irtQ (version 1.0.0)

bisection: The Bisection Method to Find a Root

Description

This function is a modified version of the bisection function in the cmna R package (Howard, 2017), designed to find a root of the function .fun with respect to its first argument. Unlike the original bisection() in cmna, this version allows additional arguments to be passed to .fun.

Usage

bisection(.fun, ..., lb, ub, tol = 1e-04, max.it = 100)

Value

A list with the following components:

• root: The estimated root of the function.

• iter: The number of iterations performed.

• accuracy: The final absolute difference between the last two interval points with opposite signs.

Arguments

.fun

A function for which the root is to be found.

...

Additional arguments to be passed to .fun.

lb

A numeric value specifying the lower bound of the search interval.

ub

A numeric value specifying the upper bound of the search interval.

tol

A numeric value specifying the tolerance for convergence. Default is 1e-4.

max.it

An integer specifying the maximum number of iterations. Default is 100.

Details

The bisection method is a well-known root-finding numerical algorithm that applies to any continuous function, provided that the function values at the lower (lb) and upper (ub) bounds have opposite signs. The method repeatedly bisects the interval until the absolute difference between successive estimates is smaller than the error tolerance (tol) or the maximum number of iterations (max.it) is reached.

References

Howard, J. P. (2017). Computational methods for numerical analysis with R. New York: Chapman and Hall/CRC.

See Also

est_score()

Examples

## Example: Find the theta value corresponding to a given probability
## of a correct response using the item response function of a 2PLM
## (a = 1, b = 0.2)

# Define a function of theta
find.th <- function(theta, p) {
  p - drm(theta = theta, a = 1, b = 0.2, D = 1)
}

# Find the theta value corresponding to p = 0.2
bisection(.fun = find.th, p = 0.2, lb = -10, ub = 10)$root

# Find the theta value corresponding to p = 0.8
bisection(.fun = find.th, p = 0.8, lb = -10, ub = 10)$root