ortho.AIC {adespatial}  R Documentation 
This function is now deprecated. Please try the new mem.select
function.
ortho.AIC(Y, X, ord.var = FALSE)
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 
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.
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).
A vector with corrected AIC if ord.var=FALSE
. A list if
ord.var=TRUE
with:
AICc 
Values of corrected AIC. 
AICc0 
Values of corrected AIC for the null model (only intercept). 
ord 
Order of variables to be enter in the model 
R2

Cumulative R2 
Stéphane Dray stephane.dray@univlyon1.fr
GodinezDominguez E. and Freire J. (2003) Informationtheoretic approach for selection of spatial and temporal models of community organization. Marine Ecology  Progress Series. 253, 17–24
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$AICc)2*(nvar*(nvar+1))/(nrow(x)nvar1) # the same lm2 < lm(y~1) res$AICc0 # corrected AIC for the null model extractAIC(lm2) # classical AIC res$AICc02*(1*(1+1))/(nrow(x)11) # the same