gic_criterion {RPANDA}

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

Description

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

Usage

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.

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.

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

Note

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

Author(s)

J. Clavel

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.

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)
}

}