FIM_logistic: 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).
Value
Fisher information matrix.
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.