phyl.RMA {phytools}

Phylogenetic reduced major axis (RMA) regression

Description

Phylogenetic reduced major axis (RMA) regression.

Usage

phyl.RMA(x, y, tree, method="BM", lambda=NULL, fixed=FALSE, h0=1.0)
## S3 method for class 'phyl.RMA'
coef(object, ...)
## S3 method for class 'phyl.RMA'
plot(x, ...)

Arguments

x

vector with names. In the case of the S3 plot method x is an object of class "phyl.RMA".

y

vector with names.

tree

a phylogenetic tree in "phylo" format.

method

method to obtain the correlation structure: can be "BM" or "lambda".

lambda

value of lambda for fixed \lambda.

fixed

logical value indicating whether or not \lambda should be optimized using likelihood.

h0

null hypothesis for \beta. Defaults to 1.0. Note that a null hypothesis of 0.0 is not allowed.

object

for coef method, an object of class "phyl.RMA".

...

optional arguments for S3 methods.

Details

Optionally jointly estimates \lambda if method="lambda". Likelihood optimization of \lambda is performed using optimize on the interval (0,1).

The statistical hypothesis testing is based on Clarke (1980; reviewed in McArdle 1988), which differs from some other implementations of non-phylogenetic major axis regression in R.

Note that some statistician think there is never a condition in which a reduced-major-axis regression is appropriate.

Value

An object of class "phyl.RMA" consisting of a list with the following elements:

RMA.beta

a vector of RMA regression coefficients.

V

a VCV matrix for the traits.

lambda

fitted value of \lambda (method="lambda" only).

logL

log-likelihood (method="lambda" only).

test

a vector containing results for hypothesis tests on \beta.

resid

a vector of residuals for y given x.

Author(s)

Liam Revell [e-mail]

References

Clarke, M. R. B. (1980) The reduced major axis of a bivariate sample. Biometrika, 67, 441-446.

McArdle, B. H. (1988) The structural relationship: Regression in biology. Can. J. Zool., 66, 2329-2339.

Revell, L. J. (2024) phytools 2.0: an updated R ecosystem for phylogenetic comparative methods (and other things). PeerJ, 12, e16505.

See Also

phyl.cca, phyl.pca, phyl.resid

Examples

## load data from Garland et al. (1992)
data(mammal.data)
data(mammal.tree)
## pull out & log transform variables
lnBodyMass<-setNames(log(mammal.data$bodyMass),
  rownames(mammal.data))
lnHomeRange<-setNames(log(mammal.data$homeRange),
  rownames(mammal.data))
## fit RMA regression & print results
fitted.rma<-phyl.RMA(lnBodyMass,lnHomeRange,
  mammal.tree)
print(fitted.rma)
## plot fitted RMA
par(las=1,bty="n")
plot(fitted.rma,las=1,bty="n")