optim
and ctmm.loglike
to maximize the likelihood function of continuous-time movement models described in Fleming et al (2014) and Fleming et al (2015), given 2D animal tracking data.ctmm(tau=NULL,isotropic=FALSE,range=TRUE,circle=FALSE,error=FALSE,axes=c("x","y"),...)ctmm.loglike(data,CTMM,REML=FALSE,verbose=FALSE)
ctmm.fit(data,CTMM=ctmm(),method="ML",control=list(maxit=.Machine$integer.max),...)
ctmm.select(data,CTMM,verbose=FALSE,level=0.99,IC="AICc",trace=FALSE,...)
telemetry
object. ctmm
movement-model object containing the initial parameter guesses conforming to the basic structure of the model hypothesis. ctmm.select
can accept a list of such objects.TRUE
. Not recommended."REML"
. Not recommended.optim
, but with parscale
overwritten with reasonable defaults.ctmm.fit
or optim
."AICc"
is currently supported.ctmm
returns a prototype ctmm
movement-model object.
By default, ctmm.loglike
returns the log-likelihood of the model CTMM
.
ctmm.fit
(and ctmm.loglike
with verbose=TRUE
) returns the maximum likelihood ctmm
movement-model object with all of the components of CTMM
plus the components listed below.
ctmm.select
returns the best model by default or the list of attempted models if verbose=TRUE
.
AICc
loglike
sigma
mu
COV.mu
mu
, assuming that the point estimate sigma
is good.DOF.mu
mu
, assuming that the point estimate of tau
is good. This can be much smaller than length(data$t)
if the data are autocorrelated.COV
c(sigma,tau,circle)
, as derived from hessian
, and where sigma
is parameterized in terms of its standard area
, eccentricity
, and angle
of orientation. Typically, sigma
's area
parameter is extremely correlated to tau[1]
, and sequential components of tau
are slightly correlated.ctmm
parameter guess can be generated by the output of ctmm.guess
, variogram.fit
or manually specified with the function ctmm(...)
, where the argument tau
is explained below and additonal model options described in vignette("ctmm")
. By default, tau
is an ordered array of autocorrelation timescales.
If length(tau)==0
, then an IID bi-variate Gaussian model is fit to the data.
If length(tau)==1
, then an Ornstein-Uhlenbeck (OU) model (Brownian motion restricted to a finite home range) is fit the data, where tau
is the position autocorrelation timescale. tau=Inf
then yields Brownian motion (BM).
If length(tau)==2
, then the OUF model (continuous-velocity motion restricted to a finite home range) is fit to the data, where tau[1]
is again the position autocorrelation timescale and tau[2]
is the velocity autocorrelation timescale. tau[1]=Inf
then yields integrated Ornstein-Uhlenbeck (IOU) motion, which is a spatially unrestricted continuous-velocity process. Model selection in ctmm.select
proceeds by first fitting the initial model guess, and then attempting to simplify the autocorrelation model and complexify the deterministic (mean) model until the information criteria fails to improve. The intent of working in these directions is to avoid fitting trends to autocorrelation.
Note that simpler models in a nested hierarchy will only be attempted if they appear credible, which can be adjusted with the level
argument. level=1
will, therefore, always attempt a simpler model.ctmm.guess
, optim
, summary.ctmm
, variogram.fit
.