoregressive model):
# see 'adjacency' documentation page

#### Matérn correlation using only the Matern() syntax
if (spaMM.getOption("example_maxtime")>2) {
 data(Loaloa)
 HLCor(cbind(npos,ntot-npos)~elev1+elev2+elev3+elev4+maxNDVI1+seNDVI
              +Matern(1|longitude+latitude),data=Loaloa,
      family=binomial(),ranPars=list(nu=0.5,rho=1/0.7)) 
}


#### Matérn correlation using a distMatrix
data(blackcap)
MLdistMat <- as.matrix(proxy::dist(blackcap[,c("latitude","longitude")]))
HLCor(migStatus ~ means+ Matern(1|latitude+longitude),data=blackcap,
      distMatrix=MLdistMat,HLmethod="ML",ranPars=list(nu=0.6285603,rho=0.0544659))