I just
pushed
a few small fixes plus a new S3 `AIC`

method for `"ratebytree"`

class objects.

This is what the function looks like:

```
AIC.ratebytree<-function(object,...,k=2){
aic<-data.frame(AIC=c(k*object$common.rate.model$k-2*object$common.rate.model$logL,
k*object$multi.rate.model$k-2*object$multi.rate.model$logL),
df=c(object$common.rate.model$k,object$multi.rate.model$k))
addtl.obj<-list(...)
if(length(addtl.obj)>0){
for(i in 1:length(addtl.obj)) aic<-rbind(aic,
c(k*addtl.obj[[i]]$multi.rate.model$k-2*addtl.obj[[i]]$multi.rate.model$logL,
addtl.obj[[i]]$multi.rate.model$k))
rownames(aic)<-c("common-rate",paste("multi-rate:",1:(length(addtl.obj)+1),sep=""))
} else rownames(aic)<-c("common-rate","multi-rate")
aic
}
```

I'm not totally sure this is *legal*, but what the method does if multiple objects are
supplied is that it *assumes* the common-rate model is the same for all supplied
objects, and then it computes AIC values for only the multiple rate (or process) model for
all subsequent objects.

Here's a demo using the same tree & data from earlier today:

```
library(phytools)
## our data:
par(mfrow=c(1,3))
nulo<-mapply(phenogram,tree=trees,x=x,MoreArgs=list(ylim=range(x),
ftype="off"))
```

```
## fit two-rate model
fit.reg<-ratebytree(trees,x,regimes=c(1,2,1))
fit.reg
```

```
## ML common-rate model:
## s^2 a[1] a[2] a[3] k logL
## value 1.2117 0.7489 0.058 1.0751 4 -223.603
## SE 0.1399 0.8292 1.1014 1.2046
##
## ML multi-rate model:
## s^2[1] s^2[2] a[1] a[2] a[3] k logL
## value 0.8862 2.1068 0.7489 0.058 1.0751 5 -217.4606
## SE 0.1195 0.4711 0.7091 1.4522 1.0302
##
## Likelihood ratio: 12.285
## P-value (based on X^2): 5e-04
##
## R thinks it has found the ML solution.
```

```
## fit all rates different model
fit.all<-ratebytree(trees,x)
fit.all
```

```
## ML common-rate model:
## s^2 a[1] a[2] a[3] k logL
## value 1.2117 0.7489 0.058 1.0751 4 -223.603
## SE 0.1399 0.8292 1.1014 1.2046
##
## ML multi-rate model:
## s^2[1] s^2[2] s^2[3] a[1] a[2] a[3] k logL
## value 0.6709 2.1068 1.0656 0.7489 0.058 1.0751 6 -216.0332
## SE 0.1342 0.4711 0.1946 0.617 1.4523 1.1297
##
## Likelihood ratio: 15.1397
## P-value (based on X^2): 5e-04
##
## R thinks it has found the ML solution.
```

```
## now compute AIC scores:
AIC(fit.reg,fit.all)
```

```
## AIC df
## common-rate 455.2061 4
## multi-rate:1 444.9211 5
## multi-rate:2 444.0664 6
```

In this case, the all-rates-different model has the lowest AIC score, but the difference in fit between that & the two-rate model is quite small. Neat.