FIM_logistic {ICAOD}

Fisher Information Matrix for the 2-Parameter Logistic (2PL) Model

Description

It provides the cpp function for FIM for the model ~1/(1 + exp(-b *(x - a))). In item response theory (IRT), a is the item difficulty parameter, b is the item discrimination parameter and x is the person ability parameter.

Usage

FIM_logistic(x, w, param)

Arguments

x

Vector of design points.

w

Vector of design weight. Its length must be equal to the length of x and sum(w) = 1.

param

Vector of values for the model parameters c(a, b).

Details

It can be shown that minimax and standardized D-optimal designs for the 2PL model is symmetric around point a_M = (a^L + a^U)/2 where a^L and a^U are the lower bound and upper bound for parameter a, respectively. In ICA.control, arguments sym and sym_point can be used to specify a_M and find accurate symmetric optimal designs.

Value

Fisher information matrix.

Examples

FIM_logistic(x = c(1, 2), w = c(.5, .5), param = c(2, 1))