fitCauchy.internal function

Maximum Likelihood estimator for a Cauchy model

Find the maximum likelihood, using numerical optimization with optim.

fitCauchy.internal(
  phy,
  X,
  y,
  model = c("cauchy", "lambda"),
  method = c("reml", "random.root", "fixed.root"),
  starting.value = list(x0 = NULL, disp = NULL, lambda = NULL),
  lower.bound = list(disp = 0, lambda = 0),
  upper.bound = list(disp = Inf, lambda = 1),
  root.edge = 100,
  optim = c("local", "global"),
  method.init.disp = "Qn",
  ...
)

Arguments

• phy: a phylogenetic tree of class phylo.
• model: a model for the trait evolution. One of "cauchy" or "lambda" (see Details).
• method: the method used to fit the process. One of reml (the default), fixed.root or random.root. See Details.
• starting.value: starting value for the parameters of the Cauchy. This should be a named list, with x0 and disp the root starting value and the dispersion parameter. The default initial values are computed from standard statistics used on (independent) Cauchy variables, see Details.
• lower.bound: named list with lower bound values for the parameters. See Details for the default values.
• upper.bound: named list with upper bound values for the parameters. See Details for the default values.
• root.edge: multiplicative factor for the root dispersion, equal to the length of the root edge. Ignored if method!=random.root.
• optim: if "local", only a local optimization around the initial parameter values is performed (the default). If "global", a global maximization is attempted using the "MLSL" approach (see nloptr).
• method.init.disp: the initialization method for the dispersion. One of "Qn", "Sn", "MAD", "IQR". Default to the "Qn" statistics. See Details.

Returns

A list, with the maximum likelihood rate parameter, and the likelihood value.

References

Rothenberg T. J., Fisher F. M., Tilanus C. B. 1964. A Note on Estimation from a Cauchy Sample. Journal of the American Statistical Association. 59:460–463.

See Also

cauphylm