| ouchModel {mvSLOUCH} | R Documentation |
Estimate parameters under a (multivariate) OU model of evolution
Description
The ouchModel function uses maximum likelihood to fit parameters of a multivariate OU
model evolving on the phylogeny. The user is recommended to install the suggested package
PCMBaseCpp which significantly speeds up the calculations (see Details).
Usage
ouchModel(phyltree, mData, regimes = NULL, regimes.times = NULL,
root.regime = NULL, predictors = NULL, M.error = NULL, Atype = "Invertible",
Syytype = "UpperTri", diagA = "Positive", estimate.root.state = FALSE,
parameter_signs = NULL, start_point_for_optim = NULL, parscale = NULL,
min_bl = 0.0003, maxiter = c(10,100))
Arguments
phyltree |
The phylogeny in |
mData |
A matrix with the rows corresponding to the tip species while the columns correspond to the traits.
The rows should be named by species |
regimes |
A vector or list of regimes. If vector then each entry corresponds to each of the branches of |
regimes.times |
A list of vectors for each tree node, it starts with |
root.regime |
The regime at the root of the tree. If not given, then it is taken as the regime that is present
on the root's daughter lineages and is the most frequent one in the |
predictors |
A vector giving the numbers of the columns from
|
M.error |
An optional measurement error covariance structure. The measurement errors between species are assumed independent. The program tries to recognize the structure of the passed matrix and accepts the following possibilities :
From version |
Atype |
What class does the A matrix in the multivariate OUOU model belong to, possible values :
|
Syytype |
What class does the Syy matrix in the multivariate OUBM model belong to, possible values :
|
diagA |
Whether the values on |
estimate.root.state |
Should the root state be estimate |
parameter_signs |
WARNING: ONLY use this option if you understand what you are doing! This option
is still in an experimental stage so some setups might not work (please report).
A list allowing the user to control whether specific entries for each model parameter
should be positive, negative, zero or set to a specific (other) value. The entries
of the list have to be named, the admissible names are |
start_point_for_optim |
A named list with starting parameters for of the parameters for be optimized by start_point_for_optim=list(A=rbind(c(2,0),(0,4)), Syy=rbind(c(1,0.5),c(0,2))). |
parscale |
A vector to calculate the |
min_bl |
Value to which PCMBase's |
maxiter |
The maximum number of iterations for different components of the estimation
algorithm. A vector of two integers. The first is the number of iterations for phylogenetic
GLS evaluations, i.e. conditional on the other parameters, the regime optima and perhaps
initial state are estimated by a phylogenetic GLS procedure. After this the other parameters are optimized over
by |
Details
The likelihood calculations are done by the PCMBase package. However, there is a C++ backend, PCMBaseCpp. If it is not available, then the likelihood is calculated slower using pure R. However, with the calculations in C++ up to a 100-fold increase in speed is possible (more realistically 10-20 times). The PCMBaseCpp package is available from https://github.com/venelin/PCMBaseCpp.
This function estimates the parameters of the following multivariate SDE,
dY(t) = -A(Y-\Psi(t))dt + \Sigma dW(t), Y(0)=Y_{0}
on a phylogenetic tree. It uses a numerical optimization over A (parametrized by its eigenvalues and
eigenvectors or its QR decomposition) and S (parametrized by its values) and conditional on
A and S estimates the values of Psi corresponding to the different regimes by a GLS estimate.
Y(0) is assumed to be equal to the root value of Psi (unless estimate.root.state=TRUE),
then Y(0) is estimated is estimated by least squares).
The setting Atype="Any" means that one assumes the matrix A is eigendecomposable.
If the estimation algorithm hits a defective A, then it sets the log-likelihood at
the minimum value and will try to get out of this dip.
The function parameter parameter_signs is special in the sense that it can give
the user great control over the estimation procedure but can also make the output
very inconsistent with what the user provides. If we have two traits,
then an EXAMPLE setting of this can be:
parameter_signs=list(signsA=rbind(c("+","-"),c(0,"+")),
signsSyy=rbind(c(NA,0),c(0,NA)).
This means that A is upper triangular with positive
values on the diagonal and a negative value on the off-diagonal, Syy is diagonal
and A is also diagonal. It is advisable to set now Atype="Any" and
Syytype="Any" (see further description).
If the given model parameter is to be estimated
by a generalized least squares (currently mPsi and vY0), then the
sign specifications are ignored. However, it is possible to set specific values.
Furthermore, the package does not check (for A
and Syy) if the specifications here agree with the Atype, Syytype
and diagA. The settings in signsA and signsSyy will override
the other settings. Hence, it is up to the user to make sure that the settings of
signsA and signsSyy are consistent with Atype, Syytype
and diagA. It is advisable to use signsA with "+"
on the diagonal and have diagA=NULL. The diagonal of Syy is forced to
be positive (unless "-" is used on the diagonal of signsSyy
but this is strongly discouraged) so it is advisable to keep NA
on the diagonal of signsSyy and not put there "+" there.
Hence, in particular using the signs mechanism result in a wrong class of the matrix
(e.g. Atype="SymmetricPositiveDefinite", but after corrections for the provided entries in
signsA one obtains a non-symmetric A with complex, negative-real-part eigenvalues).
Lastly, using signsA and signsSyy can result in
a wrong amount of dof and in turn incorrect AICc and BIC values.
What the code does is subtracts the amount of fixed values in signsA and signsSyy
from the amount of free parameters used to estimate A and Syy. For example
if one sets
Atype="SingleValueDiagonal" (estimated by one free parameter)
but specified two off-diagonal values, then the amount of dofs from A will be -1!!
The ONLY fail-safe way to use this is to set Atype="Any" (if signsA used) and
Syytype="Any" (if signsSyy used). If using Syytype="Any" and signsSyy
the it is strongly advisable to set the entries either below or above the diagonal ofSyy to 0.
The reason is that \Sigma_{yy}\Sigma_{yy}^{T} enters the likelihood and not the
given value of \Sigma_{yy}. Hence, having values below (or respectively above) the diagonal
results in an overparameterized model. The package has the option of mixing different matrix types
with specifying values in it but this is only for advanced users who need to dig into the code
to see what the dof should be and if it is possible to find a correspondence between the
parametrization and settings. If entries of mPsi and vY0 are pre-specified,
then the dof are correctly adjusted for this.
The found point is described by a list containing four fields.
The first field
HeuristicSearchPointFinalFind is the parametrization of the model parameters
at the considered point with the value of the log-likelihood. The field ParamsInModel is the point
estimate of the parameters of the SDE.
The field ParamSummary are different composite (evaluated at the tree's height) and summary statistics,
The field phylhalflife are the eigenvalues, eigenvectors and phylogenetic half lives
associated with the A matrix, expmtA is \exp(-A*(tree height)),
mPsi.rotated is each of the
regime effects multiplied by (1-\exp(-A*(tree height))),
cov.matrix is the trait vector covariance matrix at the tree's height,
corr.matrix is the trait vector correlation matrix at the tree's height,
trait.regression is a list consisting of regression coefficients when taking each trait in turn and
calculating its conditional expectation on all of the other trait, stationary.cov.matrix
is the stationary covariance matrix of process if it exists (i.e. the eigenvalues have positive real part),
stationary.corr.matrix is the stationary correlation matrix of process if it exists
(i.e. the eigenvalues have positive real part), StS the infinitesimal covariance matrix
\Sigma_{yy}\Sigma_{yy}^{T},
LogLik the log-likelihood, dof the degrees of freedom, m2loglik is -2log–likelihood,
aic is the Akaike information criterion, aic.c is the Akaike information criterion corrected for small
sample size, sic is the Schwarz information criterion, bic is the Bayesian information criterion
(which is the same as the Schwarz information criterion) and RSS is the residual sum of squares.
The field RSS_non_phylogenetic is a residual sum of squares calculated without correcting
for the phylogeny–induced between species correlations, while the extension
conditional_on_predictors indicates that we consider the RSS for the variables
labelled as responses conditioned on the remaining variables. The R2_phylaverage field is
R2, where the alternative model is the phylogenetically weighted sample average
(see OU_phylreg).
From version 2.0.0 of mvSLOUCH the data has to be passed as a matrix.
To underline this the data parameter's name has been changed to mData.
From version 2.0.0 of mvSLOUCH the parameter calcCI has been removed.
The package now offers the possibility of bootstrap confidence intervals, see
function parametric.bootstrap.
Value
FinalFound |
The point where the search procedure stopped. See Details for the description. |
MaxLikFound |
The point with the highest likelihood found by the search procedure, if it is the same as the final point then this field equals "Same as final found". |
Warning
The estimation can take a long time and should be repeated a couple of times so that it is run from different starting positions. The function can produce (a lot of) warnings and errors during the search procedure, this is nothing to worry about.
Note
The ouch package considers a similar model and looking at it could be helpful.
Author(s)
Krzysztof Bartoszek
References
Bartoszek, K. and Pienaar, J. and Mostad. P. and Andersson, S. and Hansen, T. F. (2012) A phylogenetic comparative method for studying multivariate adaptation. Journal of Theoretical Biology 314:204-215.
Butler, M.A. and A.A. King (2004) Phylogenetic comparative analysis: a modeling approach for adaptive evolution. American Naturalist 164:683-695.
Hansen, T.F. (1997) Stabilizing selection and the comparative analysis of adaptation. Evolution 51:1341-1351.
Mitov, V. and Bartoszek, K. and Asimomitis, G. and Stadler, T. (2020) Fast likelihood calculation for multivariate Gaussian phylogenetic models with shifts Theoretical Population Biology 131:66-78.
Pienaar et al (in prep) An overview of comparative methods for testing adaptation to external environments.
See Also
PCMLik, hansen, SummarizeOUCH,
simulOUCHProcPhylTree, parametric.bootstrap,
optim
Examples
RNGversion(min(as.character(getRversion()),"3.6.1"))
set.seed(12345, kind = "Mersenne-Twister", normal.kind = "Inversion")
### We will first simulate a small phylogenetic tree using functions from ape.
### For simulating the tree one could also use alternative functions, e.g. sim.bd.taxa
### from the TreeSim package
phyltree<-ape::rtree(5)
## The line below is not necessary but advisable for speed
phyltree<-phyltree_paths(phyltree)
### Define a vector of regimes.
regimes<-c("small","small","large","small","small","large","large","large")
### Define SDE parameters to be able to simulate data under the OUOU model.
## 3D model
## OUOUparameters<-list(vY0=matrix(c(1,-1,0.5),nrow=3,ncol=1),
## A=rbind(c(9,0,0),c(0,5,0),c(0,0,1)),mPsi=cbind("small"=c(1,-1,0.5),"large"=c(-1,1,0.5)),
## Syy=rbind(c(1,0.25,0.3),c(0,1,0.2),c(0,0,1)))
## 2D model used to reduce running time on CRAN
OUOUparameters<-list(vY0=matrix(c(1,-1),nrow=2,ncol=1),
A=rbind(c(9,0),c(0,5)),mPsi=cbind("small"=c(1,-1),"large"=c(-1,1)),
Syy=rbind(c(1,0.25),c(0,1)))
### Now simulate the data.
OUOUdata<-simulOUCHProcPhylTree(phyltree,OUOUparameters,regimes,NULL)
OUOUdata<-OUOUdata[phyltree$tip.label,,drop=FALSE]
### Try to recover the parameters of the OUOU model.
### maxiter here set to minimal working possibility, in reality it should be larger
### e.g. default of c(10,100)
### Also the Atype and Syytype variables should be changed, here set as simplest
### for speed of evaluation, e.g. Atype="DecomposablePositive", Syytype="UpperTri"
OUOUestim<-ouchModel(phyltree,OUOUdata,regimes,Atype="SingleValueDiagonal",
Syytype="SingleValueDiagonal",diagA="Positive",maxiter=c(1,1))
RNGversion(as.character(getRversion()))
## Not run: ##It takes too long to run this
### And finally bootstrap with particular interest in the evolutionary regression
OUOUbootstrap<-parametric.bootstrap(estimated.model=OUOUestim,phyltree=phyltree,
values.to.bootstrap=c("evolutionary.regression"),regimes=regimes,root.regime="small",
M.error=NULL,predictors=c(2),kY=NULL,numboot=5,Atype=NULL,Syytype=NULL,diagA=NULL)
## End(Not run)