The mean of response variable is $$f(x, a) = 1/(1 + \exp(-(x - a))).$$ This function returns Fisher information for the design \(\xi\) that is $$M(\xi; a) = \sum_{i = 1}^kw_iM(x_i, a).$$ Here \(M(x, a)\) is \(g(x-a)\), where \(g(z) = \frac{\exp(z)}{(1 + \exp(z))^2}\). denotes the standard logistic density.
FIM_logisitic_1par(x, w, param)vector of design points. In IRT x is the person ability parameter.
vector of design weight. Its length must be equal to the length of x and sum(w) should be 1.
parameter \(a\). In IRT, it is called difficulty parameter.
Fisher information as a one by one matrix.
The locally optimal design is a one point design with \(x^* = a\) and provides a value of \(M(\xi^*, a) = 1/4\) for the information.
Grasshoff, U., Holling, H., & Schwabe, R. (2012). Optimal designs for the Rasch model. Psychometrika, 77(4), 710-723.
Other FIM: FIM_comp_inhibition,
FIM_emax_3par, FIM_exp_2par,
FIM_exp_3par,
FIM_logistic_4par,
FIM_logistic, FIM_loglin,
FIM_michaelis,
FIM_mixed_inhibition,
FIM_noncomp_inhibition,
FIM_power_logistic,
FIM_uncomp_inhibition