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 or get_hessian calculates the gradient or Hessian matrix of the log-likelihood function at the parameter estimates of a class 'stvar' object. get_soc

returns eigenvalues of the Hessian matrix, and get_foc is the same as get_gradient

but named conveniently.

calc_gradient(x, fn, h = 0.001, ...)

calc_hessian(x, fn, h = 0.001, ...)

get_gradient(stvar, ...)

get_hessian(stvar, ...)

get_foc(stvar, ...)

get_soc(stvar, ...)

Arguments

• x: a numeric vector specifying the point where the gradient or Hessian should be calculated.
• fn: a function that takes in argument x as the first argument.
• h: difference used to approximate the derivatives: either a positive real number of a vector of positive real numbers with the same length as x.
• ...: other arguments passed to fn (or argument passed to calc_gradient or calc_hessian).
• stvar: object of class "stvar"

Returns

Gradient functions return numerical approximation of the gradient and Hessian functions return numerical approximation of the Hessian. get_soc returns eigenvalues of the Hessian matrix.

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. Note that profile log-likelihood functions can be conveniently plotted with the function profile_logliks.

Warning

No argument checks!

Examples

# Create a simple function:
foo <- function(x) x^2 + x

# Calculate the gradient at x=1 and x=-0.5:
calc_gradient(x=1, fn=foo)
calc_gradient(x=-0.5, fn=foo)

# Create a more complicated function
foo <- function(x, a, b) a*x[1]^2 - b*x[2]^2

# Calculate the gradient at x=c(1, 2) with parameter values a=0.3 and b=0.1:
calc_gradient(x=c(1, 2), fn=foo, a=0.3, b=0.1)

# Create a linear Gaussian VAR p=1 model:
theta_112 <- c(0.649526, 0.066507, 0.288526, 0.021767, -0.144024, 0.897103,
 0.601786, -0.002945, 0.067224)
mod112 <- STVAR(data=gdpdef, p=1, M=1, params=theta_112)

# Calculate the gradient of the log-likelihood function about the parameter values:
get_foc(mod112)

# Calculate the eigenvalues of the Hessian matrix of the log-likelihood function
# about the parameter values:
get_soc(mod112)