GIC {mvMORPH}

Generalized Information Criterion (GIC) to compare models fit with mvgls (or mvols) by Maximum Likelihood (ML) or Penalized Likelihood (PL)

Description

The GIC (Konishi & Kitagawa 1996) allows comparing models fit by Maximum Likelihood (ML) or Penalized Likelihood (PL).

Usage

GIC(object, ...)
  
  

Arguments

object

An object of class 'mvgls'. See ?mvgls or ?mvols

...

Options to be passed through.

Details

The Generalized Information Criterion (GIC) allows comparing the fit of various models estimated by Penalized Likelihood (see ?mvgls or ?mvols). See also the gic_criterion function in the RPANDA package. Under maximum likelihood (method="LL" in mvgls or mvols) and on large sample sizes, the GIC should converges to the classical AIC (Akaike Information Criterion). Note that the current implementation of the criterion has not been tested for multiple predictors comparison (especially under REML). Prefer simulation based comparisons or the EIC criterion instead.

Value

a list with the following components

LogLikelihood

the log-likelihood estimated for the model with estimated parameters

GIC

the GIC criterion

bias

the value of the bias term estimated to compute the GIC

Author(s)

J. Clavel

References

Clavel, J., Aristide, L., Morlon, H., 2019. A Penalized Likelihood framework for high-dimensional phylogenetic comparative methods and an application to new-world monkeys brain evolution. Systematic Biology 68(1): 93-116.

Konishi S., Kitagawa G. 1996. Generalised information criteria in model selection. Biometrika. 83:875-890.

See Also

mvgls mvols manova.gls

Examples

set.seed(1)
n <- 32 # number of species
p <- 50 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- crossprod(matrix(runif(p*p), ncol=p)) # a random symmetric matrix (covariance)
# simulate a dataset
Y <- mvSIM(tree, model="BM1", nsim=1, param=list(sigma=R))

fit1 <- mvgls(Y~1, tree=tree, model="BM", method="H&L")
fit2 <- mvgls(Y~1, tree=tree, model="OU", method="H&L")


GIC(fit1); GIC(fit2)