title: A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models.
abstract: OBJECTIVE
  Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space.
  
  
  METHODS
  MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [a, b] will be given for several standard weight functions.
  
  
  RESULTS
  The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution.
  
  
  CONCLUSIONS
  Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights.
authors.affiliation: Universidad de Castilla-La Mancha, Spain. Electronic address: victormanuel.casero@uclm.es.
authors.forename: V
authors.initials: V
authors.lastname: Casero-Alonso
authors.affiliation: Universidad de Castilla-La Mancha, Spain.
authors.forename: J
authors.initials: J
authors.lastname: López-Fidalgo
authors.affiliation: University of Glasgow, UK.
authors.forename: B
authors.initials: B
authors.lastname: Torsney
mesh_terms: D003198:Computer Simulation; D006801:Humans; D016014:Linear Models
keywords: Applet; Equal variance optimality; Equivalence theorem; Fisher information matrix; Optimal design; c-optimality