Fit a model in which a trait tracks a covariate
opt.covTrack( y, z, pool = TRUE, cl = list(fnscale = -1), meth = "L-BFGS-B", hess = FALSE ) opt.joint.covTrack( y, z, pool = TRUE, cl = list(fnscale = -1), meth = "L-BFGS-B", hess = FALSE )
a vector of covariate values
if TRUE, sample variances are substituted with their pooled estimate
optional control list, passed to
optimization algorithm, passed to
if TRUE, return standard errors of parameter estimates from the hessian matrix
In this model, changes in a trait are linearly related to changes in
a covariate with a slope of
b and residual variance
dx = b * dz + eps, where
eps ~ N(0, evar). This model was
described, and applied to an example in which body size changes tracked
changes in temperature, by Hunt et al. (2010).
For the AD version (
opt.covTrack), a trait sequence of
ns, the covariate,
z, can be of length
ns - 1,
interpreted as the vector of changes,
ns, differences are taken and these are used as the
dx's, with a warning issued.
The Joint version
z should be of length
there is an additional parameter that is the intercept of the linear
relationship between trait and covariate. See warning below about using the
paleoTSfit object with the results of the model fitting
opt.joint.covTrack(): fits the covTrack model using the joint parameterization
The Joint parameterization of this model can be fooled by temporal autocorrelation and, especially, trends in the trait and the covariate. The latter is tested for, but the AD parameterization is generally safer for this model.
Hunt, G, S. Wicaksono, J. E. Brown, and K. G. Macleod. 2010. Climate-driven body size trends in the ostracod fauna of the deep Indian Ocean. Palaeontology 53(6): 1255-1268.
set.seed(13) z <- c(1, 2, 2, 4, 0, 8, 2, 3, 1, 9, 4, 3) x <- sim.covTrack(ns = 12, z = z, b = 0.5, evar = 0.2) w.urw <- opt.URW(x) w.cov <- opt.covTrack(x, z = z) compareModels(w.urw, w.cov)
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