gic_criterion function

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

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

gic_criterion(Y, tree, model="BM", method=c("RidgeAlt", "RidgeArch", "LASSO", "ML", 
                                "RidgeAltapprox", "LASSOapprox"), targM=c("null", 
                                "Variance", "unitVariance"), param=NULL, 
                                tuning=0, REML=TRUE, ...)

Arguments

• Y: A matrix of phenotypic traits values (the variables are represented as columns)
• tree: An object of class 'phylo' (see ape documentation)
• model: The evolutionary model, "BM" is Brownian Motion, "OU" is Ornstein-Uhlenbeck, "EB" is Early Burst, and "lambda" is Pagel's lambda transformation.
• method: The penalty method. "RidgeArch": Archetype (linear) Ridge penalty, "RidgeAlt": Quadratic Ridge penalty, "LASSO": Least Absolute Selection and Shrinkage Operator, "ML": Maximum Likelihood.
• targM: The target matrix used for the Ridge regularizations. "null" is a null target, "Variance" for a diagonal unequal variance target, "unitVariance" for an equal diagonal target. Only works with "RidgeArch","RidgeAlt" methods.
• param: Parameter for the evolutionary model (see "model" above).
• tuning: The tuning/regularization parameter.
• REML: Use REML (default) or ML for estimating the parameters.
• ...: Additional options. Not used yet.

Returns

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

Details

gic_criterion allows comparing the fit of various models estimated by Penalized Likelihood (see ?fit_t_pl). Use the wrapper GIC instead for models fit with fit_t_pl.

Note

The tuning parameter is assumed to be zero when using the "ML" method.

References

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

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. Syst. Biol. 68: 93-116.

Author(s)

J. Clavel

See Also

GIC.fit_pl.rpanda, fit_t_pl

Examples

if(test){

if(require(mvMORPH)){
set.seed(123)
n <- 32 # number of species
p <- 2 # number of traits

tree <- pbtree(n=n) # phylogenetic tree
R <- Posdef(p)      # a random symmetric matrix (covariance)

# simulate a dataset
Y <- mvSIM(tree, model="BM1", nsim=1, param=list(sigma=R))

# Compute the GIC for ML
gic_criterion(Y, tree, model="BM", method="ML", tuning=0) # ML

# Compare with PL?
#test <- fit_t_pl(Y, tree, model="BM", method="RidgeAlt")
#GIC(test)
}

}