calc_gradient function

Calculate gradient or Hessian matrix

calc_gradient or calc_hessian calculates the gradient or Hessian matrix of the given function at the given point using central difference numerical approximation. get_gradient (and get_foc) or get_hessian calculates the gradient or Hessian matrix of the log-likelihood function at the parameter values of a class 'gsmar' object. get_soc returns eigenvalues of the Hessian matrix.

calc_gradient(x, fn, h = 6e-06, varying_h = NULL, ...)

calc_hessian(x, fn, h = 6e-06, varying_h = NULL, ...)

get_gradient(gsmar, custom_h = NULL)

get_foc(gsmar, custom_h = NULL)

get_hessian(gsmar, custom_h = NULL)

get_soc(gsmar, custom_h = NULL)

Arguments

• x: a numeric vector specifying the point at which the gradient or Hessian should be evaluated.

• fn: a function that takes in the argument x as the first argument.

• h: the difference used to approximate the derivatives.

• varying_h: a numeric vector with the same length as x specifying the difference h

  for each dimension separately. If NULL (default), then the difference given as parameter h

  will be used for all dimensions.

• ...: other arguments passed to fn.

• gsmar: a class 'gsmar' object, typically generated by fitGSMAR or GSMAR.

• custom_h: same as varying_h but if NULL (default), then the difference h used for differentiating overly large degrees of freedom parameters is adjusted to avoid numerical problems, and the difference is 6e-6 for the other parameters.

Returns

The gradient functions return numerical approximation of the gradient, and the Hessian functions return numerical approximation of the Hessian. get_soc returns eigenvalues of the Hessian matrix, get_foc

is the same as get_gradient but named conveniently.

Details

In particular, the functions get_foc and get_soc can be used to check whether the found estimates denote a (local) maximum point, a saddle point, or something else.

Warning

No argument checks!

Examples

# Simple function
foo <- function(x) x^2 + x
calc_gradient(x=1, fn=foo)
calc_gradient(x=-0.5, fn=foo)
calc_hessian(x=2, fn=foo)

# More complicated function
foo <- function(x, a, b) a*x[1]^2 - b*x[2]^2
calc_gradient(x=c(1, 2), fn=foo, a=0.3, b=0.1)
calc_hessian(x=c(1, 2), fn=foo, a=0.3, b=0.1)

# GMAR model
params12 <- c(1.70, 0.85, 0.30, 4.12, 0.73, 1.98, 0.63)
gmar12 <- GSMAR(data=simudata, p=1, M=2, params=params12, model="GMAR")
get_gradient(gmar12)
get_foc(gmar12)
get_hessian(gmar12)
get_soc(gmar12)

See Also

profile_logliks