circmax: Circular Regression with Maximum Likelihood Estimation
In circtree: Regression Trees and Forests for Circular Responses

Description Usage Arguments Details Value Examples

Fit a regression model for a circular response by maximum likelihood estimation employing the von Mises distribution.

circmax(formula, data, subset, na.action,
  model = TRUE, y = TRUE, x = FALSE,
  control = circmax_control(...), ...)

circmax_fit(x, y, z = NULL, control)

circmax_control(maxit = 5000, start = NULL, method = "Nelder-Mead",
  solve_kappa = "Newton-Fourier", 
  gradient = FALSE, hessian = TRUE, ...)

`formula`	a formula expression of the form `y ~ x \| z` where `y` is the response and `x` and `z` are regressor variables for the location and the concentration of the von Mises distribution.
`data`	an optional data frame containing the variables occurring in the formulas; y has to be given in radians.
`subset`	an optional vector specifying a subset of observations to be used for fitting.
`na.action`	a function which indicates what should happen when the data contain `NA`s.
`model`	logical. If `TRUE` model frame is included as a component of the returned value.
`x, y`	for `circmax`: logical. If `TRUE` the model matrix and response vector used for fitting are returned as components of the returned value. For `circmax_fit`: `x` is a design matrix with regressors for the location and `y` is a vector of observations given in radians.
`z`	a design matrix with regressors for the concentration.
`...`	arguments to be used to form the default `control` argument if it is not supplied directly.
`control, maxit, start`	a list of control parameters passed to `optim`.
`method`	The `method` to be used for optimization.
`solve_kappa`	Which kappa solver should be used for the starting values for kappa. By default a Newton Fourier is used (`"Newton-Fourier"`). Alternatively, a uniroot provides a safe option (`"Uniroot"`) or code"Banerjee_et_al_2005" provides a quick approximation).
`gradient`	logical. Should gradients be used for optimization? If `TRUE`, the default `method` is `"BFGS"`. Otherwise `method = "Nelder-Mead"` is used.
`hessian`	logical or character. Should a numeric approximation of the (negative) Hessian matrix by `optim` be computed?

circmax fits a regression model for a circular response assuming a von Mises distribution.

circmax_fit is the lower level function where the parameters of the von Mises distribution are fitted by maximum likelihood estimation.

An object of class "circmax".

## Example 1: Simulated Data:

sdat <- circmax_simulate(n = 1000, beta = c(3, 5, 2), gamma = c(3, 3))

(m1.circmax <- circmax(y ~ x1 + x2 | x3, data = sdat))

## Example 2: Periwinkle Dataset of Fisher and Lee, 1992:
require("circular")
distance <- c(107, 46, 33, 67, 122, 69, 43, 30, 12, 25, 37, 69, 5, 83, 
  68, 38, 21, 1, 71, 60, 71, 71, 57, 53, 38, 70, 7, 48, 7, 21, 27)
directdeg <- c(67, 66, 74, 61, 58, 60, 100, 89, 171, 166, 98, 60, 197, 
  98, 86, 123, 165, 133, 101, 105, 71, 84, 75, 98, 83, 71, 74, 91, 38, 200, 56)
cdirect <- circular(directdeg * 2 * pi/360)
plot(as.numeric(cdirect) ~ distance, ylim = c(0, 4*pi), pch = 20)
points(as.numeric(cdirect) + 2*pi ~ distance, pch = 20)

(m2.circ <- lm.circular(type = "c-l", y = cdirect, x = distance, init = 0.0))
(m2.circmax <- circmax(cdirect ~ distance, data = data.frame(cbind(distance, cdirect))))