ortho.AIC: Function to compute AIC in the case of orthogonal explanatory...

In spacemakeR: Spatial modelling

Description

This function compute corrected AIC for models with orthonormal and centered explanatory variables. 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).

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

See the reference for the multivariate extension of corrected AIC.

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)

Stephane Dray

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

spacemakeR documentation built on May 2, 2019, 4:51 p.m.