adespatial (version 0.0-7)

ortho.AIC: Compute AIC for models with orthonormal explanatory variables

Description

This function compute corrected AIC for models with orthonormal and centered explanatory variables such as MEM spatial eigenfunctions. Variables are sorted by their contribution to R2. .

Usage

ortho.AIC(Y, X, ord.var = FALSE)

Arguments

Y

A matrix with response variables (univariate or multivariate response)

X

A set of orthonormal and centered vectors

ord.var

A logical value indicating if the order of variables and cumulative R2 must be returned

Value

A vector with corrected AIC if ord.var=FALSE. A list if ord.var=TRUE with: with:

Details

It ensures that a model with k variables is the best one that can be obtained. By default, response variables are centered (model with intercept).

References

Godinez-Dominguez E. and Freire J. (2003) Information-theoretic approach for selection of spatial and temporal models of community organization. Marine Ecology - Progress Series. 253, 17--24

Examples

y <- matrix(rnorm(50),50,1)
x <- svd(scale(y \%*\% c(0.1,0.5,2,0,0.7)+matrix(rnorm(250),50,5)))$u
res <- ortho.AIC(y,x,ord.var=TRUE)
minAIC <- which.min(res$AICc)
nvar <- length(1:minAIC)+1 # number of orthogonal vectors + 1 for intercept
lm1 <- lm(y~x[,res$ord[1:minAIC]])
summary(lm1)$r.squared # R2
res$R2[minAIC] # the same
min(res$AICc) # corrected AIC
extractAIC(lm1) # classical AIC
min(res$AICc)-2*(nvar*(nvar+1))/(nrow(x)-nvar-1) # the same

lm2 <- lm(y~1)

res$AICc0 # corrected AIC for the null model
extractAIC(lm2) # classical AIC
res$AICc0-2*(1*(1+1))/(nrow(x)-1-1) # the same