fit_cylcop_ml: Estimate Parameters of a Circular-Linear Copula According to...

In cylcop: Circular-Linear Copulas with Angular Symmetry for Movement Data

Estimate Parameters of a Circular-Linear Copula According to Maximum Likelihood

Description

The code of this function is based on copula::fitCopula(). A circular-linear copula is fit to a set of bivariate observations.

Usage

fit_cylcop_ml(
  copula,
  theta,
  x,
  parameters = NULL,
  start = NULL,
  lower = NULL,
  upper = NULL,
  optim.method = "L-BFGS-B",
  optim.control = list(maxit = 100),
  estimate.variance = FALSE,
  traceOpt = FALSE
)

optML(
  copula,
  theta,
  x,
  parameters = NULL,
  start = NULL,
  lower = NULL,
  upper = NULL,
  optim.method = "L-BFGS-B",
  optim.control = list(maxit = 100),
  estimate.variance = FALSE,
  traceOpt = FALSE
)

Arguments

copula	R object of class 'cyl_copula'.
theta	numeric vector of angles (measurements of a circular variable) or "circular" component of pseudo-observations.
x	numeric vector of step lengths (measurements of a linear variable) or "linear" component of pseudo-observations.
parameters	vector of character strings holding the names of the parameters to be optimized. These can be any parameters in copula@parameters. Default is to optimize the first 2 parameters or the single parameter if copula only has 1.
start	vector of starting values of the parameters. Default is to take the starting values from copula.
lower	(optional) vector of lower bounds of the parameters.
upper	(optional) vector of upper bounds of the parameters.
optim.method	character string, optimizer used in optim(), can be "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", or "Brent". Default is "L-BFGS-B".
optim.control	list of additional controls passed to optim().
estimate.variance	logical value, denoting whether to include an estimate of the variance (NOT YET IMPLEMENTED).
traceOpt	logical value, whether to print information regarding convergence, current values, etc. during the optimization process.

Details

The data is first converted to pseudo observations to which the copula is then fit. Therefore, the result of the optimization will be exactly the same whether measurements (theta=theta and x=x) or pseudo observations (theta=copula::pobs(theta,x)[,1] and x=copula::pobs(theta,x)[,2]) are provided. If you wish to fit parameters of a 'Copula' object (package 'copula'), use the function copula::fitCopula(). optML() is an alias for fit_cylcop_ml.

Value

A list of length 3 containing the same type of 'cyl_copula' object as copula, but with optimized parameters, the log-likelihood and the AIC.

References

\insertRef

Hodelapplcylcop

\insertRef

Hodelmethodcylcop

See Also

copula::fitCopula(), fit_cylcop_cor(), opt_auto().

Examples

set.seed(123)

sample <- rcylcop(100,cyl_quadsec(0.1))
fit_cylcop_ml(copula = cyl_quadsec(),
  theta = sample[,1],
  x = sample[,2],
  parameters = "a",
  start = 0
)
fit_cylcop_ml(copula = cyl_rect_combine(copula::frankCopula()),
  theta = sample[,1],
  x = sample[,2],
  parameters = "alpha",
  start = 1
)


sample <- rjoint(
  n = 100,
  copula = cyl_cubsec(0.1, -0.08),
  marginal_1 = list(name = "vonmisesmix", coef = list(
     mu = c(pi, 0),
     kappa = c(2, 5),
     prop = c(0.3, 0.7)
    )),
  marginal_2 = list(name = "exp", coef = list(0.3))
  )
  fit_cylcop_ml(copula = cyl_cubsec(),
  theta = sample[,1],
  x = sample[,2],
  parameters = c("a","b"),
  start = c(0,0),
  upper= c(0.1, 1/(2*pi))
)

optML(copula = cyl_quadsec(),
  theta = sample[,1],
  x = sample[,2],
  parameters = "a",
  start = 0
)

cylcop documentation built on Oct. 30, 2022, 1:05 a.m.