# relltest {scaleboot}

### Description

Performs the RELL test for finding the largest item. This calculates AU p-values for each item via the multiscale bootstrap resampling. This is particularly useful for testing tree topologies in phylogenetic analysis.

### Usage

relltest(dat,nb=10000,sa=9^seq(-1,1,length=13),ass=NULL, cluster=NULL,nofit=FALSE,models=NULL,seed=100)

### Arguments

- dat
- a matrix. Row vectors are to be resampled. Each column vector gives score values to be evaluated for an item. For the phylogenetic analysis,
`dat[i,j]`

is the site-wise log-likelihood value at site-i for tree-j, and we are to find the tree with the largest expected value of`sum(dat[,j])`

. - nb
- Number of replicates for each scale.
- sa
- Scales in sigma squared (σ^2).
- ass
- A list of association vectors for testing edges as well as trees. If
`ass=NULL`

, then only the results for trees are returned. - cluster
- snow cluster object which may be generated by function
`makeCluster`

. - nofit
- logical. Passed to
`sbfit`

. - models
- character vectors. Passed to
`sbfit`

. - seed
- If non NULL, then a random seed is set. Specifying a seed is particularly important when
`cluster`

is non NULL, in this case`seed + seq(along=cluster)`

are set to cluster nodes.

### Details

`relltest`

performs the resampling of estimated log-likelihoods (RELL) method of Kishino et al. (1990). For resampling indices stored in a vector `i`

, the resampled log-likelihood for a tree-j is approximately calculated by `sum(dat[i,j])`

. This approximation avoids time-consuming recalculation of the maximum likelihood estimates of tree parameters, which are to be calculated by an external phylogenetic software such as PAML as described in `mam15`

. In the implementation of `relltest`

, the resampled log-likelihood is calculated by `sum(dat[i,j])`

`*nrow(dat)/length(i)`

so that the statistic is comparable to the case when n'=n.

`relltest`

first calls `scaleboot`

internally for multiscale bootstrap resampling, and then `scaleboot`

calls `sbfit`

for fitting models to the bootstrap probabilities. The AU p-values (named "k.3") produced by the `summary`

method are improvements of the third-order p-values calculated by CONSEL software (Shimodaira and Hasegawa 2001). In addition, `relltest`

calls `scaleboot`

with `sa=1`

for calculating p-values via the Shimodaira-Hasegawa test (SH-test) of Shimodaira and Hasegawa (1999).

See `mam15`

for details through an example.

### Values

`relltest`

returns an object of class `"relltest"`

that is inherited from the class `"scalebootv"`

by adding two extra components called "stat" and "shtest". "stat" is a vector of the test statistics from the SH-test (i.e., the log-likelihood differences), and "shtest" is a list with two components: "pv", a vector of SH-test p-values, and "pe", a vector of standard errors of the p-values. The results of multiscale bootstrap resampling are stored in the `"scalebootv"`

components returned by a call to `sbfit`

.

### References

Kishino, H., Miyata, T. and Hasegawa, M. (1990). Maximum likelihood inference of protein phylogeny and the origin of chloroplasts., *J. Mol. Evol.*, 30, 151-160.

Shimodaira, H. and Hasegawa, M. (1999). Multiple comparisons of log-likelihoods with applications to phylogenetic inference, *Molecular Biology and Evolution*, 16, 1114-1116.

Shimodaira, H. and Hasegawa, M. (2001). CONSEL: for assessing the confidence of phylogenetic tree selection, *Bioinformatics*, 17, 1246-1247 (software is available from http://www.is.titech.ac.jp/~shimo/prog/consel/).

Luke Tierney, A. J. Rossini, Na Li and H. Sevcikova. snow: Simple Network of Workstations. R package version 0.2-1.

### See Also

`sbfit`

, `scaleboot`

, `mam15`

.

### Examples

## Not run: ## An example from data(mam15). ## It may take 20 mins to run relltest below. mam15.mt <- read.mt("mam15.mt") # site-wise log-likelihoods mam15.trees <- relltest(mam15.mt) # resampling and fitting summary(mam15.trees) # AU p-values ## End(Not run)

Documentation reproduced from package scaleboot, version 0.3-3. License: GPL (>= 2)