LRT {mvMORPH}

Likelihood Ratio Test

Description

This function compares the fit of two nested models of trait evolution with a loglikelihood-ratio statistic.

Usage

LRT(model1, model2, echo = TRUE, ...)

Arguments

model1

The most parameterized model. A fitted object from an mvMORPH model.

model2

The second model under comparison (fitted object).

echo

Whether to return the result or not.

...

Options to be passed through. (Not yet available)

Details

The LRT function extracts the log-likelihood of two nested models to compute the loglikelihood-ratio statistic which is compared to a Chi-square distribution. Note that if the models are not nested, the LRT is not an appropriate test and you should rely instead on Information criteria, evidence ratios, or simulated distributions (e.g., Lewis et al. 2011). This can be achieved using the simulate function (see examples below).

Value

pval

The p-value of the LRT test (comparison with Chi-square distribution).

ratio

The LRT (Loglikelihood-ratio test) statistic.

ddf

The number of degrees of freedom between the two models.

model1

Name of the first model.

model2

Name of the second model.

Note

When comparing BM models to OU models, the LRT test might not be at it's nominal level. You should prefer a simulations based test.

Author(s)

Julien Clavel

References

Neyman J., Pearson E.S. 1933. On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. R. Soc. A. 231:289-337.

Lewis F., Butler A., Gilbert L. 2011. A unified approach to model selection using the likelihood ratio test. Meth. Ecol. Evol. 2:155-162.

See Also

mvMORPH mvOU mvEB mvBM mvSHIFT

Examples

## Simulated dataset
set.seed(14)
# Generating a random tree
tree<-pbtree(n=50)

# Setting the regime states of tip species
sta<-as.vector(c(rep("Forest",20),rep("Savannah",30))); names(sta)<-tree$tip.label

# Making the simmap tree with mapped states
tree<-make.simmap(tree,sta , model="ER", nsim=1)
col<-c("blue","orange"); names(col)<-c("Forest","Savannah")

# Plot of the phylogeny for illustration
plotSimmap(tree,col,fsize=0.6,node.numbers=FALSE,lwd=3, pts=FALSE)

# Simulate two correlated traits evolving along the phylogeny
traits<-mvSIM(tree,nsim=1, model="BMM", param=list(sigma=list(matrix(c(2,1,1,1.5),2,2),
         matrix(c(4,1,1,4),2,2)), ntraits=2, names_traits=c("head.size","mouth.size")))

# Fit of model 1
mod1<-mvBM(tree,traits,model="BMM")

# Fit of model 2
mod2<-mvBM(tree,traits,model="BM1")

# comparing the fit using LRT...
LRT(mod1,mod2)



# Simulation based test
nsim = 500
boot <- simulate(mod2, tree=tree, nsim=nsim)
simulations <- sapply(1:nsim, function(i){
  mod1boot<-mvBM(tree, boot[[i]], model="BMM", diagnostic=FALSE, echo=FALSE)
  mod2boot<-mvBM(tree, boot[[i]], model="BM1", diagnostic=FALSE, echo=FALSE, method="pic")
  2*(mod1boot$LogLik-mod2boot$LogLik)
})

# Compute the p-value
LRT_stat<-(2*((mod1$LogLik-mod2$LogLik)))
mean(simulations>=LRT_stat)

plot(density(simulations), main="Non-parametric LRT");
abline(v=LRT_stat, col="red")