Functions to find maximum likelihood solutions to general random walk (
opt.GRW), unbiased random walk
opt.URW, and stasis models
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opt.GRW(y, pool = TRUE, cl = list(fnscale = -1), meth = "L-BFGS-B", hess = FALSE) opt.URW(y, pool = TRUE, cl = list(fnscale=-1), meth = "L-BFGS-B", hess = FALSE) opt.Stasis(y, pool = TRUE, cl = list(fnscale=-1), meth = "L-BFGS-B", hess = FALSE) opt.StrictStasis(y, pool = TRUE, cl = list(fnscale=-1), meth = "L-BFGS-B", hess = FALSE)
control list, passed to function
logical indicating whether to pool variances across samples
optimization method, passed to function
logical, indicating whether to calculate standard errors from the Hessian matrix
These functions numerically search a log-likelihood surface for its optimum–they are a convenient wrapper to
hess are passed to
optim; see that function's help for details. These are included to allow sophisticated users greater control over the optimization; the defaults seem to work well for most, but not all sequences. For
meth="L-BFGS-B", some parameters are constrained to be non-negative, which is useful paramters which cannot truly be negative, such as
vstep (random walk) and
omega (stasis model).
Initial estimates to start the optimization come from analytical solutions based on assuming equal sampling error across samples and evenly spaced samples in time (functions
Standard errors computed from the Hessian matrix are reasonably accurate for
theta, but not as useful for the vstep and omega because of the asymmetry of the log-likelihood surfaces.
Hunt, G. 2006. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32:578–601.
Hunt, G., M. J. Hopkins, and S. L. Lidgard 2015. Simple versus complex models of trait evolution and stasis as a response to environmental change. PNAS 112:4885–4890.
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