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

In adespatial: Multivariate Multiscale Spatial Analysis

Compute AIC for models with orthonormal explanatory variables

Description

This function is now deprecated. Please try the new mem.select function.

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

Details

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).

Value

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

Author(s)

Stéphane Dray [e-mail]

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

adespatial documentation built on Oct. 19, 2023, 1:06 a.m.